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<Text-field style="Heading 3" layout="Heading 3"><Font italic="false">Example 2.2 Reversible Series Reactions (see equations (2.10))</Font></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(linalg):</Text-field>
</Input>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots):</Text-field>
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<Input>
<Text-field style="Text" layout="Normal">Specify the equations.</Text-field>
</Input>
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<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[1]:=diff(Ca(t),t)=-k1*Ca(t)+k2*Cb(t);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSNDYUc2IjYjSSJ0R0YpRissJiomSSNrMUdGKSIiIkYnRi8hIiIqJkkjazJHRilGLy1JI0NiR0YpRipGL0Yv</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[2]:=diff(Cb(t),t)=k1*Ca(t)-k2*Cb(t)-k3*Cb(t)+k4*Cc(t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSNDYkc2IjYjSSJ0R0YpRissKiomSSNrMUdGKSIiIi1JI0NhR0YpRipGL0YvKiZJI2syR0YpRi9GJ0YvISIiKiZJI2szR0YpRi9GJ0YvRjQqJkkjazRHRilGLy1JI0NjR0YpRipGL0Yv</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[3]:=diff(Cc(t),t)=k3*Cb(t)-k4*Cc(t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSNDY0c2IjYjSSJ0R0YpRissJiomSSNrM0dGKSIiIi1JI0NiR0YpRipGL0YvKiZJI2s0R0YpRi9GJ0YvISIi</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Specify the variables.</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=[Ca(t),Cb(t),Cc(t)];</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyUtSSNDYUc2IjYjSSJ0R0YlLUkjQ2JHRiVGJi1JI0NjR0YlRiY=</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Specify the right hand side of the equations.</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=[seq(rhs(eq[i]),i=1..3)];</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyUsJiomSSNrMUc2IiIiIi1JI0NhR0YmNiNJInRHRiZGJyEiIiomSSNrMkdGJkYnLUkjQ2JHRiZGKkYnRicsKkYkRidGLUYsKiZJI2szR0YmRidGL0YnRiwqJkkjazRHRiZGJy1JI0NjR0YmRipGJ0YnLCZGMkYnRjRGLA==</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Generate the coefficient matrix A.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=genmatrix(eqs,vars,A);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Pi1JI21pRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliR0YoNiVRIkFGKC8lJ2l0YWxpY0dRJXRydWVGKC8lLG1hdGh2YXJpYW50R1EnaXRhbGljRigtSShtZmVuY2VkR0YlNiYtSSVtcm93R0YlNiMtSSdtdGFibGVHRiU2Ny1JJG10ckdGJTYoLUkkbXRkR0YlNigtRjc2JC1JI21vR0YlNi1RKiZ1bWludXMwO0YoL0YxUSdub3JtYWxGKC8lJmZlbmNlR1EmZmFsc2VGKC8lKnNlcGFyYXRvckdGTC8lKXN0cmV0Y2h5R0ZMLyUqc3ltbWV0cmljR0ZMLyUobGFyZ2VvcEdGTC8lLm1vdmFibGVsaW1pdHNHRkwvJSdhY2NlbnRHRkwvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYoLyUncnNwYWNlR0Zlbi1GJDYlUSNrMUYoRi1GMC8lKXJvd2FsaWduR1EhRigvJSxjb2x1bW5hbGlnbkdGXW8vJStncm91cGFsaWduR0Zdby8lKHJvd3NwYW5HUSIxRigvJStjb2x1bW5zcGFuR0Zkby1GQDYoLUYkNiVRI2syRihGLUYwRltvRl5vRmBvRmJvRmVvLUZANigtSSNtbkdGJTYkUSIwRihGSEZbb0Zeb0Zgb0Zib0Zlb0Zbb0Zeb0Zgby1GPTYoLUZANihGaG5GW29GXm9GYG9GYm9GZW8tRkA2KC1GNzYmLUkqbXZlcmJhdGltR0YlNiNRJCEiIkYoRmlvRmpwLUYkNiVRI2szRihGLUYwRltvRl5vRmBvRmJvRmVvLUZANigtRiQ2JVEjazRGKEYtRjBGW29GXm9GYG9GYm9GZW9GW29GXm9GYG8tRj02KEZccC1GQDYoRl5xRltvRl5vRmBvRmJvRmVvLUZANigtRjc2JEZERmNxRltvRl5vRmBvRmJvRmVvRltvRl5vRmBvLyUmYWxpZ25HUSVheGlzRigvRlxvUSliYXNlbGluZUYoL0Zfb1EnY2VudGVyRigvRmFvUSd8ZnJsZWZ0fGhyRigvJS9hbGlnbm1lbnRzY29wZUdGLy8lLGNvbHVtbndpZHRoR1ElYXV0b0YoLyUmd2lkdGhHRltzLyUrcm93c3BhY2luZ0dRJjEuMGV4RigvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GKC8lKXJvd2xpbmVzR1Elbm9uZUYoLyUsY29sdW1ubGluZXNHRmZzLyUmZnJhbWVHRmZzLyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGKC8lKmVxdWFscm93c0dGTC8lLWVxdWFsY29sdW1uc0dGTC8lLWRpc3BsYXlzdHlsZUdGTC8lJXNpZGVHUSZyaWdodEYoLyUwbWlubGFiZWxzcGFjaW5nR0Zjc0ZILyUlb3BlbkdRIltGKC8lJmNsb3NlR1EiXUYo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Generate the exponential matrix of A.</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">mat:=exponential(A,t):</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Set the initial conditions vector:</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=matrix(3,1,[1,0,0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Obtain the solution.</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=evalm(mat&amp;*Y0):</Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Pull out the components of the solution.</Text-field>
