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Subject: PowerPoint Presentation - Chapter 19 Chemical Thermodynamics
Date: Thu, 27 Mar 2008 09:23:42 -0700
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	}
}

function GetCurSldNum()
{  =20
	obj=3DGetHrefObj(gCurSld)
	if( obj.mOrigVis =3D=3D 1 )
		return obj.mSldIdx
	else  =20
		return gCurSld
}

function GetNumSlds()
{  =20
	if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 )
		return GetSldList().mNumVisSlds;
	else
		return GetSldList().mList.length
}

function GetSldNum( href )
{
	for(ii=3D0; ii<GetSldList().mList.length; ii++) {
		if ( GetSldList().mList[ii].mSldHref =3D=3D href )
			return ii+1
	}
	return 1
}

function GetHrefObj( sldIdx ){ return GetSldList().mList[sldIdx-1] }

function IsFramesMode(){ return ( SCREEN_MODE =3D=3D "Frames" ) }

function IsFullScrMode(){ return ( SCREEN_MODE =3D=3D "FullScreen" ) }

function GoToNextSld()
{
	ii=3DgCurSld + 1
	if( GetHrefObj( ii-1 ).mOrigVis =3D=3D 0 ) {
		if( ii<=3DGetSldList().mList.length ) {
			obj=3DGetHrefObj(ii)
			obj.mVis=3D1
			GoToSldNum(ii)
			return
		}
	}
	else {
		obj=3DGetHrefObj( ii )
		while ( obj && ( obj.mOrigVis =3D=3D 0 ) )
			obj=3DGetHrefObj(++ii)
		if( obj && obj.mOrigVis ) {
			GoToSldNum(ii)
			return
		}
	}
	if( gSldStack.length > 1 )
		PopSldList();
	else if( !IsFramesMode() ) {
                if( gLoopCont )
			GoToFirst()
                else
			EndShow()
	}
}

function GoToPrevSld()
{
	ii=3DgCurSld-1
	if( ii > 0 ) {
		obj=3DGetHrefObj(ii)
		while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) )
			obj=3DGetHrefObj(--ii)
        if( ii =3D=3D 0 ) ii=3D1
		GoToSldNum(ii)
	}
}

function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) }

function GoToLast()
{
	ii=3DGetSldList().mList.length
	if( ii !=3D gCurSld )
		GoToSld( GetHrefObj(ii).mSldHref )
}

function GoToSldNum( num )
{
	if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
	obj =3D GetHrefObj( num )
	obj.mVis=3D1
	gPrevSld=3DgCurSld
	gCurSld =3D num;
	PPTSld.location.replace(MHTMLPrefix+obj.mSldHref)
	if( IsFramesMode() ) {
		UpdNavPane(); UpdOtlPane(); UpdNtsPane()
	}
}

function GoToSld( href )
{
	if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
	GetHrefObj( GetSldNum(href) ).mVis=3D1
	PPTSld.location.replace(MHTMLPrefix+href)
}

function SldUpdated( id )
{
	if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return
	gPrevSld=3DgCurSld
	gCurSld=3DGetSldNum(id)
	if( IsFramesMode() ) {
		UpdNavPane(); UpdOtlPane(); UpdNtsPane()
	}
}

function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) }
function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && =
GetHrefObj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) }
function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) }

function CloseWindow() {
	if( HideMenu() ) return;
=09
	var event =3D PPTSld.event;
	if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || =
event.keyCode=3D=3D32 || event.type=3D=3D"click" ) )
		window.close( self );
	CatchNumKeys( self, event );
}

function Unload() { gIsEndShow=3D0; }

function SetupEndShow() {
	gIsEndShow=3D1;
	PPTSld.document.body.scroll=3D"no";
	PPTSld.document.onkeypress=3DCloseWindow;
	PPTSld.document.onclick=3DCloseWindow;
	PPTSld.document.oncontextmenu=3D_CM;
}

function EndShow()
{
	if( IsFramesMode() ) return
	if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue

	doc=3DPPTSld.document
	var dir =3D doc.body.dir
	if( dir !=3D "rtl" ) dir =3D "ltr";
	doc.open()
	doc.writeln('<html><body dir=3D' + dir + ' bgcolor=3Dblack =
onload=3Dparent.SetupEndShow() =
onunload=3Dparent.Unload()><center><p><font face=3DTahoma color=3Dwhite =
size=3D2><br><b>' + ENDSHOW_MESG + =
'</b></font></p></center></body></html>')
	doc.close()
}

function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue =
}

function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited }

function hrefList( sldHref, visible, advDelay, advClk )
{
	this.mSldHref=3D this.mNtsHref =3D sldHref
	this.mOrigVis=3D this.mVis =3D visible
	this.mVisited=3D false
	this.mAdvDelay=3D advDelay
	this.mAdvOnClk=3D advClk
}

function SldList(arr,curSld,fEnd)
{
	this.mCurSld =3D curSld;
	this.mList =3D new Array();

	var idx =3D 1;
	for(ii=3D0;ii<arr.length;ii++) {
		this.mList[ii] =3D new hrefList( arr[ii].mSldHref, arr[ii].mOrigVis, =
arr[ii].mAdvDelay, arr[ii].mAdvOnClk );
		if( arr[ii].mOrigVis )
			this.mList[ii].mSldIdx =3D idx++;
	}
	this.mNumVisSlds =3D idx-1;
	this.fEndShow =3D fEnd;
}

function GetSldList() {	return gSldStack[gSldStack.length-1] }
function GetCurSld() { return parent.GetSldList().mList[parent.gCurSld - =
1] }

gSldStack =3D new Array();
gSldStack[0] =3D new SldList(gMainDoc,gCurSld,1)
function ToggleOtlPane()
{
	frmset=3Ddocument.all("PPTHorizAdjust")
	frm=3Ddocument.all("PPTOtl")

	if( gOtlOpen )
		frmset.cols=3D"*,100%"
	else
		frmset.cols=3D"25%,*"

	gOtlOpen=3D!gOtlOpen
	frm.noResize=3D!frm.noResize
	UpdOtNavPane()
}

function ToggleNtsPane()
{
	frmset=3Ddocument.all("PPTVertAdjust")
	frm=3Ddocument.all("PPTNts")

	if( gNtsOpen )
		frmset.rows=3D"100%,*"
	else
		frmset.rows=3D"*,20%"

	gNtsOpen=3D!gNtsOpen
	UpdNtsPane()
}

/*********************************************
Custom Shows implementation

When ViewCustomShow() is called, we create
a new array that is a subset of the slides in=20
the main doc. This list pushed on a stack so
we can return after the end of the custom
show.
*********************************************/
function ViewCustomShow(idx,fEnd)
{
	if( !IsFullScrMode() ) return;
	var sldList =3D new Array();
	var custShow =3D custShowList[idx-1];
	var jj =3D 0;
	for( ii=3D0;ii<custShow.length;ii++ ) {
		if( custShow[ii] <=3D gMainDoc.length )
			sldList[jj++] =3D gMainDoc[custShow[ii]-1];
	}
	if (sldList.length > 0) {
	PushSldList(sldList,fEnd);
	gCurSld =3D 1;
	}
	else
		if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue
}

function PushSldList(arr,fEnd) {
	var ii =3D gSldStack.length;
	gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd);
	GoToSld( gSldStack[ii].mList[0].mSldHref );
}

function PopSldList() {
	if (gSldStack[gSldStack.length-1].fEndShow)
		EndShow()
	else {
	gCurSld =3D gSldStack[gSldStack.length-1].mCurSld;
	gSldStack[gSldStack.length-1] =3D null;
	gSldStack.length--;
	var sldList =3D gSldStack[gSldStack.length-1];
	GoToSld( sldList.mList[gCurSld - 1].mSldHref );
	}
}
var custShowList=3Dnew Array();

/*********************************************
 Navigation button implementation

 There are 2 types of buttons: ImgBtn, TxtBtn
 implemented as function objects. They share
 a similiar interface so the event handlers
 can call SetActive, for example, on a button=20
 object without needing to know exactly=20
 what type of button it is.
**********************************************/

//----------------------------------
function ImgBtn( oId,bId,w,action )
//----------------------------------
{
	var t=3Dthis
	t.Perform    =3D _IBP
	t.SetActive  =3D _IBSetA
	t.SetInactive=3D _IBSetI
	t.SetPressed =3D _IBSetP
	t.SetDisabled=3D _IBSetD
	t.Enabled    =3D _IBSetE
	t.ChangeIcon =3D null
	t.UserAction =3D action
	t.ChgState   =3D _IBUI
	t.mObjId   =3D oId
	t.mBorderId=3D bId
	t.mWidth   =3D w
	t.mIsOn    =3D t.mCurState =3D 0
}

function _IBSetA()
{
	if( this.mIsOn ) {
		obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 )
		obj.style.posTop=3D0
	}
}

function _IBSetI()
{
	if( this.mIsOn ) {
		obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 )
		obj.style.posTop=3D0=20
	}
}

function _IBSetP()
{
	if( this.mIsOn ) {
		obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 )
		obj.style.posLeft+=3D1; obj.style.posTop+=3D1
	}
}

function _IBSetD()
{ =20
	obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 )
	obj.style.posTop=3D0=20
}

function _IBSetE( state )
{
	var t=3Dthis
	GetObj( t.mBorderId ).style.visibility=3D"visible"
	if( state !=3D t.mIsOn ) {
		t.mIsOn=3Dstate
		if( state )
			t.SetInactive()
		else
			t.SetDisabled()
	}
}

function _IBP()
{
	var t=3Dthis
	if( t.mIsOn ) {
		if( t.UserAction !=3D null )
			t.UserAction()
		if( t.ChangeIcon ) {
			obj=3DGetObj(t.mObjId)
			if( t.ChangeIcon() )
				obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth
			else
				obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth
		}
		t.SetActive()
	} =20
}

function _IBUI( clr1,clr2,nextState )
{
	var t=3Dthis
	SetBorder( GetObj( t.mBorderId ),clr1,clr2 )
	obj=3DGetObj( t.mObjId )
	=
obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-ob=
j.style.posTop
	t.mCurState=3DnextState
	return obj
}

