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<Text-field style="Heading 2" layout="Heading 2">2.1.3 First Order Irreversible Series Reactions</Text-field>
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<Text-field style="Text" layout="Normal">Consider the first order series reactions<Font superscript="true">[4]</Font><Font mathcolor="[0,0,0]" mathvariant="normal" mathsize="12" fontfamily="Times New Roman" mathbackground="[255,255,255]">(<Image height="34" width="185" zoomable="false">[encoded data, 5096 characters]</Image></Font>).  The governing equations for this reaction scheme can be written as</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="Text" input-equation="" display="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">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</Equation>= <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">                                                                                                                           (2.8) </Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="Text" input-equation="" display="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">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</Equation>= <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
<Text-field style="Text" layout="Normal">where k<Font subscript="true">1</Font> and k<Font subscript="true">2</Font> are rate constants and the initial conditions are C<Font subscript="true">A</Font>(0) = 1 mol/l, C<Font subscript="true">B</Font>(0) = 0, and  C<Font subscript="true">C</Font>(0) = 0.  The concentration of species C (C<Font subscript="true">C</Font>(t)) at any time is given by the material balance:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal" alignment="centred">                                                         C<Font subscript="true">C</Font> (t) = 1 mol/1 - C<Font subscript="true">A</Font>(t) - C<Font subscript="true">B</Font>(t)                                 (2.9)                    </Text-field>
<Text-field style="Text" layout="Normal" alignment="centred">   </Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">A Maple procedure for solving equations subject to the initial conditions is presented below.  This procedure is useful for developing the correct coefficient matrix A to avoid \342\200\234by hand\342\200\235 errors.</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">Procedure</Font></Text-field>
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<Text-field style="List Item" layout="List Item" bullet="none">1.    Start the Maple program with a 'restart' command to clear all variables.</Text-field>
<Text-field style="List Item" layout="List Item" bullet="none">2.    Call Maple's linear algebra package by using the 'with(linalg)' command.</Text-field>
<Text-field style="List Item" layout="List Item" bullet="none">3.    Call Maple's plotting package by using the 'with(plots)' command.</Text-field>
<Text-field style="List Item" layout="List Item" bullet="none">4.    Use Maple to enter the governing equations.</Text-field>
<Text-field style="List Item" layout="List Item" bullet="none">5.    Name the variable vars.</Text-field>
<Text-field style="List Item" layout="List Item" bullet="none">6.    Name the right hand side of the equations eqs.</Text-field>
<Text-field style="List Item" layout="List Item" bullet="none">7.    Next, use Maple to generate the coefficient matrix (<Font bold="true">A</Font>) using Maple's genmatrix command.</Text-field>
<Text-field style="List Item" layout="List Item" bullet="none">8.    Store the initial conditions for the dependent variables in the vector <Font bold="true">Y0</Font>.  The first row of <Font bold="true">Y0</Font> corresponds to the initial condition for the first dependent variable (C<Font subscript="true">A</Font>).  The second row of <Font bold="true">Y0 </Font>corresponds to the initial condition for the second variable (C<Font subscript="true">B</Font>).</Text-field>