</Input>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ca:=sol[1,1]:</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cb:=sol[2,1]:</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc:=sol[3,1]:</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution vector 'sol' and its elements (sol [1,1], e.g.) are too long to present here.  They are functions of the rate constants (k<Font subscript="true">1</Font>, k<Font subscript="true">2</Font>, k<Font subscript="true">3</Font>, and k<Font subscript="true">4</Font><Font encoding="UTF-8">) and the independent variable t.   One can obtain the solution from the CD with this book by changing the colons to semicolons at the end of the command line in the worksheet.  As in Example 2.1, the solution obtained can be plotted for a particular set of values for the rate constants.  Let\342\200\231s set these to be the same as those used on page 282 of Constantinides and Mostoufi.</Font><Font superscript="true">[6]</Font></Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={k1=1.,k2=0.,k3=2.,k4=3.};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCYvSSNrMUc2IiQiIiIiIiEvSSNrMkdGJSRGKEYoL0kjazNHRiUkIiIjRigvSSNrNEdGJSQiIiRGKA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Obtain the concentrations as functions of time by substituting  these values for the rate constants into the components of the solution vector:</Text-field>
</Input>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=subs(pars,ca);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJiQiKysrKys1ISIqIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComRiRGJ0kidEdGLUYnISIiRidGJw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cb:=subs(pars,cb);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJiQiKysrKytdISM1IiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComJCIrKysrKzUhIipGJ0kidEdGLUYnISIiRidGNSomJEYyRiZGJy1GKTYjLCQqJiRGJUYzRidGNEYnRjVGJ0Y1JCIrKysrK2dGJkYn</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cc:=subs(pars,cc);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJiQiKysrKys1ISM1IiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComJCIrKysrK10hIipGJ0kidEdGLUYnISIiRidGJyQiKysrKytTRiZGJyomJEYyRiZGJy1GKTYjLCQqJiRGJUYzRidGNEYnRjVGJ0Y1</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal">Plot the results.</Text-field>
</Input>
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<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[1]:=plot(Ca,t=0..10,thickness=4,linestyle=1,color=blue,labels=[&quot;t(min)&quot;,&quot;Concentration (mol/1)&quot;],labeldirections=[horizontal, vertical],legend='C[A]'): </Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct</Text-field>
</Output>
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<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[2]:=plot(Cb,t=0..10,thickness=4,linestyle=1,labels=[&quot;t(min)&quot;,&quot;Concentrations(mol/1)&quot;],labeldirections=[horizontal, vertical],legend='C[B]'):</Text-field>
</Input>
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<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[3]:=plot(Cc,t=0..10,thickness=4,linestyle=1,color=green,labels=[&quot;t(min)&quot;,&quot;Concentration (mol/1)&quot;],labeldirections=[horizontal,vertical],legend='C[C]'):</Text-field>
</Input>
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<Group labelreference="L94" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[4]:=textplot([4,.9,k1=1.0*Unit(min^(-1))]),textplot([6,.9,k2=0]):</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"></Text-field>
</Input>
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<Group labelreference="L105" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[5]:=textplot([4,.7,k3=2.0*Unit(min^(-1))]),textplot([7,.7,k4=3.0*Unit(min^(-1))]):</Text-field>
</Input>
<Input>
<Text-field prompt="&gt; " style="Maple Input" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"></Text-field>
</Input>
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<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(p[i],i=1..5)}, title=&quot;Figure Exp. 2.2.1 Concentrations of A, B, and C as functions of time.&quot;, axes=boxed);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="442" type="two-dimensional" width="406" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="true">[encoded data, 36680 characters]</Plot></Text-field>
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<Input>