//-----------------------------------------
function TxtBtn( oId,oeId,action,chkState )
//-----------------------------------------
{
	var t=3Dthis
	t.Perform    =3D _TBP
	t.SetActive  =3D _TBSetA
	t.SetInactive=3D _TBSetI
	t.SetPressed =3D _TBSetP
	t.SetDisabled=3D _TBSetD
	t.SetEnabled =3D _TBSetE
	t.GetState   =3D chkState
	t.UserAction =3D action
	t.ChgState   =3D _TBUI
	t.mObjId      =3D oId
	t.m_elementsId=3D oeId
	t.mIsOn       =3D 1
}

function _TBSetA()
{
	var t=3Dthis
	if( t.mIsOn && !t.GetState() )
		t.ChgState( gHiliteClr,gShadowClr,0,0 )
}

function _TBSetI()
{
	var t=3Dthis
	if( t.mIsOn && !t.GetState() )
		t.ChgState( gFaceClr,gFaceClr,0,0 )
}

function _TBSetP()
{
	if( this.mIsOn )
		this.ChgState( gShadowClr,gHiliteClr,1,1 )
}

function _TBSetD()
{  =20
	this.ChgState( gFaceClr,gFaceClr,0,0 )
	this.mIsOn =3D 0
}

function _TBSetE()
{
	var t=3Dthis
	if( !t.GetState() )
		t.ChgState( gFaceClr,gFaceClr,0,0 )
	else
		t.ChgState( gShadowClr,gHiliteClr,1,1 )
	t.mIsOn =3D 1
}

function _TBP()
{
	var t=3Dthis
	if( t.mIsOn ) {=20
		if( t.UserAction !=3D null )
			t.UserAction()
        if( !t.GetState )
            return
		if( t.GetState() )
			t.SetPressed()
		else
			t.SetActive()
	} =20
}

function _TBUI( clr1,clr2,lOffset,tOffset )
{
	SetBorder( GetObj( this.mObjId ),clr1,clr2 )
	Offset( GetObj( this.m_elementsId ),lOffset,tOffset )
}

function Offset( obj, top, left ){ obj.style.top=3Dtop; =
obj.style.left=3Dleft }

function SetBorder( obj, upperLeft, lowerRight )
{
	s=3Dobj.style;
	s.borderStyle      =3D "solid"
	s.borderWidth      =3D 1=20
	s.borderLeftColor  =3D s.borderTopColor =3D upperLeft
	s.borderBottomColor=3D s.borderRightColor =3D lowerRight
}

function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] }

function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() }

function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() =
}

function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() =
}

function BtnOnUp()
{
	b=3DGetBtnObj()
	if( b !=3D null )
		b.Perform()
	else
		Upd()
}
function GetNtsState(){ return parent.gNtsOpen }

function GetOtlState(){ return parent.gOtlOpen }

function GetOtlTxtState(){ return parent.gOtlTxtExp }

function NtsBtnSetFlag( fVal )
{
	s=3Ddocument.all.item( this.m_flagId ).style
	s.display=3D"none"
	if( fVal )
		s.display=3D""
	else
		s.display=3D"none"
}

function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) =
b.SetActive() }

function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) =
b.SetInactive() }

function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) =
b.SetPressed() }

function _BSetA_BorderImg()
{=20
	b =3D gBtnArr[this.mBorderId]=20
	if( b !=3D null && this.mIsOn && !b.GetState() ) {
		obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 )
		obj.style.posTop=3D0
	}
}

function _BSetI_BorderImg()
{=20
	b =3D gBtnArr[this.mBorderId]
	if( b !=3D null && this.mIsOn && !b.GetState() ) {
		obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 )
		obj.style.posTop=3D0
	}
}


var =
gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"TH=
REEDFACE"
var gBtnArr =3D new Array()
gBtnArr["nb_otl"] =3D new TxtBtn( =
"nb_otl","nb_otlElem",parent.ToggleOtlPane,GetOtlState )
gBtnArr["nb_otlElem"] =3D new TxtBtn( =
"nb_otl","nb_otlElem",parent.ToggleOtlPane,GetOtlState )
gBtnArr["nb_nts"] =3D new ImgBtn( =
"nb_nts","nb_ntsBorder",10,parent.ToggleNtsPane )
gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg;
gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg;
gBtnArr["nb_ntsBorder"] =3D new TxtBtn( =
"nb_ntsBorder","nb_ntsElem",parent.ToggleNtsPane,GetNtsState )
gBtnArr["nb_ntsElem"] =3D new TxtBtn( =
"nb_ntsBorder","nb_ntsElem",parent.ToggleNtsPane,GetNtsState )
gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( =
"nb_prev","nb_prevBorder",30,parent.GoToPrevSld )
gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( =
"nb_next","nb_nextBorder",30,parent.GoToNextSld )
gBtnArr["nb_sldshw"]=3D new ImgBtn( =
"nb_sldshw","nb_sldshwBorder",18,parent.FullScreen )
gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( =
"nb_sldshw","nb_sldshwBorder",parent.FullScreen,null )
gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border;
gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border;
gBtnArr["nb_sldshwText"] =3D new TxtBtn( =
"nb_sldshw","nb_sldshwText",parent.FullScreen,null )
gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border;
gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border;
gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( =
"nb_voice","nb_voiceBorder",18,parent.ToggleVNarration )
gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( =
"nb_otlTxt","nb_otlTxtBorder",23,parent.ToggleOtlText )
gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts"
gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag
gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState

/*********************************************
 Context menu implementation

 _CM() is the function that's hooked up to
 the oncontextmenu event. Once we're asked to
 show the menu, we first build it by creating
 DIVs on-the-fly. Then we position it=20
 within the screen area so it doesn't get
 clipped.

 Creating the DIVs using createElement() means
 we don't have to write out any extra HTML
 into the slide HTML files.
**********************************************/
var sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End =
Show",sFont=3D"Arial",sArrow=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Re=
ctangle",sOval=3D"Oval"

function ShowMenu()
{
	BuildMenu();
	var =
doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y=3DPP=
TSld.event.clientY+doc.scrollTop
	m =3D PPTSld.document.all.item("ctxtmenu")
	m.style.pixelLeft=3Dx
	if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) )
		m.style.pixelLeft=3Dx-m.scrollWidth

	m.style.pixelTop=3Dy
	if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) )
		m.style.pixelTop=3Dy-m.scrollHeight

	m.style.display=3D""
}

function _CM()
{
	if( !parent.IsFullScrMode() ) return;
	if(!PPTSld.event.ctrlKey) {
		ShowMenu()
		return false
	} else
		HideMenu()
}

function BuildMenu()
{
	if( PPTSld.document.all.item("ctxtmenu") ) return

	var mObj=3DCreateItem( PPTSld.document.body )
	mObj.id=3D"ctxtmenu"
	mObj.style.visibility=3D"hidden"
	var s=3DmObj.style
	s.position=3D"absolute"
	s.cursor=3D"default"
	s.width=3D"120px"
	SetCMBorder(mObj,"menu","black")

	var iObj=3DCreateItem( mObj )
	SetCMBorder( iObj, "threedhighlight","threedshadow" )
	iObj.style.padding=3D2
	CreateMenuItem( iObj,sNext,M_GoNextSld,M_True )
	CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld )
=09
	CreateSeparator( iObj )
	CreateMenuItem( iObj,sEnd,M_End,M_True )
	mObj.style.visibility=3D"visible"
}

function Cancel() { window.event.cancelBubble=3Dtrue; =
window.event.returnValue=3Dfalse }

function Highlight() { ChangeClr("activecaption","threedhighlight") }

function Deselect() { ChangeClr("threedface","menutext") }

function Perform()
{
	e=3DPPTSld.event.srcElement
	if( e.type=3D=3D"menuitem" && e.IsActive() )
		e.Action()
	else
		PPTSld.event.cancelBubble=3Dtrue
}
function ChangeClr( bg,clr )
{
	e=3DPPTSld.event.srcElement
	if( e.type=3D=3D"menuitem" && e.IsActive() ) {
		e.style.backgroundColor=3Dbg
		e.style.color=3Dclr
	}
}

function M_HasPrevSld() { return( parent.HasPrevSld() ) }

function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() }

function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; =
history.back(); PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() }

function M_True() { return true }

function M_End() { window.close( self ) }

function CreateMenuItem( node,text,action,eval )
{
	var e=3DCreateItem( node )
	e.type=3D"menuitem"
	e.Action=3Daction
	e.IsActive=3Deval
	e.innerHTML=3Dtext

	if( !e.IsActive() )
		e.style.color=3D"threedshadow"

	e.onclick=3DPerform
	e.onmouseover=3DHighlight
	e.onmouseout=3DDeselect
	s=3De.style;
	s.fontFamily=3DsFont
	s.fontSize=3D"9pt"
	s.paddingLeft=3D2
}