<Text-field style="List Item" layout="List Item" bullet="none">9.    Find the matrix exponential of <Font bold="true">A</Font> (i.e., exp(<Font bold="true">A</Font>t)) as a function of the parameters (rate constants) and the independent variable (t) using the Maple command 'exponential(<Font bold="true">A</Font>,t)'.  Call this matrix mat.</Text-field>
<Text-field style="List Item" layout="List Item" bullet="none">10.  Next, find the solution (sol) by multiplying mat by <Font bold="true">Y0</Font> using Maple's 'evalm' command.</Text-field>
<Text-field style="List Item" layout="List Item" bullet="none">11.  The first row of the sol vector corresponds to C<Font subscript="true">A(t)</Font> and the second row corresponds to C<Font subscript="true">B(t)</Font>.</Text-field>
<Text-field style="List Item" layout="List Item" bullet="none">12.  Note that the analytical solutions for C<Font subscript="true">A</Font> and C<Font subscript="true">B</Font> are obtained as functions of the parameters (rate constants) and the independent variable, t.  Lower case letters are used for these variables with k<Font subscript="true">1</Font> and k<Font subscript="true">2</Font> as parameters.</Text-field>
<Text-field style="List Item" layout="List Item" bullet="none">13.  For a given set of rate constants, plot the concentration profiles.</Text-field>
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<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 2.1 Irreversible Series Reactions</Font></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(linalg):</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots):</Text-field>
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<Text-field style="Text" layout="Normal">Enter the governing equations as follows:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[1]:=diff(C[A](t),t)=-k1*C[A](t);</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJDR0YlNiNJIkFHRiU2I0kidEdGJUYzLCQqJkkjazFHRiVGJ0YtRichIiI=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkiQ0c2IjYjSSJBR0YqNiNJInRHRipGLiwkKiZJI2sxR0YqIiIiRidGMiEiIg==</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[2]:=diff(C[B](t),t)=k1*C[A](t)-k2*C[B](t);</Text-field>
<Text-field style="Text" layout="Normal">Store the variables in vars:</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJI2VxRzYiNiMiIiMvLUklZGlmZkclKnByb3RlY3RlZEc2JC0mSSJDR0YlNiNJIkJHRiU2I0kidEdGJUYzLCYqJkkjazFHRiUiIiItJkYvNiNJIkFHRiVGMkY3RjcqJkkjazJHRiVGN0YtRjchIiI=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkiQ0c2IjYjSSJCR0YqNiNJInRHRipGLiwmKiZJI2sxR0YqIiIiLSZGKTYjSSJBR0YqRi1GMkYyKiZJI2syR0YqRjJGJ0YyISIi</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=[C[A](t),C[B](t)];</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkldmFyc0c2IjckLSZJIkNHRiQ2I0kiQUdGJDYjSSJ0R0YkLSZGKDYjSSJCR0YkRis=">NyQtJkkiQ0c2IjYjSSJBR0YmNiNJInRHRiYtJkYlNiNJIkJHRiZGKQ==</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Next, store the right hand sides of equations 1 and 2 in eqs.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=[rhs(eq[1]),rhs(eq[2])];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNyQsJComSSNrMUdGJCIiIi0mSSJDR0YkNiNJIkFHRiQ2I0kidEdGJEYpISIiLCZGJ0YpKiZJI2syR0YkRiktJkYsNiNJIkJHRiRGL0YpRjE=">NyQsJComSSNrMUc2IiIiIi0mSSJDR0YmNiNJIkFHRiY2I0kidEdGJkYnISIiLCZGJEYnKiZJI2syR0YmRictJkYqNiNJIkJHRiZGLUYnRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Now use the 'genmatrix' Maple command to produce the coefficient matrix <Font bold="true">A.</Font></Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=genmatrix(eqs,vars);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiQUc2Ii1JJ21hdHJpeEdGJDYjNyQ3JCwkSSNrMUdGJCEiIiIiITckRissJEkjazJHRiRGLA==">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Specify the initial conditions.</Text-field>