<Text-field style="Text" layout="Normal">This figure matches Figure Exp. 5.2 on page 282 of Constantinides and Mostoufi, 1999.<Font superscript="true">[6]</Font>  For a different set of values for the parameters, the solution can be obtained by just substituting the numerical values of the rate constants into the solution vector components.  We did not observe a maximum for Cb for this particular set of values of the rate constants.  However, we can use different values of the rate constants to illustrate that a maximum can exist in the concentration of species B:</Text-field>
</Input>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={k1=10.,k2=0.5,k3=2.,k4=3.};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCYvSSNrM0c2IiQiIiMiIiEvSSNrNEdGJSQiIiRGKC9JI2sxR0YlJCIjNUYoL0kjazJHRiUkIiImISIi</Equation></Text-field>
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<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=subs(pars,ca);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJiQiK1VObyUzKiEjNSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiQiKylcPHcxIiEiKUYnSSJ0R0YtRichIiJGJ0YnKiYkIitdSmFTaSEjNkYnLUYpNiMsJComJCIrQV0jUSNbISIqRidGNEYnRjVGJ0YnJCIrIVFARSJIRjlGJw==</Equation></Text-field>
</Output>
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<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cb:=subs(pars,cb);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJiQiK3MnRy9ZJyEjNSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiQiK0FdI1EjWyEiKkYnSSJ0R0YtRichIiJGJ0YnKiYkIitScmNHN0YzRictRik2IywkKiYkIispXDx3MSIhIilGJ0Y0RidGNUYnRjUkIis7RkNEZUYmRic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cc:=subs(pars,cc);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJiQiK1V5KTQ/JCEjNSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiQiKylcPHcxIiEiKUYnSSJ0R0YtRichIiJGJ0YnKiYkIispKUhbJTMoRiZGJy1GKTYjLCQqJiQiK0FdI1EjWyEiKkYnRjRGJ0Y1RidGNSQiK1deXCQpUUYmRic=</Equation></Text-field>
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<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[1]:=plot(Ca,t=0..5,thickness=4,color=blue,linestyle=1,labels=[&quot;t(min)&quot;,&quot;Concentration (mol/1)&quot;],labeldirections=[horizontal, vertical],legend='C[A]'):</Text-field>
</Input>
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<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[2]:=plot(Cb,t=0..5,thickness=4,linestyle=1,labels=[&quot;t(min)&quot;,&quot;Concentration (mol/1)&quot;],labeldirections=[horizontal, vertical],legend='C[B]'):</Text-field>
</Input>
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<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[3]:=plot(Cc,t=0..5,thickness=4,color=green,linestyle=1,labels=[&quot;t(min)&quot;,&quot;Concentration (mol/1)&quot;],labeldirections=[horizontal, vertical],legend='C[C]'):</Text-field>
</Input>
</Group>
<Group labelreference="L107" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[4]:=textplot([2,.9,k1=10.0*Unit(min^(-1))]),textplot([3.5,.9,k2=0.5*Unit(min^(-1))]):</Text-field>
</Input>
</Group>
<Group labelreference="L108" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[5]:=textplot([2,.7,k3=2.0*Unit(min^(-1))]),textplot([3.5,.7,k4=3.0*Unit(min^(-1))]):</Text-field>
</Input>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(p[i],i=1..5)},title=&quot;Figure Exp. 2.2.2 Concentrations of A, B, and C as functions of time.&quot;,axes=boxed);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="454" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="true">[encoded data, 41708 characters]</Plot></Text-field>
</Output>
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<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">We can find an equation in terms of the rate constants that will provide a means of finding the time at which the maximum in Cb occurs.  We do this by using Maple's 'simplify' command and by finding \342\210\202cb/\342\210\202t by using Maple's 'diff' command.</Font></Text-field>
</Input>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=simplify(diff(cb,t)):</Text-field>
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<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, we use Maple's 'solve' command to set the equation (eq) equal to zero and solve for 'tmax':</Text-field>
</Input>