function CreateSeparator( node )
{
	var sObj=3DCreateItem( node )
	SetCMBorder(sObj,"menu","menu")
	var s=3DsObj.style
	s.borderTopColor=3D"threedshadow"
	s.borderBottomColor=3D"threedhighlight"
	s.height=3D1
	s.fontSize=3D"0px"
}

function CreateItem( node )
{
	var elem=3DPPTSld.document.createElement("DIV")
	node.insertBefore( elem )
	return elem
}

function SetCMBorder( o,ltClr,rbClr )
{
	var s=3Do.style
	s.backgroundColor=3D"menu"
	s.borderStyle=3D"solid"
	s.borderWidth=3D1
	s.borderColor=3DltClr+" "+rbClr+" "+rbClr+" "+ltClr
}
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onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>1</FONT></DIV></TD>
    <TD width=3D"100%">
      <DIV class=3DPTxt id=3DPPTP1><FONT size=3D2><A id=3DPPTL1=20
      href=3D"javascript:GoToSld('slide0001.htm');">Chapter =
19<BR>Chemical=20
      Thermodynamics</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
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      <DIV class=3DsldNum><FONT size=3D2>2</FONT></DIV></TD>
    <TD>
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      href=3D"javascript:GoToSld('slide0011.htm');">First Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC2 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>You will recall from Chapter 5 that energy cannot be created =
nor=20
        destroyed.=20
        <LI>Therefore, the total energy of the universe is a constant.=20
        <LI>Energy can, however, be converted from one form to another =
or=20
        transferred from a system to the surroundings or vice versa.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>3</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP3><FONT size=3D2><A id=3DPPTL3=20
      href=3D"javascript:GoToSld('slide0002.htm');">Spontaneous=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC3 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Spontaneous processes are those that can proceed without any =
outside=20
        intervention.=20
        <LI>The gas in vessel B will spontaneously effuse into vessel A, =
but=20
        once the gas is in both vessels, it will not spontaneously =
return to one=20
        side </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>4</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP4><FONT size=3D2><A id=3DPPTL4=20
      href=3D"javascript:GoToSld('slide0003.htm');">Spontaneous=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC4 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <UL>
          <LI>Processes that are spontaneous in one direction are =
nonspontaneous=20
          in the reverse direction. =
</LI></UL></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>5</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP5><FONT size=3D2><A id=3DPPTL5=20
      href=3D"javascript:GoToSld('slide0004.htm');">Spontaneous=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC5 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Processes that are spontaneous at one temperature may be=20
        nonspontaneous at other temperatures.=20
        <LI>Above 0<FONT face=3DSymbol>=B0</FONT><FONT face=3DArial>C it =
is=20
        spontaneous for ice to melt.</FONT>=20
        <LI>Below 0<FONT face=3DSymbol>=B0</FONT><FONT face=3DArial>C =
the reverse=20
        process is spontaneous.</FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>6</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP6><FONT size=3D2><A id=3DPPTL6=20
      href=3D"javascript:GoToSld('slide0005.htm');">Reversible=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC6 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <UL>
          <LI>In a reversible process the system changes in such a way =
that the=20
          system and surroundings can be put back in their original =
states by=20
          exactly reversing the process. <BR><BR>
          <LI>Changes are infinitesimally small in a reversible process. =

      </LI></UL></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>7</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP7><FONT size=3D2><A id=3DPPTL7=20
      href=3D"javascript:GoToSld('slide0006.htm');">Irreversible=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC7 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Irreversible processes cannot be undone by exactly reversing =
the=20
        change to the system.=20
        <LI>All Spontaneous processes are irreversible.=20
        <LI>All Real processes are irreversible. =
</LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>8</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP8><FONT size=3D2><A id=3DPPTL8=20
      =
href=3D"javascript:GoToSld('slide0007.htm');">Entropy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC8 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy (S) is a term coined by Rudolph Clausius in the 19th =

        century.=20
        <LI>Clausius was convinced of the significance of the ratio of =
heat=20
        delivered and the temperature at which it is delivered,=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>9</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP9><FONT size=3D2><A id=3DPPTL9=20
      =
href=3D"javascript:GoToSld('slide0008.htm');">Entropy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC9 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy can be thought of as a measure of the randomness of =
a=20
        system.=20
        <LI>It is related to the various modes of motion in molecules.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>10</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP10><FONT size=3D2><A id=3DPPTL10=20
      =
href=3D"javascript:GoToSld('slide0009.htm');">Entropy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC10 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Like total energy, E, and enthalpy, H, entropy is a state =
function.=20
        <LI>Therefore,=20
        <LI><FONT face=3DSymbol>D</FONT><FONT face=3DArial>S =3D =
S<SUB>final</SUB>=20
        </FONT><FONT face=3DSymbol>-</FONT><FONT face=3DArial>=20
        S<SUB>initial</SUB></FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>11</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP11><FONT size=3D2><A id=3DPPTL11=20
      =
href=3D"javascript:GoToSld('slide0010.htm');">Entropy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC11 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>For a process occurring at constant temperature (an =
isothermal=20
        process): </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>12</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP12><FONT size=3D2><A id=3DPPTL12=20
      href=3D"javascript:GoToSld('slide0012.htm');">Second Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC12 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The second law of thermodynamics: The entropy of the =
universe does=20
        not change for reversible processes=20
        <LI>and=20
        <LI><SPAN style=3D"mso-spacerun: yes">&nbsp;</SPAN>increases for =

        spontaneous processes. </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>13</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP13><FONT size=3D2><A id=3DPPTL13=20
      href=3D"javascript:GoToSld('slide0013.htm');">Second Law of=20
      Thermodynamics</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>14</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP14><FONT size=3D2><A id=3DPPTL14=20
      href=3D"javascript:GoToSld('slide0014.htm');">Second Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC14 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The entropy of the universe increases (real, spontaneous =
processes).=20

        <LI>But, entropy can decrease for individual systems.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>15</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP15><FONT size=3D2><A id=3DPPTL15=20
      href=3D"javascript:GoToSld('slide0015.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC15 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Ludwig Boltzmann described the concept of entropy on the =
molecular=20
        level.=20
        <LI>Temperature is a measure of the average kinetic energy of =
the=20
        molecules in a sample. </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>16</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP16><FONT size=3D2><A id=3DPPTL16=20
      href=3D"javascript:GoToSld('slide0016.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC16 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Molecules exhibit several types of motion:=20
        <UL>
          <LI>Translational:<SPAN style=3D"mso-spacerun: yes">&nbsp;=20
          </SPAN>Movement of the entire molecule from one place to =
another.=20
          <LI>Vibrational:<SPAN style=3D"mso-spacerun: yes">&nbsp; =
</SPAN>Periodic=20
          motion of atoms within a molecule.=20
          <LI>Rotational:<SPAN style=3D"mso-spacerun: yes">&nbsp; =
</SPAN>Rotation=20
          of the molecule on about an axis or rotation about <FONT=20
          face=3DSymbol>s</FONT><FONT face=3DArial> bonds.</FONT>=20
      </LI></UL></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>17</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP17><FONT size=3D2><A id=3DPPTL17=20
      href=3D"javascript:GoToSld('slide0017.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC17 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Boltzmann envisioned the motions of a sample of molecules at =
a=20
        particular instant in time.=20
        <UL>
          <LI>This would be akin to taking a snapshot of all the =
molecules.=20
        </LI></UL>
        <LI>He referred to this sampling as a microstate of the =
thermodynamic=20
        system. </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>18</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP18><FONT size=3D2><A id=3DPPTL18=20
      href=3D"javascript:GoToSld('slide0018.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC18 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Each thermodynamic state has a specific number of =
microstates, W,=20
        associated with it.=20
        <LI>Entropy is=20
        <LI>S =3D k lnW=20
        <LI>where k is the Boltzmann constant, 1.38 <FONT=20
        face=3DSymbol>=B4</FONT><FONT face=3DArial> 10</FONT><FONT=20
        face=3DSymbol><SUP>-</SUP></FONT><FONT =
face=3DArial><SUP>23</SUP>=20
        J/K.</FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>19</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP19><FONT size=3D2><A id=3DPPTL19=20
      href=3D"javascript:GoToSld('slide0040.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC19 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Implications: <BR><BR>
        <LI>=95 more particles=20
        <LI>-&gt; more states -&gt; more entropy=20
        <LI>=95 higher T=20
        <LI>-&gt; more energy states -&gt; more entropy=20
        <LI>=95 less structure (gas vs solid)=20
        <LI>-&gt; more states -&gt; more entropy=20
  <BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>20</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP20><FONT size=3D2><A id=3DPPTL20=20
      href=3D"javascript:GoToSld('slide0020.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC20 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The number of microstates and, therefore, the entropy tends =
to=20
        increase with increases in=20
        <UL>
          <LI>Temperature.=20
          <LI>Volume (gases).=20
          <LI>The number of independently moving molecules.=20
      </LI></UL></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>21</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP21><FONT size=3D2><A id=3DPPTL21=20
      href=3D"javascript:GoToSld('slide0021.htm');">Entropy and Physical =