</Input>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y0:=matrix(2,1,[1,0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjWTBHNiItSSdtYXRyaXhHRiQ2IzckNyMiIiI3IyIiIQ==">PiUjWTBHLUkobWZlbmNlZEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGKTYmLUklbXJvd0dGJjYjLUknbXRhYmxlR0YmNjYtSSRtdHJHRiY2Ji1JJG10ZEdGJjYoLUkjbW5HRiY2JFEiMUYpLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGKS8lKXJvd2FsaWduR1EhRikvJSxjb2x1bW5hbGlnbkdGQi8lK2dyb3VwYWxpZ25HRkIvJShyb3dzcGFuR1EiMUYpLyUrY29sdW1uc3BhbkdGSUZARkNGRS1GNDYmLUY3NigtRjo2JFEiMEYpRj1GQEZDRkVGR0ZKRkBGQ0ZFLyUmYWxpZ25HUSVheGlzRikvRkFRKWJhc2VsaW5lRikvRkRRJnJpZ2h0RikvRkZRJ3xmcmxlZnR8aHJGKS8lL2FsaWdubWVudHNjb3BlR1EldHJ1ZUYpLyUsY29sdW1ud2lkdGhHUSVhdXRvRikvJSZ3aWR0aEdGW28vJStyb3dzcGFjaW5nR1EmMS4wZXhGKS8lLmNvbHVtbnNwYWNpbmdHUSYwLjhlbUYpLyUpcm93bGluZXNHUSVub25lRikvJSxjb2x1bW5saW5lc0dGZm8vJSZmcmFtZUdGZm8vJS1mcmFtZXNwYWNpbmdHUSwwLjRlbX4wLjVleEYpLyUqZXF1YWxyb3dzR1EmZmFsc2VGKS8lLWVxdWFsY29sdW1uc0dGYHAvJS1kaXNwbGF5c3R5bGVHRmBwLyUlc2lkZUdGWS8lMG1pbmxhYmVsc3BhY2luZ0dGY29GPS8lJW9wZW5HUSJbRikvJSZjbG9zZUdRIl1GKQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Use Maple's 'exponential(A,t)' command to produce the exponential (<Font bold="true">A</Font>t) matrix.</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>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkbWF0RzYiLUknbWF0cml4R0YkNiM3JDckLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComSSNrMUdGJCIiIkkidEdGJEYzISIiIiIhNyQsJCooRjJGMywmLUYrNiMsJComSSNrMkdGJEYzRjRGM0Y1RjVGKkYzRjMsJkY/RjVGMkYzRjVGNUY7">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Obtain the solution vector using Maple's 'evalm' command and matrix multiplication (&amp;*).</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=evalm(mat&amp;*Y0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkkc29sRzYiLUknbWF0cml4R0YkNiM3JDcjLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComSSNrMUdGJCIiIkkidEdGJEYzISIiNyMsJCooRjJGMywmLUYrNiMsJComSSNrMkdGJEYzRjRGM0Y1RjVGKkYzRjMsJkY+RjVGMkYzRjVGNQ==">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The first row of 'sol' is the solution for the concentration of species A (C<Font subscript="true">A</Font>) and the second row is for the concentration of species B (C<Font subscript="true">B</Font>).</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ca:=sol[1,1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjY2FHNiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiZJI2sxR0YkIiIiSSJ0R0YkRi4hIiI=">LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComSSNrMUdGJyIiIkkidEdGJ0YsISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cb:=sol[2,1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjY2JHNiIsJCooSSNrMUdGJCIiIiwmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComSSNrMkdGJEYoSSJ0R0YkRighIiJGNC1GKzYjLCQqJkYnRihGM0YoRjRGKEYoLCZGMkY0RidGKEY0RjQ=">LCQqKEkjazFHNiIiIiIsJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCQqJkkjazJHRiVGJkkidEdGJUYmISIiRjItRik2IywkKiZGJEYmRjFGJkYyRiZGJiwmRjBGMkYkRiZGMkYy</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The concentration of species C is obtained from the material balance equation.</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc:=1-ca-cb;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjY2NHNiIsKCIiIkYmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComSSNrMUdGJEYmSSJ0R0YkRiYhIiJGMSooRi9GJiwmLUYoNiMsJComSSNrMkdGJEYmRjBGJkYxRjFGJ0YmRiYsJkY4RjFGL0YmRjFGJg==">LCgiIiJGIy1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJkkjazFHRilGI0kidEdGKUYjISIiRi8qKEYtRiMsJi1GJTYjLCQqJkkjazJHRilGI0YuRiNGL0YvRiRGI0YjLCZGNkYvRi1GI0YvRiM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Note that the concentrations of the species are obtained as functions of the rate constants (k<Font subscript="true">1</Font> and k<Font subscript="true">2</Font>) and<Equation executable="false" style="Text" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L98" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Text" executable="true" layout="Normal"><Font style="Maple Input">pars:={k1=2,k2=1};</Font></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkL0kjazJHRiQiIiIvSSNrMUdGJCIiIw==">PCQvSSNrMkc2IiIiIi9JI2sxR0YlIiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, substitute these values for the rate constants into the concentrations store as C<Font subscript="true">A</Font>, B<Font subscript="true">B</Font>, and C<Font subscript="true">C</Font>.</Text-field>