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<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tmax:=solve(eq,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJi1JI2xuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJiwsSSNrMUdGKSIiIkkjazNHRilGLiokKSw2KiQpRi0iIiNGLkYuKihGNUYuRi1GLkkjazJHRilGLkYuKihGNUYuRi1GLkYvRi4hIiIqKEY1Ri5GLUYuSSNrNEdGKUYuRjkqJClGN0Y1Ri5GLiooRjVGLkYvRi5GN0YuRi4qKEY1Ri5GN0YuRjtGLkY5KiQpRi9GNUYuRi4qKEY1Ri5GO0YuRi9GLkYuKiQpRjtGNUYuRi4jRi5GNUYuRjlGN0YuRjtGOUYuLCxGLUYuRi9GLkYwRi5GN0YuRjtGOUY5Ri5GMUY5Rjk=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The concentration of B at 'tmax' can be obtained by substitution of the 'tmax' expression into the solution for the concentration of B as a function of time.</Text-field>
</Input>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cbmax:=simplify(subs(t=tmax,cb)):</Text-field>
</Input>
</Group>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution 'cbmax' is not printed to conserve space.  We can find if a maximum exists or not by substituting  numerical values for the rate constants.  If Cb has a maximum, 'tmax' should be real and positive.  A value for 'tmax' can be obtained by substituting the same rate constants into the derived equations.</Text-field>
</Input>
</Group>
<Group labelreference="L56" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(subs(k1=1.,k2=0.,k3=2.,k4=3.0,tmax));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYkIiIhRiQhIiIqJiQiK047KVImeSEjNSIiIl4jRipGKkYl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(subs(k1=2.,k2=0.,k3=2.,k4=3.0,tmax));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYkIistMVw1QiEjNSIiIiomJCIrXnY+WjUhIipGJl4jRiZGJiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(subs(k1=10.,k2=1.,k3=1.,k4=1.0,tmax));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrMHBZTkUhIzU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">An interesting case is when k<Font subscript="true">1</Font> = k<Font subscript="true">3</Font> and k<Font subscript="true">2</Font> =  k<Font subscript="true">4</Font>.</Text-field>
</Input>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={k1=2,k2=1/2,k3=2,k4=1/2};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCYvSSNrMUc2IiIiIy9JI2szR0YlRiYvSSNrMkdGJSMiIiJGJi9JI2s0R0YlRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A1:=evalm(subs(pars,evalm(A)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L62" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eigenvalues(A1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiUiIiEjISIkIiIjIyEiKEYm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L63" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">One of the eigenvalues is zero in this case.</Text-field>
</Input>
</Group>
<Group labelreference="L64" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=evalf(subs(pars,ca));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgkIitpWiE+dyUhIzYiIiIqJiQiK29tbW1tISM1RiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkKiYkIisrKysrOiEiKkYmSSJ0R0YwRiYhIiJGJkYmKiYkIitlRzlkR0YqRiYtRiw2IywkKiYkIisrKysrTkY2RiZGN0YmRjhGJkYm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L65" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cb:=evalf(subs(pars,cb));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJiQiK29tbW1tISM1IiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComJCIrKysrKzohIipGJ0kidEdGLUYnISIiRidGJyomJCIrdCZHOWQpRiZGJy1GKTYjLCQqJiQiKysrKytORjNGJ0Y0RidGNUYnRjUkIiswPncvPkYmRic=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L66" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cc:=evalf(subs(pars,cc));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgqJiQiKztkRzlkISM1IiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComJCIrKysrK04hIipGJ0kidEdGLUYnISIiRidGJyomJCIrTUxMTDhGM0YnLUYpNiMsJComJCIrKysrKzpGM0YnRjRGJ0Y1RidGNSQiKz93Lz53RiZGJw==</Equation></Text-field>
</Output>
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<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[1]:=plot(Ca,t=0..5,thickness=4,color=blue,linestyle=1,labels=[&quot;t(min)&quot;,&quot;Concentration (mols/1)&quot;],labeldirections=[horizontal, vertical],legend='C[A]'):</Text-field>
</Input>
</Group>
<Group labelreference="L68" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[2]:=plot(Cb,t=0..5,thickness=4,linestyle=1,labels=[&quot;t(min)&quot;,&quot;Concentration (mols/1)&quot;],labeldirections=[horizontal, vertical],legend='C[B]'):</Text-field>
</Input>
</Group>
<Group labelreference="L69" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[3]:=plot(Cc,t=0..5,thickness=4,color=green,linestyle=1,labels=[&quot;t(min)&quot;,&quot;Concentration (mols/1)&quot;],labeldirections=[horizontal, vertical],legend='C[C]'):</Text-field>
</Input>
</Group>