      States</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC21 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy increases with the freedom of motion of molecules.=20
        <LI>Therefore,=20
        <LI>S(g) &gt; S(l) &gt; S(s) </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>22</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP22><FONT size=3D2><A id=3DPPTL22=20
      =
href=3D"javascript:GoToSld('slide0022.htm');">Solutions</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC22 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <UL>
          <LI>Dissolution of a solid:=20
          <LI>Ions have more entropy (more states)=20
          <LI>But,=20
          <LI>Some water molecules have less entropy (they are grouped =
around=20
          ions). </LI></UL></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>23</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP23><FONT size=3D2><A id=3DPPTL23=20
      href=3D"javascript:GoToSld('slide0023.htm');">Entropy=20
      Changes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC23 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>In general, entropy increases when=20
        <UL>
          <LI>Gases are formed from liquids and solids.=20
          <LI>Liquids or solutions are formed from solids.=20
          <LI>The number of gas molecules increases.=20
          <LI>The number of moles increases. =
</LI></UL></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>24</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP24><FONT size=3D2><A id=3DPPTL24=20
      href=3D"javascript:GoToSld('slide0024.htm');">Third Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC24 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The entropy of a pure crystalline substance at absolute zero =
is 0.=20
        <BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>25</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP25><FONT size=3D2><A id=3DPPTL25=20
      href=3D"javascript:GoToSld('slide0041.htm');">Third Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC25 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The entropy of a pure crystalline substance at absolute zero =
is 0.=20
        <BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>26</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP26><FONT size=3D2><A id=3DPPTL26=20
      href=3D"javascript:GoToSld('slide0025.htm');">Standard=20
      Entropies</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC26 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>These are molar entropy values of substances in their =
standard=20
        states.=20
        <LI>Standard entropies tend to increase with increasing molar =
mass.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>27</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP27><FONT size=3D2><A id=3DPPTL27=20
      href=3D"javascript:GoToSld('slide0026.htm');">Standard=20
      Entropies</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC27 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Larger and more complex molecules have greater entropies.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>28</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP28><FONT size=3D2><A id=3DPPTL28=20
      href=3D"javascript:GoToSld('slide0027.htm');">Entropy=20
      Changes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC28 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy changes for a reaction can be calculated the same =
way we=20
        used for <FONT face=3DSymbol>D</FONT><FONT =
face=3DArial>H:</FONT>=20
        <LI></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>29</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP29><FONT size=3D2><A id=3DPPTL29=20
      href=3D"javascript:GoToSld('slide0028.htm');">Practical uses: =
surroundings=20
      &amp; system</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC29 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy Changes in Surroundings=20
        <LI>Heat that flows into or out of the system also changes the =
entropy=20
        of the surroundings.=20
        <LI>For an isothermal process: </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>30</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP30><FONT size=3D2><A id=3DPPTL30=20
      href=3D"javascript:GoToSld('slide0042.htm');">Practical uses: =
surroundings=20
      &amp; system</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC30 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy Changes in Surroundings=20
        <LI>Heat that flows into or out of the system also changes the =
entropy=20
        of the surroundings.=20
        <LI>For an isothermal process: </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>31</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP31><FONT size=3D2><A id=3DPPTL31=20
      href=3D"javascript:GoToSld('slide0043.htm');">Link S and <FONT=20
      face=3DSymbol>D</FONT><FONT face=3DArial>H: Phase=20
      changes</FONT></A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>32</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP32><FONT size=3D2><A id=3DPPTL32=20
      href=3D"javascript:GoToSld('slide0029.htm');">"Entropy Change in =
the=20
      Universe"</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC32 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy Change in the Universe=20
        <LI>The universe is composed of the system and the surroundings. =

<BR><BR>
        <LI>Therefore,=20
        <LI><FONT face=3DSymbol>D</FONT><FONT =
face=3DArial>S<SUB>universe</SUB> =3D=20
        </FONT><FONT face=3DSymbol>D</FONT><FONT =
face=3DArial>S<SUB>system</SUB> +=20
        </FONT><FONT face=3DSymbol>D</FONT><FONT=20
        face=3DArial>S<SUB>surroundings</SUB></FONT> <BR><BR>
        <LI>For spontaneous processes=20
        <LI><SPAN style=3D"mso-spacerun: yes">&nbsp;</SPAN><FONT=20
        face=3DSymbol>D</FONT><FONT face=3DArial>S<SUB>universe =
</SUB>&gt; 0</FONT>=20
        <BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>33</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP33><FONT size=3D2><A id=3DPPTL33=20
      href=3D"javascript:GoToSld('slide0030.htm');">Practical uses: =
surroundings=20
      &amp; system</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>34</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP34><FONT size=3D2><A id=3DPPTL34=20
      href=3D"javascript:GoToSld('slide0044.htm');">Practical uses: =
surroundings=20
      &amp; system</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>35</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP35><FONT size=3D2><A id=3DPPTL35=20
      href=3D"javascript:GoToSld('slide0031.htm');">"<FONT=20
      face=3DSymbol>-</FONT><FONT face=3DArial>TDS<SUB>universe</SUB> is =
defined=20
      as</FONT>..."</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC35 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI><FONT face=3DSymbol>-</FONT><FONT =
face=3DArial>TDS<SUB>universe</SUB> is=20
        defined as the Gibbs free energy, </FONT><FONT =
face=3DSymbol>D</FONT><FONT=20
        face=3DArial>G.</FONT>=20
        <LI>For spontaneous processes: <FONT face=3DSymbol>D</FONT><FONT =

        face=3DArial>S<SUB>universe</SUB> &gt; 0</FONT>=20
        <LI>And therefore:<SPAN style=3D"mso-spacerun: yes">&nbsp; =
</SPAN><FONT=20
        face=3DSymbol>D</FONT><FONT face=3DArial>G &lt; 0</FONT>=20
      <BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>36</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP36><FONT size=3D2><A id=3DPPTL36=20
      href=3D"javascript:GoToSld('slide0032.htm');">Gibbs Free=20
      Energy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC36 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>If DG is negative, the forward reaction is spontaneous.=20
        <LI>If DG is 0, the system is at equilibrium.=20
        <LI>If <FONT face=3DSymbol>D</FONT><FONT face=3DArial>G is =
positive, the=20
        reaction is spontaneous in the reverse direction.</FONT>=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>37</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP37><FONT size=3D2><A id=3DPPTL37=20
      href=3D"javascript:GoToSld('slide0033.htm');">Standard Free Energy =

      Changes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC37 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Standard free energies of formation, <FONT =
face=3DSymbol>D</FONT><FONT=20
        face=3DArial>G<SUB>f</SUB></FONT><FONT =
face=3DSymbol>=B0</FONT><FONT=20
        face=3DArial> are analogous to standard enthalpies of formation, =

        </FONT><FONT face=3DSymbol>D</FONT><FONT=20
        face=3DArial>H<SUB>f</SUB></FONT><FONT =
face=3DSymbol>=B0</FONT><FONT=20
        face=3DArial>.</FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>38</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP38><FONT size=3D2><A id=3DPPTL38=20
      href=3D"javascript:GoToSld('slide0034.htm');">Free Energy=20
      Changes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC38 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Very key equation: <BR><BR><BR><BR>
        <LI>This equation shows how <FONT face=3DSymbol>D</FONT><FONT=20
        face=3DArial>G</FONT><FONT face=3DSymbol>=B0</FONT><FONT =
face=3DArial> changes=20
        with temperature.</FONT>=20
        <LI>(We assume S=B0 &amp; <FONT face=3DSymbol>D</FONT><FONT =
face=3DArial>H=B0=20
        are independent of T.)</FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>39</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP39><FONT size=3D2><A id=3DPPTL39=20
      href=3D"javascript:GoToSld('slide0035.htm');">Free Energy and=20
      Temperature</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC39 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>There are two parts to the free energy equation:=20
        <UL>
          <LI><SPAN style=3D"mso-spacerun: yes">&nbsp; </SPAN>DH<FONT=20
          face=3DSymbol>=B0</FONT><FONT face=3DArial>=97 the enthalpy =
term</FONT>=20
          <LI><SPAN style=3D"mso-spacerun: yes">&nbsp;</SPAN>T<FONT=20
          face=3DSymbol>D</FONT><FONT face=3DArial>S</FONT><FONT=20
          face=3DSymbol>=B0</FONT><FONT face=3DArial> =97 the entropy =
term</FONT>=20
          <BR><BR></LI></UL>
        <LI>The temperature dependence of free energy comes from the =
entropy=20
        term. </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>40</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP40><FONT size=3D2><A id=3DPPTL40=20
      href=3D"javascript:GoToSld('slide0037.htm');">Free Energy and=20
      Temperature</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>41</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP41><FONT size=3D2><A id=3DPPTL41=20
      href=3D"javascript:GoToSld('slide0038.htm');">Free Energy and=20
      Equilibrium</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC41 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Remember from above:=20
        <LI>If DG is 0, the system is at equilibrium.=20
        <LI>
        <LI>So DG must be related to the equilibrium constant, K =
(chapter 15).=20
        The standard free energy, DG=B0, is directly linked to =
K<SUB>eq</SUB> by:=20
        <BR><BR><BR><BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>42</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP42><FONT size=3D2><A id=3DPPTL42=20
      href=3D"javascript:GoToSld('slide0039.htm');">Free Energy and=20
      Equilibrium</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC42 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Under non-standard conditions, we need to use DG instead of =
DG=B0.=20
        <BR><BR><BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>43</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP43><FONT size=3D2><A id=3DPPTL43=20
      href=3D"javascript:GoToSld('slide0045.htm');">Gibbs Free=20
      Energy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC43 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>If DG is negative, the forward reaction is spontaneous.=20
        <LI>If DG is 0, the system is at equilibrium.=20
        <LI>If <FONT face=3DSymbol>D</FONT><FONT face=3DArial>G is =
positive, the=20
        reaction is spontaneous in the reverse direction.</FONT>=20
      </LI></UL></FONT></DIV></TD></TR></TBODY></TABLE></DIV>
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      <DIV class=3DPTxt id=3DPPTP1><FONT size=3D2><A id=3DPPTL1=20
      href=3D"javascript:GoToSld('slide0001.htm');">Chapter =
19<BR>Chemical=20
      Thermodynamics</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>2</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP2><FONT size=3D2><A id=3DPPTL2=20
      href=3D"javascript:GoToSld('slide0011.htm');">First Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC2 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>You will recall from Chapter 5 that energy cannot be created =
nor=20
        destroyed.=20
        <LI>Therefore, the total energy of the universe is a constant.=20
        <LI>Energy can, however, be converted from one form to another =
or=20
        transferred from a system to the surroundings or vice versa.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>3</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP3><FONT size=3D2><A id=3DPPTL3=20
      href=3D"javascript:GoToSld('slide0002.htm');">Spontaneous=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC3 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Spontaneous processes are those that can proceed without any =
outside=20
        intervention.=20
        <LI>The gas in vessel B will spontaneously effuse into vessel A, =
but=20
        once the gas is in both vessels, it will not spontaneously =
return to one=20
        side </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>4</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP4><FONT size=3D2><A id=3DPPTL4=20
      href=3D"javascript:GoToSld('slide0003.htm');">Spontaneous=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC4 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <UL>
          <LI>Processes that are spontaneous in one direction are =
nonspontaneous=20
          in the reverse direction. =
</LI></UL></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>5</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP5><FONT size=3D2><A id=3DPPTL5=20
      href=3D"javascript:GoToSld('slide0004.htm');">Spontaneous=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC5 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Processes that are spontaneous at one temperature may be=20
        nonspontaneous at other temperatures.=20
        <LI>Above 0<FONT face=3DSymbol>=B0</FONT><FONT face=3DArial>C it =
is=20
        spontaneous for ice to melt.</FONT>=20
        <LI>Below 0<FONT face=3DSymbol>=B0</FONT><FONT face=3DArial>C =
the reverse=20
        process is spontaneous.</FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>6</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP6><FONT size=3D2><A id=3DPPTL6=20
      href=3D"javascript:GoToSld('slide0005.htm');">Reversible=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC6 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <UL>
          <LI>In a reversible process the system changes in such a way =
that the=20
          system and surroundings can be put back in their original =
states by=20
          exactly reversing the process. <BR><BR>
          <LI>Changes are infinitesimally small in a reversible process. =