</Input>
</Group>
<Group labelreference="L29" 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="PkkjQ2FHNiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiYiIiMiIiJJInRHRiRGLiEiIg==">LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComIiIjIiIiSSJ0R0YnRiwhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" 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="PkkjQ2JHNiIsJiomIiIjIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJEkidEdGJCEiIkYoRigqJkYnRigtRio2IywkKiZGJ0YoRjBGKEYxRihGMQ==">LCYqJiIiIyIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCRJInRHRishIiJGJUYlKiZGJEYlLUYnNiMsJComRiRGJUYuRiVGL0YlRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" 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="PkkjQ2NHNiIsKCIiIkYmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComIiIjRiZJInRHRiRGJiEiIkYmKiZGL0YmLUYoNiMsJEYwRjFGJkYx">LCgiIiJGIy1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiIiI0YjSSJ0R0YpRiMhIiJGIyomRi1GIy1GJTYjLCRGLkYvRiNGLw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Plot the concentration profiles for these values of the rate constants as shown in Figure Exp. 2.1.1.</Text-field>
</Input>
</Group><Presentation-Block>
<Group labelreference="L135" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p1:=plot(Ca,t=0..10,thickness=3,color=blue,labels=[&quot;t(min)&quot;,&quot;Concentration (mols/l)&quot;],labeldirections=[horizontal, vertical],legend='C[A]'):</Text-field>
</Input>
</Group>
<Group labelreference="L133" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p2:=plot(Cb,t=0..10,linestyle=1,thickness=3,labels=[&quot;t(min)&quot;,&quot;Concentration (mols/l)&quot;],labeldirections=[horizontal, vertical],legend='C[B]'):</Text-field>
</Input>
</Group>
<Group labelreference="L134" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p3:=plot(Cc,t=0..10,linestyle=1,thickness=3,color=green,labels=[&quot;t(min)&quot;,&quot;Concentration (mols/l)&quot;],labeldirections=[horizontal, vertical],legend='C[C]'):</Text-field>
</Input>
</Group></Presentation-Block>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p4:=textplot([6,.9,k1=2.0*Unit(min^(-1))]):</Text-field>
</Input>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p5:=textplot([6,.7,k2=1.0*Unit(min^(-1))]):</Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display([p1,p2,p3,p4,p5],title=&quot;Figure Exp. 2.1.1 Concentrations of A, B, and C as functions of time.&quot;);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="true">[encoded data, 28820 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L101" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L100" drawlabel="true">
<Input>
<Text-field style="Text" layout="Text Output">Suppose <Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZLLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1JI21uR0YkNiRRIjFGJ0Y1RjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkjbW9HRiQ2LVEifkYnRjUvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZYLUZFNi1RIj1GJ0Y1RkhGSkZMRk5GUEZSRlQvRldRLDAuMjc3Nzc3OGVtRicvRlpGaW5GRC1GLDYmRi4tRiM2JC1GOzYkUSIyRidGNUY1Rj5GQUZlbkY6RkQtRi82JVEkbWluRidGMkY1LUklbXN1cEdGJDYlRkQtRiM2JS1GRTYtUSomdW1pbnVzMDtGJ0Y1RkhGSkZMRk5GUEZSRlQvRldRLDAuMjIyMjIyMmVtRicvRlpGXnBGOkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdGQC1GRTYtUSIuRidGNUZIRkpGTEZORlBGUkZURlZGWUZERkQtRi82JVEjV2VGJ0YyRjVGRC1GLzYlUSRjYW5GJ0YyRjVGRC1GLzYlUSdvYnRhaW5GJ0YyRjVGRC1GLzYlUSNhbkYnRjJGNUZELUYvNiVRK2V4cHJlc3Npb25GJ0YyRjVGRC1GRTYuUSRmb3JGJy8lJWJvbGRHRjRGNUZIRkpGTEZORlBGUkZURlZGWUZELUYvNiVRIkNGJ0YyRjUtRi82JlEiQUYnRjIvJSpzdWJzY3JpcHRHUSV0cnVlRidGNUZELUYvNiVRJXdpdGhGJ0YyRjVGRC1GLzYlUSZ0aGVzZUYnRjJGNUZELUYvNiVRJnZhbHVzRidGMkY1RkRGZHFGRC1GLzYlUSR0aGVGJ0YyRjVGRC1GLzYlUStwYXJhbWV0ZXJzRidGMkY1RmJwRjU=">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</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={k1=1,k2=2};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkL0kjazFHRiQiIiIvSSNrMkdGJCIiIw==">PCQvSSNrMUc2IiIiIi9JI2syR0YlIiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L157" 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="PkkjQ2FHNiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkSSJ0R0YkISIi">LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJEkidEdGJyEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L171" drawlabel="true">