<Group labelreference="L109" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[4]:=textplot([1.5,.9,k1=1.0*Unit(min^(-1))]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LSUlUExPVEc2Iy1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckJCIjOiEiIiQiIipGLy9JI2sxR0YqLCQqJiQiIzVGLyIiIi1JJVVuaXRHRio2IyokSSRtaW5HRipGL0Y4Rjg=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L110" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[5]:=textplot([3.5,.9,k2=0.5*Unit(min^(-1))]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LSUlUExPVEc2Iy1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckJCIjTiEiIiQiIipGLy9JI2syR0YqLCQqJiQiIiZGLyIiIi1JJVVuaXRHRio2IyokSSRtaW5HRipGL0Y4Rjg=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L121" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[6]:=textplot([3.5,.6,k3=1.0*Unit(min^(-1))]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LSUlUExPVEc2Iy1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckJCIjTiEiIiQiIidGLy9JI2szR0YqLCQqJiQiIzVGLyIiIi1JJVVuaXRHRio2IyokSSRtaW5HRipGL0Y4Rjg=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L119" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[7]:=textplot([3.5,.4,k4=0.5*Unit(min^(-1))]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LSUlUExPVEc2Iy1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckJCIjTiEiIiQiIiVGLy9JI2s0R0YqLCQqJiQiIiZGLyIiIi1JJVVuaXRHRio2IyokSSRtaW5HRipGL0Y4Rjg=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L70" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(p[i],i=1..7)},title=&quot;Figure 2.2.3 Concentrations of A, B, and C as functions of time.&quot;,axes=boxed);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="493" type="two-dimensional" width="444" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="true">[encoded data, 41080 characters]</Plot></Text-field>
</Output>
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<Group labelreference="L118" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L72" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Another interesting case is when k<Font subscript="true">2</Font>= k<Font subscript="true">4</Font>=0.</Text-field>
</Input>
</Group>
<Group labelreference="L73" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={k1=1,k2=0,k3=1,k4=0};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVElcGFyc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSShtZmVuY2VkR0YkNiYtRiM2Ky1GIzYnLUYsNiVRI2sxRidGL0YyLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUkjbW5HRiQ2JFEiMUYnRjkvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRjktRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GIzYnLUYsNiVRI2szRidGL0YyRllGZm5Gam5GOUZdby1GIzYnLUYsNiVRI2s0RidGL0YyRlktRmduNiRRIjBGJ0Y5RmpuRjlGXW8tRiM2Jy1GLDYlUSNrMkYnRi9GMkZZRl9wRmpuRjlGam5GOUY5LyUlb3BlbkdRInxmckYnLyUmY2xvc2VHUSJ8aHJGJ0ZqbkY5">PCYvSSNrMUc2IiIiIi9JI2szR0YlRiYvSSNrNEdGJSIiIS9JI2syR0YlRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L74" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A1:=evalm(subs(pars,evalm(A)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L75" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eigenvalues(A1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiUhIiJGIyIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L76" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">One of the eigenvalues is zero and the other two eigenvalues are repeated in this case.</Text-field>
</Input>
</Group>
<Group labelreference="L77" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=evalf(subs(pars,ca));</Text-field>
</Input>
<Output>
<Text-field style="Error" layout="Error">Error, numeric exception: division by zero</Text-field>
</Output>
</Group>
<Group labelreference="L78" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We get division by zero again as we did in Example 2.1.  The solution can be obtained by using Maple's 'limit' command.</Text-field>
</Input>
</Group>
<Group labelreference="L79" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=limit(ca,k1=1):</Text-field>
</Input>
</Group>
<Group labelreference="L80" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=limit(Ca,k2=0):</Text-field>
</Input>
</Group>
<Group labelreference="L81" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=limit(Ca,k3=1):</Text-field>
</Input>
</Group>
<Group labelreference="L82" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=limit(Ca,k4=0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJEkidEdGJyEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L83" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Alternatively, the four lines can be successively applied in the same statement as</Text-field>