      </LI></UL></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>7</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP7><FONT size=3D2><A id=3DPPTL7=20
      href=3D"javascript:GoToSld('slide0006.htm');">Irreversible=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC7 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Irreversible processes cannot be undone by exactly reversing =
the=20
        change to the system.=20
        <LI>All Spontaneous processes are irreversible.=20
        <LI>All Real processes are irreversible. =
</LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>8</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP8><FONT size=3D2><A id=3DPPTL8=20
      =
href=3D"javascript:GoToSld('slide0007.htm');">Entropy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC8 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy (S) is a term coined by Rudolph Clausius in the 19th =

        century.=20
        <LI>Clausius was convinced of the significance of the ratio of =
heat=20
        delivered and the temperature at which it is delivered,=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>9</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP9><FONT size=3D2><A id=3DPPTL9=20
      =
href=3D"javascript:GoToSld('slide0008.htm');">Entropy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC9 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy can be thought of as a measure of the randomness of =
a=20
        system.=20
        <LI>It is related to the various modes of motion in molecules.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>10</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP10><FONT size=3D2><A id=3DPPTL10=20
      =
href=3D"javascript:GoToSld('slide0009.htm');">Entropy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC10 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Like total energy, E, and enthalpy, H, entropy is a state =
function.=20
        <LI>Therefore,=20
        <LI><FONT face=3DSymbol>D</FONT><FONT face=3DArial>S =3D =
S<SUB>final</SUB>=20
        </FONT><FONT face=3DSymbol>-</FONT><FONT face=3DArial>=20
        S<SUB>initial</SUB></FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>11</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP11><FONT size=3D2><A id=3DPPTL11=20
      =
href=3D"javascript:GoToSld('slide0010.htm');">Entropy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC11 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>For a process occurring at constant temperature (an =
isothermal=20
        process): </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>12</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP12><FONT size=3D2><A id=3DPPTL12=20
      href=3D"javascript:GoToSld('slide0012.htm');">Second Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC12 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The second law of thermodynamics: The entropy of the =
universe does=20
        not change for reversible processes=20
        <LI>and=20
        <LI><SPAN style=3D"mso-spacerun: yes">&nbsp;</SPAN>increases for =

        spontaneous processes. </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>13</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP13><FONT size=3D2><A id=3DPPTL13=20
      href=3D"javascript:GoToSld('slide0013.htm');">Second Law of=20
      Thermodynamics</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>14</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP14><FONT size=3D2><A id=3DPPTL14=20
      href=3D"javascript:GoToSld('slide0014.htm');">Second Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC14 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The entropy of the universe increases (real, spontaneous =
processes).=20

        <LI>But, entropy can decrease for individual systems.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>15</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP15><FONT size=3D2><A id=3DPPTL15=20
      href=3D"javascript:GoToSld('slide0015.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC15 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Ludwig Boltzmann described the concept of entropy on the =
molecular=20
        level.=20
        <LI>Temperature is a measure of the average kinetic energy of =
the=20
        molecules in a sample. </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>16</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP16><FONT size=3D2><A id=3DPPTL16=20
      href=3D"javascript:GoToSld('slide0016.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC16 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Molecules exhibit several types of motion:=20
        <UL>
          <LI>Translational:<SPAN style=3D"mso-spacerun: yes">&nbsp;=20
          </SPAN>Movement of the entire molecule from one place to =
another.=20
          <LI>Vibrational:<SPAN style=3D"mso-spacerun: yes">&nbsp; =
</SPAN>Periodic=20
          motion of atoms within a molecule.=20
          <LI>Rotational:<SPAN style=3D"mso-spacerun: yes">&nbsp; =
</SPAN>Rotation=20
          of the molecule on about an axis or rotation about <FONT=20
          face=3DSymbol>s</FONT><FONT face=3DArial> bonds.</FONT>=20
      </LI></UL></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>17</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP17><FONT size=3D2><A id=3DPPTL17=20
      href=3D"javascript:GoToSld('slide0017.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC17 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Boltzmann envisioned the motions of a sample of molecules at =
a=20
        particular instant in time.=20
        <UL>
          <LI>This would be akin to taking a snapshot of all the =
molecules.=20
        </LI></UL>
        <LI>He referred to this sampling as a microstate of the =
thermodynamic=20
        system. </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>18</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP18><FONT size=3D2><A id=3DPPTL18=20
      href=3D"javascript:GoToSld('slide0018.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC18 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Each thermodynamic state has a specific number of =
microstates, W,=20
        associated with it.=20
        <LI>Entropy is=20
        <LI>S =3D k lnW=20
        <LI>where k is the Boltzmann constant, 1.38 <FONT=20
        face=3DSymbol>=B4</FONT><FONT face=3DArial> 10</FONT><FONT=20
        face=3DSymbol><SUP>-</SUP></FONT><FONT =
face=3DArial><SUP>23</SUP>=20
        J/K.</FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>19</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP19><FONT size=3D2><A id=3DPPTL19=20
      href=3D"javascript:GoToSld('slide0040.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC19 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Implications: <BR><BR>
        <LI>=95 more particles=20
        <LI>-&gt; more states -&gt; more entropy=20
        <LI>=95 higher T=20
        <LI>-&gt; more energy states -&gt; more entropy=20
        <LI>=95 less structure (gas vs solid)=20
        <LI>-&gt; more states -&gt; more entropy=20
  <BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>20</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP20><FONT size=3D2><A id=3DPPTL20=20
      href=3D"javascript:GoToSld('slide0020.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC20 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The number of microstates and, therefore, the entropy tends =
to=20
        increase with increases in=20
        <UL>
          <LI>Temperature.=20
          <LI>Volume (gases).=20
          <LI>The number of independently moving molecules.=20
      </LI></UL></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>21</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP21><FONT size=3D2><A id=3DPPTL21=20
      href=3D"javascript:GoToSld('slide0021.htm');">Entropy and Physical =