<Input>
<Text-field style="Text" layout="Title" alignment="left">We get division by zero because we  have <Equation executable="false" style="Text" input-equation="" display="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">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</Equation><Equation executable="false" style="Text" input-equation="" display="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">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</Equation>  First, the limit command is applied with respect to the first parameter, <Equation executable="false" style="Text" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L144" 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="PkkjQ2JHNiIsJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqJiIiIyIiIkkidEdGJEYvISIiRjEtRic2IywkRjBGMUYv">LCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkKiYiIiMiIiJJInRHRihGLSEiIkYvLUYkNiMsJEYuRi9GLQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, the 'limit' command is applied with respect to the second parameter,  for <Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYmLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1JI21uR0YkNiRRIjJGJ0Y1RjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkjbW9HRiQ2LVEtJlJpZ2h0QXJyb3c7RidGNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHUSV0cnVlRicvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlktRjs2JFEiMUYnRjVGNQ==</Equation> also:              </Text-field>
</Input>
</Group>
<Group labelreference="L167" 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="PkkjQ2NHNiIsKCIiIkYmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComIiIjRiZJInRHRiRGJiEiIkYmKiZGL0YmLUYoNiMsJEYwRjFGJkYx">LCgiIiJGIy1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiIiI0YjSSJ0R0YpRiMhIiJGIyomRi1GIy1GJTYjLCRGLkYvRiNGLw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L190" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cb:=limit(cb,k1=1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjQ2JHNiIsJComLCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiZJI2syR0YkIiIiSSJ0R0YkRjEhIiJGMS1GKTYjLCRGMkYzRjNGMSwmRjBGMUYxRjNGM0Yz">LCQqJiwmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComSSNrMkdGKiIiIkkidEdGKkYvISIiRi8tRiY2IywkRjBGMUYxRi8sJkYuRi9GL0YxRjFGMQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cb:=limit(Cb,k2=1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjQ2JHNiIqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjSSJ0R0YkISIiRiwiIiI=">KiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kidEdGKCEiIkYqIiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L179" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Similarly, limits can be applied for Cc also:</Text-field>
</Input>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cc:=limit(Cc,k1=1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjQ2NHNiIsKCIiIkYmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComIiIjRiZJInRHRiRGJiEiIkYmKiZGL0YmLUYoNiMsJEYwRjFGJkYx">LCgiIiJGIy1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiIiI0YjSSJ0R0YpRiMhIiJGIyomRi1GIy1GJTYjLCRGLkYvRiNGLw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L108" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cc:=limit(Cc,k2=1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjQ2NHNiIsKCIiIkYmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJComIiIjRiZJInRHRiRGJiEiIkYmKiZGL0YmLUYoNiMsJEYwRjFGJkYx">LCgiIiJGIy1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiIiI0YjSSJ0R0YpRiMhIiJGIyomRi1GIy1GJTYjLCRGLkYvRiNGLw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We can use these results to plot the concentration profiles for the case when