</Input>
</Group>
<Group labelreference="L84" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cb:=limit(limit(limit(limit(cb,k1=1),k2=0),k3=1),k4=0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiZJInRHNiIiIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YjISIi</Equation></Text-field>
</Output>
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<Group labelreference="L85" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cc:=limit(limit(limit(limit(cc,k1=1),k2=0),k3=1),k4=0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsKC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ0R0YpIiIiRishIiJGLEYtRixGJEYt</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L86" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[1]:=plot(Ca,t=0..5,thickness=4,linestyle=1,color=blue,labels=[&quot;t(min)&quot;,&quot;Concentration (mols/1)&quot;],labeldirections=[horizontal, vertical],legend='C[A]'):</Text-field>
</Input>
</Group>
<Group labelreference="L87" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[2]:=plot(Cb,t=0..5,thickness=4,linestyle=1,labels=[&quot;t(min)&quot;,&quot;Concentration (mols/1)&quot;],labeldirections=[horizontal, vertical],legend='C[B]'):</Text-field>
</Input>
</Group>
<Group labelreference="L88" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[3]:=plot(Cc,t=0..5,thickness=4,color=green,linestyle=1,labels=[&quot;t(min)&quot;,&quot;Concentration (mols/1)&quot;],labeldirections=[horizontal, vertical],legend='C[C]'):</Text-field>
</Input>
</Group>
<Group labelreference="L114" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[4]:=textplot([1.5,.9,k1=1.0*Unit(min^(-1))]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiNEYnL0Y2USdub3JtYWxGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGPi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEjOj1GJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZMLyUpc3RyZXRjaHlHRkwvJSpzeW1tZXRyaWNHRkwvJShsYXJnZW9wR0ZMLyUubW92YWJsZWxpbWl0c0dGTC8lJ2FjY2VudEdGTC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmVuLUYjNictRi82JVElUExPVEYnRjJGNS1GRzYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y+RkpGTUZPRlFGU0ZVRlcvRlpRJjAuMGVtRicvRmduRmFvLUkobWZlbmNlZEdGJDYkLUYvNiVRJC4uLkYnRjJGNUY+RkBGPkZARj4=">LSUlUExPVEc2Iy1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckJCIjOiEiIiQiIipGLy9JI2sxR0YqLCQqJiQiIzVGLyIiIi1JJVVuaXRHRio2IyokSSRtaW5HRipGL0Y4Rjg=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L115" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[5]:=textplot([1.5,.7,k2=0*Unit(min^(-1))]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LSUlUExPVEc2Iy1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckJCIjOiEiIiQiIihGLy9JI2syR0YqIiIh</Equation></Text-field>
</Output>
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<Group labelreference="L116" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[6]:=textplot([4,.6,k3=1.0*Unit(min^(-1))]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LSUlUExPVEc2Iy1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckJCIiJSIiISQiIichIiIvSSNrM0dGKiwkKiYkIiM1RjIiIiItSSVVbml0R0YqNiMqJEkkbWluR0YqRjJGOUY5</Equation></Text-field>
</Output>
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<Group labelreference="L117" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[7]:=textplot([4,.4,k4=0*Unit(min^(-1))]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiN0YnL0Y2USdub3JtYWxGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGPi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEjOj1GJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZMLyUpc3RyZXRjaHlHRkwvJSpzeW1tZXRyaWNHRkwvJShsYXJnZW9wR0ZMLyUubW92YWJsZWxpbWl0c0dGTC8lJ2FjY2VudEdGTC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmVuLUYjNictRi82JVElUExPVEYnRjJGNS1GRzYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y+RkpGTUZPRlFGU0ZVRlcvRlpRJjAuMGVtRicvRmduRmFvLUkobWZlbmNlZEdGJDYkLUYvNiVRJC4uLkYnRjJGNUY+RkBGPkZARj4=">LSUlUExPVEc2Iy1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckJCIiJSIiISRGLiEiIi9JI2s0R0YqRi8=</Equation></Text-field>
</Output>
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<Text-field style="Text" layout="No Name208" alignment="left">As can be seen by comparison, Figure Exp. 2.2.4 is the same as Figure Exp. 2.1.2 as expected.</Text-field>
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