      States</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC21 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy increases with the freedom of motion of molecules.=20
        <LI>Therefore,=20
        <LI>S(g) &gt; S(l) &gt; S(s) </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>22</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP22><FONT size=3D2><A id=3DPPTL22=20
      =
href=3D"javascript:GoToSld('slide0022.htm');">Solutions</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC22 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <UL>
          <LI>Dissolution of a solid:=20
          <LI>Ions have more entropy (more states)=20
          <LI>But,=20
          <LI>Some water molecules have less entropy (they are grouped =
around=20
          ions). </LI></UL></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>23</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP23><FONT size=3D2><A id=3DPPTL23=20
      href=3D"javascript:GoToSld('slide0023.htm');">Entropy=20
      Changes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC23 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>In general, entropy increases when=20
        <UL>
          <LI>Gases are formed from liquids and solids.=20
          <LI>Liquids or solutions are formed from solids.=20
          <LI>The number of gas molecules increases.=20
          <LI>The number of moles increases. =
</LI></UL></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>24</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP24><FONT size=3D2><A id=3DPPTL24=20
      href=3D"javascript:GoToSld('slide0024.htm');">Third Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC24 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The entropy of a pure crystalline substance at absolute zero =
is 0.=20
        <BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>25</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP25><FONT size=3D2><A id=3DPPTL25=20
      href=3D"javascript:GoToSld('slide0041.htm');">Third Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC25 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The entropy of a pure crystalline substance at absolute zero =
is 0.=20
        <BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>26</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP26><FONT size=3D2><A id=3DPPTL26=20
      href=3D"javascript:GoToSld('slide0025.htm');">Standard=20
      Entropies</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC26 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>These are molar entropy values of substances in their =
standard=20
        states.=20
        <LI>Standard entropies tend to increase with increasing molar =
mass.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>27</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP27><FONT size=3D2><A id=3DPPTL27=20
      href=3D"javascript:GoToSld('slide0026.htm');">Standard=20
      Entropies</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC27 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Larger and more complex molecules have greater entropies.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>28</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP28><FONT size=3D2><A id=3DPPTL28=20
      href=3D"javascript:GoToSld('slide0027.htm');">Entropy=20
      Changes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC28 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy changes for a reaction can be calculated the same =
way we=20
        used for <FONT face=3DSymbol>D</FONT><FONT =
face=3DArial>H:</FONT>=20
        <LI></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>29</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP29><FONT size=3D2><A id=3DPPTL29=20
      href=3D"javascript:GoToSld('slide0028.htm');">Practical uses: =
surroundings=20
      &amp; system</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC29 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy Changes in Surroundings=20
        <LI>Heat that flows into or out of the system also changes the =
entropy=20
        of the surroundings.=20
        <LI>For an isothermal process: </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>30</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP30><FONT size=3D2><A id=3DPPTL30=20
      href=3D"javascript:GoToSld('slide0042.htm');">Practical uses: =
surroundings=20
      &amp; system</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC30 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy Changes in Surroundings=20
        <LI>Heat that flows into or out of the system also changes the =
entropy=20
        of the surroundings.=20
        <LI>For an isothermal process: </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>31</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP31><FONT size=3D2><A id=3DPPTL31=20
      href=3D"javascript:GoToSld('slide0043.htm');">Link S and <FONT=20
      face=3DSymbol>D</FONT><FONT face=3DArial>H: Phase=20
      changes</FONT></A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>32</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP32><FONT size=3D2><A id=3DPPTL32=20
      href=3D"javascript:GoToSld('slide0029.htm');">"Entropy Change in =
the=20
      Universe"</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC32 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy Change in the Universe=20
        <LI>The universe is composed of the system and the surroundings. =

<BR><BR>
        <LI>Therefore,=20
        <LI><FONT face=3DSymbol>D</FONT><FONT =
face=3DArial>S<SUB>universe</SUB> =3D=20
        </FONT><FONT face=3DSymbol>D</FONT><FONT =
face=3DArial>S<SUB>system</SUB> +=20
        </FONT><FONT face=3DSymbol>D</FONT><FONT=20
        face=3DArial>S<SUB>surroundings</SUB></FONT> <BR><BR>
        <LI>For spontaneous processes=20
        <LI><SPAN style=3D"mso-spacerun: yes">&nbsp;</SPAN><FONT=20
        face=3DSymbol>D</FONT><FONT face=3DArial>S<SUB>universe =
</SUB>&gt; 0</FONT>=20
        <BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>33</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP33><FONT size=3D2><A id=3DPPTL33=20
      href=3D"javascript:GoToSld('slide0030.htm');">Practical uses: =
surroundings=20
      &amp; system</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>34</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP34><FONT size=3D2><A id=3DPPTL34=20
      href=3D"javascript:GoToSld('slide0044.htm');">Practical uses: =
surroundings=20
      &amp; system</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>35</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP35><FONT size=3D2><A id=3DPPTL35=20
      href=3D"javascript:GoToSld('slide0031.htm');">"<FONT=20
      face=3DSymbol>-</FONT><FONT face=3DArial>TDS<SUB>universe</SUB> is =
defined=20
      as</FONT>..."</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC35 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI><FONT face=3DSymbol>-</FONT><FONT =
face=3DArial>TDS<SUB>universe</SUB> is=20
        defined as the Gibbs free energy, </FONT><FONT =
face=3DSymbol>D</FONT><FONT=20
        face=3DArial>G.</FONT>=20
        <LI>For spontaneous processes: <FONT face=3DSymbol>D</FONT><FONT =

        face=3DArial>S<SUB>universe</SUB> &gt; 0</FONT>=20
        <LI>And therefore:<SPAN style=3D"mso-spacerun: yes">&nbsp; =
</SPAN><FONT=20
        face=3DSymbol>D</FONT><FONT face=3DArial>G &lt; 0</FONT>=20
      <BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>36</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP36><FONT size=3D2><A id=3DPPTL36=20
      href=3D"javascript:GoToSld('slide0032.htm');">Gibbs Free=20
      Energy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC36 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>If DG is negative, the forward reaction is spontaneous.=20
        <LI>If DG is 0, the system is at equilibrium.=20
        <LI>If <FONT face=3DSymbol>D</FONT><FONT face=3DArial>G is =
positive, the=20
        reaction is spontaneous in the reverse direction.</FONT>=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>37</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP37><FONT size=3D2><A id=3DPPTL37=20
      href=3D"javascript:GoToSld('slide0033.htm');">Standard Free Energy =

      Changes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC37 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Standard free energies of formation, <FONT =
face=3DSymbol>D</FONT><FONT=20
        face=3DArial>G<SUB>f</SUB></FONT><FONT =
face=3DSymbol>=B0</FONT><FONT=20
        face=3DArial> are analogous to standard enthalpies of formation, =

        </FONT><FONT face=3DSymbol>D</FONT><FONT=20
        face=3DArial>H<SUB>f</SUB></FONT><FONT =
face=3DSymbol>=B0</FONT><FONT=20
        face=3DArial>.</FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>38</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP38><FONT size=3D2><A id=3DPPTL38=20
      href=3D"javascript:GoToSld('slide0034.htm');">Free Energy=20
      Changes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC38 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Very key equation: <BR><BR><BR><BR>
        <LI>This equation shows how <FONT face=3DSymbol>D</FONT><FONT=20
        face=3DArial>G</FONT><FONT face=3DSymbol>=B0</FONT><FONT =
face=3DArial> changes=20
        with temperature.</FONT>=20
        <LI>(We assume S=B0 &amp; <FONT face=3DSymbol>D</FONT><FONT =
face=3DArial>H=B0=20
        are independent of T.)</FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>39</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP39><FONT size=3D2><A id=3DPPTL39=20
      href=3D"javascript:GoToSld('slide0035.htm');">Free Energy and=20
      Temperature</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC39 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>There are two parts to the free energy equation:=20
        <UL>
          <LI><SPAN style=3D"mso-spacerun: yes">&nbsp; </SPAN>DH<FONT=20
          face=3DSymbol>=B0</FONT><FONT face=3DArial>=97 the enthalpy =
term</FONT>=20
          <LI><SPAN style=3D"mso-spacerun: yes">&nbsp;</SPAN>T<FONT=20
          face=3DSymbol>D</FONT><FONT face=3DArial>S</FONT><FONT=20
          face=3DSymbol>=B0</FONT><FONT face=3DArial> =97 the entropy =
term</FONT>=20
          <BR><BR></LI></UL>
        <LI>The temperature dependence of free energy comes from the =
entropy=20
        term. </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>40</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP40><FONT size=3D2><A id=3DPPTL40=20
      href=3D"javascript:GoToSld('slide0037.htm');">Free Energy and=20
      Temperature</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>41</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP41><FONT size=3D2><A id=3DPPTL41=20
      href=3D"javascript:GoToSld('slide0038.htm');">Free Energy and=20
      Equilibrium</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC41 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Remember from above:=20
        <LI>If DG is 0, the system is at equilibrium.=20
        <LI>
        <LI>So DG must be related to the equilibrium constant, K =
(chapter 15).=20
        The standard free energy, DG=B0, is directly linked to =
K<SUB>eq</SUB> by:=20
        <BR><BR><BR><BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>42</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP42><FONT size=3D2><A id=3DPPTL42=20
      href=3D"javascript:GoToSld('slide0039.htm');">Free Energy and=20
      Equilibrium</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC42 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Under non-standard conditions, we need to use DG instead of =
DG=B0.=20
        <BR><BR><BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>43</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP43><FONT size=3D2><A id=3DPPTL43=20
      href=3D"javascript:GoToSld('slide0045.htm');">Gibbs Free=20
      Energy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC43 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>If DG is negative, the forward reaction is spontaneous.=20
        <LI>If DG is 0, the system is at equilibrium.=20
        <LI>If <FONT face=3DSymbol>D</FONT><FONT face=3DArial>G is =
positive, the=20
        reaction is spontaneous in the reverse direction.</FONT>=20
      </LI></UL></FONT></DIV></TD></TR></TBODY></TABLE></DIV>
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<TABLE style=3D"FONT-SIZE: 9pt; FONT-FAMILY: Arial" width=3D"100%">
  <TBODY>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>1</FONT></DIV></TD>
    <TD width=3D"100%">
      <DIV class=3DPTxt id=3DPPTP1><FONT size=3D2><A id=3DPPTL1=20
      href=3D"javascript:GoToSld('slide0001.htm');">Chapter =
19<BR>Chemical=20
      Thermodynamics</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>2</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP2><FONT size=3D2><A id=3DPPTL2=20
      href=3D"javascript:GoToSld('slide0011.htm');">First Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC2 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>You will recall from Chapter 5 that energy cannot be created =
nor=20
        destroyed.=20
        <LI>Therefore, the total energy of the universe is a constant.=20
        <LI>Energy can, however, be converted from one form to another =
or=20
        transferred from a system to the surroundings or vice versa.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>3</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP3><FONT size=3D2><A id=3DPPTL3=20
      href=3D"javascript:GoToSld('slide0002.htm');">Spontaneous=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC3 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Spontaneous processes are those that can proceed without any =
outside=20
        intervention.=20
        <LI>The gas in vessel B will spontaneously effuse into vessel A, =
but=20
        once the gas is in both vessels, it will not spontaneously =
return to one=20
        side </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>4</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP4><FONT size=3D2><A id=3DPPTL4=20
      href=3D"javascript:GoToSld('slide0003.htm');">Spontaneous=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC4 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <UL>
          <LI>Processes that are spontaneous in one direction are =
nonspontaneous=20
          in the reverse direction. =
</LI></UL></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>5</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP5><FONT size=3D2><A id=3DPPTL5=20
      href=3D"javascript:GoToSld('slide0004.htm');">Spontaneous=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC5 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Processes that are spontaneous at one temperature may be=20
        nonspontaneous at other temperatures.=20
        <LI>Above 0<FONT face=3DSymbol>=B0</FONT><FONT face=3DArial>C it =
is=20
        spontaneous for ice to melt.</FONT>=20
        <LI>Below 0<FONT face=3DSymbol>=B0</FONT><FONT face=3DArial>C =
the reverse=20
        process is spontaneous.</FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>6</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP6><FONT size=3D2><A id=3DPPTL6=20
      href=3D"javascript:GoToSld('slide0005.htm');">Reversible=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC6 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <UL>
          <LI>In a reversible process the system changes in such a way =
that the=20
          system and surroundings can be put back in their original =
states by=20
          exactly reversing the process. <BR><BR>
          <LI>Changes are infinitesimally small in a reversible process. =

      </LI></UL></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>7</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP7><FONT size=3D2><A id=3DPPTL7=20
      href=3D"javascript:GoToSld('slide0006.htm');">Irreversible=20
      Processes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC7 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Irreversible processes cannot be undone by exactly reversing =
the=20
        change to the system.=20
        <LI>All Spontaneous processes are irreversible.=20
        <LI>All Real processes are irreversible. =
</LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>8</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP8><FONT size=3D2><A id=3DPPTL8=20
      =
href=3D"javascript:GoToSld('slide0007.htm');">Entropy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC8 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy (S) is a term coined by Rudolph Clausius in the 19th =

        century.=20
        <LI>Clausius was convinced of the significance of the ratio of =
heat=20
        delivered and the temperature at which it is delivered,=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>9</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP9><FONT size=3D2><A id=3DPPTL9=20
      =
href=3D"javascript:GoToSld('slide0008.htm');">Entropy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC9 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy can be thought of as a measure of the randomness of =
a=20
        system.=20
        <LI>It is related to the various modes of motion in molecules.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>10</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP10><FONT size=3D2><A id=3DPPTL10=20
      =
href=3D"javascript:GoToSld('slide0009.htm');">Entropy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC10 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Like total energy, E, and enthalpy, H, entropy is a state =
function.=20
        <LI>Therefore,=20
        <LI><FONT face=3DSymbol>D</FONT><FONT face=3DArial>S =3D =
S<SUB>final</SUB>=20
        </FONT><FONT face=3DSymbol>-</FONT><FONT face=3DArial>=20
        S<SUB>initial</SUB></FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>11</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP11><FONT size=3D2><A id=3DPPTL11=20
      =
href=3D"javascript:GoToSld('slide0010.htm');">Entropy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC11 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>For a process occurring at constant temperature (an =
isothermal=20
        process): </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>12</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP12><FONT size=3D2><A id=3DPPTL12=20
      href=3D"javascript:GoToSld('slide0012.htm');">Second Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC12 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The second law of thermodynamics: The entropy of the =
universe does=20
        not change for reversible processes=20
        <LI>and=20
        <LI><SPAN style=3D"mso-spacerun: yes">&nbsp;</SPAN>increases for =

        spontaneous processes. </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>13</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP13><FONT size=3D2><A id=3DPPTL13=20
      href=3D"javascript:GoToSld('slide0013.htm');">Second Law of=20
      Thermodynamics</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>14</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP14><FONT size=3D2><A id=3DPPTL14=20
      href=3D"javascript:GoToSld('slide0014.htm');">Second Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC14 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The entropy of the universe increases (real, spontaneous =
processes).=20

        <LI>But, entropy can decrease for individual systems.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>15</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP15><FONT size=3D2><A id=3DPPTL15=20
      href=3D"javascript:GoToSld('slide0015.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC15 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Ludwig Boltzmann described the concept of entropy on the =
molecular=20
        level.=20
        <LI>Temperature is a measure of the average kinetic energy of =
the=20
        molecules in a sample. </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>16</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP16><FONT size=3D2><A id=3DPPTL16=20
      href=3D"javascript:GoToSld('slide0016.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC16 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Molecules exhibit several types of motion:=20
        <UL>
          <LI>Translational:<SPAN style=3D"mso-spacerun: yes">&nbsp;=20
          </SPAN>Movement of the entire molecule from one place to =
another.=20
          <LI>Vibrational:<SPAN style=3D"mso-spacerun: yes">&nbsp; =
</SPAN>Periodic=20
          motion of atoms within a molecule.=20
          <LI>Rotational:<SPAN style=3D"mso-spacerun: yes">&nbsp; =
</SPAN>Rotation=20
          of the molecule on about an axis or rotation about <FONT=20
          face=3DSymbol>s</FONT><FONT face=3DArial> bonds.</FONT>=20
      </LI></UL></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>17</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP17><FONT size=3D2><A id=3DPPTL17=20
      href=3D"javascript:GoToSld('slide0017.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC17 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Boltzmann envisioned the motions of a sample of molecules at =
a=20
        particular instant in time.=20
        <UL>
          <LI>This would be akin to taking a snapshot of all the =
molecules.=20
        </LI></UL>
        <LI>He referred to this sampling as a microstate of the =
thermodynamic=20
        system. </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>18</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP18><FONT size=3D2><A id=3DPPTL18=20
      href=3D"javascript:GoToSld('slide0018.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC18 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Each thermodynamic state has a specific number of =
microstates, W,=20
        associated with it.=20
        <LI>Entropy is=20
        <LI>S =3D k lnW=20
        <LI>where k is the Boltzmann constant, 1.38 <FONT=20
        face=3DSymbol>=B4</FONT><FONT face=3DArial> 10</FONT><FONT=20
        face=3DSymbol><SUP>-</SUP></FONT><FONT =
face=3DArial><SUP>23</SUP>=20
        J/K.</FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>19</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP19><FONT size=3D2><A id=3DPPTL19=20
      href=3D"javascript:GoToSld('slide0040.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC19 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Implications: <BR><BR>
        <LI>=95 more particles=20
        <LI>-&gt; more states -&gt; more entropy=20
        <LI>=95 higher T=20
        <LI>-&gt; more energy states -&gt; more entropy=20
        <LI>=95 less structure (gas vs solid)=20
        <LI>-&gt; more states -&gt; more entropy=20
  <BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>20</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP20><FONT size=3D2><A id=3DPPTL20=20
      href=3D"javascript:GoToSld('slide0020.htm');">Entropy on the =
Molecular=20
      Scale</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC20 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The number of microstates and, therefore, the entropy tends =
to=20
        increase with increases in=20
        <UL>
          <LI>Temperature.=20
          <LI>Volume (gases).=20
          <LI>The number of independently moving molecules.=20
      </LI></UL></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>21</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP21><FONT size=3D2><A id=3DPPTL21=20
      href=3D"javascript:GoToSld('slide0021.htm');">Entropy and Physical =

      States</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC21 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy increases with the freedom of motion of molecules.=20
        <LI>Therefore,=20
        <LI>S(g) &gt; S(l) &gt; S(s) </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>22</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP22><FONT size=3D2><A id=3DPPTL22=20
      =
href=3D"javascript:GoToSld('slide0022.htm');">Solutions</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC22 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <UL>
          <LI>Dissolution of a solid:=20
          <LI>Ions have more entropy (more states)=20
          <LI>But,=20
          <LI>Some water molecules have less entropy (they are grouped =
around=20
          ions). </LI></UL></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>23</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP23><FONT size=3D2><A id=3DPPTL23=20
      href=3D"javascript:GoToSld('slide0023.htm');">Entropy=20
      Changes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC23 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>In general, entropy increases when=20
        <UL>
          <LI>Gases are formed from liquids and solids.=20
          <LI>Liquids or solutions are formed from solids.=20
          <LI>The number of gas molecules increases.=20
          <LI>The number of moles increases. =
</LI></UL></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>24</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP24><FONT size=3D2><A id=3DPPTL24=20
      href=3D"javascript:GoToSld('slide0024.htm');">Third Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC24 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The entropy of a pure crystalline substance at absolute zero =
is 0.=20
        <BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>25</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP25><FONT size=3D2><A id=3DPPTL25=20
      href=3D"javascript:GoToSld('slide0041.htm');">Third Law of=20
      Thermodynamics</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC25 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>The entropy of a pure crystalline substance at absolute zero =
is 0.=20
        <BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>26</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP26><FONT size=3D2><A id=3DPPTL26=20
      href=3D"javascript:GoToSld('slide0025.htm');">Standard=20
      Entropies</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC26 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>These are molar entropy values of substances in their =
standard=20
        states.=20
        <LI>Standard entropies tend to increase with increasing molar =
mass.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>27</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP27><FONT size=3D2><A id=3DPPTL27=20
      href=3D"javascript:GoToSld('slide0026.htm');">Standard=20
      Entropies</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC27 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Larger and more complex molecules have greater entropies.=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>28</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP28><FONT size=3D2><A id=3DPPTL28=20
      href=3D"javascript:GoToSld('slide0027.htm');">Entropy=20
      Changes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC28 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy changes for a reaction can be calculated the same =
way we=20
        used for <FONT face=3DSymbol>D</FONT><FONT =
face=3DArial>H:</FONT>=20
        <LI></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>29</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP29><FONT size=3D2><A id=3DPPTL29=20
      href=3D"javascript:GoToSld('slide0028.htm');">Practical uses: =
surroundings=20
      &amp; system</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC29 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy Changes in Surroundings=20
        <LI>Heat that flows into or out of the system also changes the =
entropy=20
        of the surroundings.=20
        <LI>For an isothermal process: </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>30</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP30><FONT size=3D2><A id=3DPPTL30=20
      href=3D"javascript:GoToSld('slide0042.htm');">Practical uses: =
surroundings=20
      &amp; system</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC30 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy Changes in Surroundings=20
        <LI>Heat that flows into or out of the system also changes the =
entropy=20
        of the surroundings.=20
        <LI>For an isothermal process: </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>31</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP31><FONT size=3D2><A id=3DPPTL31=20
      href=3D"javascript:GoToSld('slide0043.htm');">Link S and <FONT=20
      face=3DSymbol>D</FONT><FONT face=3DArial>H: Phase=20
      changes</FONT></A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>32</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP32><FONT size=3D2><A id=3DPPTL32=20
      href=3D"javascript:GoToSld('slide0029.htm');">"Entropy Change in =
the=20
      Universe"</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC32 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Entropy Change in the Universe=20
        <LI>The universe is composed of the system and the surroundings. =

<BR><BR>
        <LI>Therefore,=20
        <LI><FONT face=3DSymbol>D</FONT><FONT =
face=3DArial>S<SUB>universe</SUB> =3D=20
        </FONT><FONT face=3DSymbol>D</FONT><FONT =
face=3DArial>S<SUB>system</SUB> +=20
        </FONT><FONT face=3DSymbol>D</FONT><FONT=20
        face=3DArial>S<SUB>surroundings</SUB></FONT> <BR><BR>
        <LI>For spontaneous processes=20
        <LI><SPAN style=3D"mso-spacerun: yes">&nbsp;</SPAN><FONT=20
        face=3DSymbol>D</FONT><FONT face=3DArial>S<SUB>universe =
</SUB>&gt; 0</FONT>=20
        <BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>33</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP33><FONT size=3D2><A id=3DPPTL33=20
      href=3D"javascript:GoToSld('slide0030.htm');">Practical uses: =
surroundings=20
      &amp; system</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>34</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP34><FONT size=3D2><A id=3DPPTL34=20
      href=3D"javascript:GoToSld('slide0044.htm');">Practical uses: =
surroundings=20
      &amp; system</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>35</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP35><FONT size=3D2><A id=3DPPTL35=20
      href=3D"javascript:GoToSld('slide0031.htm');">"<FONT=20
      face=3DSymbol>-</FONT><FONT face=3DArial>TDS<SUB>universe</SUB> is =
defined=20
      as</FONT>..."</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC35 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI><FONT face=3DSymbol>-</FONT><FONT =
face=3DArial>TDS<SUB>universe</SUB> is=20
        defined as the Gibbs free energy, </FONT><FONT =
face=3DSymbol>D</FONT><FONT=20
        face=3DArial>G.</FONT>=20
        <LI>For spontaneous processes: <FONT face=3DSymbol>D</FONT><FONT =

        face=3DArial>S<SUB>universe</SUB> &gt; 0</FONT>=20
        <LI>And therefore:<SPAN style=3D"mso-spacerun: yes">&nbsp; =
</SPAN><FONT=20
        face=3DSymbol>D</FONT><FONT face=3DArial>G &lt; 0</FONT>=20
      <BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>36</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP36><FONT size=3D2><A id=3DPPTL36=20
      href=3D"javascript:GoToSld('slide0032.htm');">Gibbs Free=20
      Energy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC36 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>If DG is negative, the forward reaction is spontaneous.=20
        <LI>If DG is 0, the system is at equilibrium.=20
        <LI>If <FONT face=3DSymbol>D</FONT><FONT face=3DArial>G is =
positive, the=20
        reaction is spontaneous in the reverse direction.</FONT>=20
      </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>37</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP37><FONT size=3D2><A id=3DPPTL37=20
      href=3D"javascript:GoToSld('slide0033.htm');">Standard Free Energy =

      Changes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC37 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Standard free energies of formation, <FONT =
face=3DSymbol>D</FONT><FONT=20
        face=3DArial>G<SUB>f</SUB></FONT><FONT =
face=3DSymbol>=B0</FONT><FONT=20
        face=3DArial> are analogous to standard enthalpies of formation, =

        </FONT><FONT face=3DSymbol>D</FONT><FONT=20
        face=3DArial>H<SUB>f</SUB></FONT><FONT =
face=3DSymbol>=B0</FONT><FONT=20
        face=3DArial>.</FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>38</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP38><FONT size=3D2><A id=3DPPTL38=20
      href=3D"javascript:GoToSld('slide0034.htm');">Free Energy=20
      Changes</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC38 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Very key equation: <BR><BR><BR><BR>
        <LI>This equation shows how <FONT face=3DSymbol>D</FONT><FONT=20
        face=3DArial>G</FONT><FONT face=3DSymbol>=B0</FONT><FONT =
face=3DArial> changes=20
        with temperature.</FONT>=20
        <LI>(We assume S=B0 &amp; <FONT face=3DSymbol>D</FONT><FONT =
face=3DArial>H=B0=20
        are independent of T.)</FONT> </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>39</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP39><FONT size=3D2><A id=3DPPTL39=20
      href=3D"javascript:GoToSld('slide0035.htm');">Free Energy and=20
      Temperature</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC39 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>There are two parts to the free energy equation:=20
        <UL>
          <LI><SPAN style=3D"mso-spacerun: yes">&nbsp; </SPAN>DH<FONT=20
          face=3DSymbol>=B0</FONT><FONT face=3DArial>=97 the enthalpy =
term</FONT>=20
          <LI><SPAN style=3D"mso-spacerun: yes">&nbsp;</SPAN>T<FONT=20
          face=3DSymbol>D</FONT><FONT face=3DArial>S</FONT><FONT=20
          face=3DSymbol>=B0</FONT><FONT face=3DArial> =97 the entropy =
term</FONT>=20
          <BR><BR></LI></UL>
        <LI>The temperature dependence of free energy comes from the =
entropy=20
        term. </LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>40</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP40><FONT size=3D2><A id=3DPPTL40=20
      href=3D"javascript:GoToSld('slide0037.htm');">Free Energy and=20
      Temperature</A></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>41</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP41><FONT size=3D2><A id=3DPPTL41=20
      href=3D"javascript:GoToSld('slide0038.htm');">Free Energy and=20
      Equilibrium</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC41 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Remember from above:=20
        <LI>If DG is 0, the system is at equilibrium.=20
        <LI>
        <LI>So DG must be related to the equilibrium constant, K =
(chapter 15).=20
        The standard free energy, DG=B0, is directly linked to =
K<SUB>eq</SUB> by:=20
        <BR><BR><BR><BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>42</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP42><FONT size=3D2><A id=3DPPTL42=20
      href=3D"javascript:GoToSld('slide0039.htm');">Free Energy and=20
      Equilibrium</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC42 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>Under non-standard conditions, we need to use DG instead of =
DG=B0.=20
        <BR><BR><BR><BR><BR></LI></UL></FONT></DIV></TD></TR>
  <TR onmouseover=3DOver(this) style=3D"CURSOR: hand" =
onclick=3DFollow(this)=20
  onmouseout=3DOut(this)>
    <TD vAlign=3Dtop align=3Dright>
      <DIV class=3DsldNum><FONT size=3D2>43</FONT></DIV></TD>
    <TD>
      <DIV class=3DPTxt id=3DPPTP43><FONT size=3D2><A id=3DPPTL43=20
      href=3D"javascript:GoToSld('slide0045.htm');">Gibbs Free=20
      Energy</A></FONT></DIV>
      <DIV class=3DCTxt id=3DPPTC43 style=3D"DISPLAY: none"><FONT =
size=3D2>
      <UL>
        <LI>If DG is negative, the forward reaction is spontaneous.=20
        <LI>If DG is 0, the system is at equilibrium.=20
        <LI>If <FONT face=3DSymbol>D</FONT><FONT face=3DArial>G is =
positive, the=20
        reaction is spontaneous in the reverse direction.</FONT>=20
      </LI></UL></FONT></DIV></TD></TR></TBODY></TABLE></DIV>
<DIV style=3D"DISPLAY: none"><A=20
href=3D"http://drschrempp.com/AP%20Powerpoint%20Files/Chp%2019%20-%20Ther=
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