k<Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY1LUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiZGKy1GIzYkLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJy1JI21vR0YkNi1RIn5GJ0Y4LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZHLyUpc3RyZXRjaHlHRkcvJSpzeW1tZXRyaWNHRkcvJShsYXJnZW9wR0ZHLyUubW92YWJsZWxpbWl0c0dGRy8lJ2FjY2VudEdGRy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlYtRkI2LVEiPUYnRjhGRUZIRkpGTEZORlBGUi9GVVEsMC4yNzc3Nzc4ZW1GJy9GWEZnbkZBLUYwNiYtRiw2JVEia0YnLyUnaXRhbGljR0ZHRjgtRiM2JC1GNTYkUSIyRidGOEY4RjtGPkZBLUYsNiVRI2FzRidGXm9GOEZBLUYsNiVRJnNob3duRidGXm9GOEZBLUZCNi5RI2luRicvJSVib2xkR0ZHRjhGRUZIRkpGTEZORlBGUkZURldGQS1GLDYlUSdGaWd1cmVGJ0Zeb0Y4RkEtRjU2JFEkMi4xRidGOC1GNTYkUSMuMkYnRjgtRkI2LVEiLkYnRjhGRUZIRkpGTEZORlBGUkZURldGOA==">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</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L183" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p1:=plot(Ca,t=0..10,thickness=3,color=blue,labels=[&quot;t(min)&quot;,&quot;Concentration (mol/l)&quot;],labeldirections=[horizontal, vertical],legend='C[B]'):</Text-field>
</Input>
</Group>
<Group labelreference="L181" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p2:=plot(Cb,t=0..10,linestyle=1,thickness=3,color=red,labels=[&quot;t(min)&quot;,&quot;Concentration (mol/l)&quot;],labeldirections=[horizontal, vertical],legend='C[B]'):</Text-field>
</Input>
</Group>
<Group labelreference="L184" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p3:=plot(Cc,t=0..10,linestyle=1,thickness=3,color=green,labels=[&quot;t(min)&quot;,&quot;Concentration (mol/l)&quot;],labeldirections=[horizontal, vertical],legend='C[C]'):</Text-field>
</Input>
</Group>
<Group labelreference="L182" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p4:=textplot([6,.8,(k1=1.0*Unit(min^(-1)))]):</Text-field>
</Input>
</Group>
<Group labelreference="L185" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p5:=textplot([6,.6,(k2=1.0*Unit(min^(-1)))]):</Text-field>
</Input>
</Group>
<Group labelreference="L186" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display([p1,p2,p3,p4,p5],title=&quot;Figure Exp. 2.1.2 Concentrations of A, B, and C as functions of time.&quot;);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="true">[encoded data, 28408 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We can solve for the time at which B is at its maximum by differentiating cb with respect to t:</Text-field>
</Input>
</Group>
<Group labelreference="L58" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eqmax:=diff(cb,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmRXFtYXhHNiIsJCooSSNrMUdGJCIiIiwmKiZJI2syR0YkRigtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiZGK0YoSSJ0R0YkRighIiJGKEYoKiZGJ0YoLUYtNiMsJComRidGKEY0RihGNUYoRjVGKCwmRitGNUYnRihGNUY1">LCQqKEkjazFHNiIiIiIsJiomSSNrMkdGJUYmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJComRilGJkkidEdGJUYmISIiRiZGJiomRiRGJi1GKzYjLCQqJkYkRiZGMkYmRjNGJkYzRiYsJkYpRjNGJEYmRjNGMw==</Equation></Text-field>
</Output>
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<Group labelreference="L59" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"><Font style="Text">Next solve 'eqmax' to find the time at which cb is at a maximum in terms of the rate constants </Font><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L60" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tmax:=solve(Eqmax,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkldG1heEc2IiwkKiYtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjKiZJI2syR0YkIiIiSSNrMUdGJCEiIkYvLCZGLkYxRjBGL0YxRjE=">LCQqJi1JI2xuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJkkjazJHRikiIiJJI2sxR0YpISIiRi0sJkYsRi9GLkYtRi9GLw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L61" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"><Font style="Text">Substitute this value for time into the concentration equation for B(cb(t)) to find the maximum value of Cb as a function of the rate constants </Font><Equation executable="false" style="Text" input-equation="" display="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">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</Equation></Text-field>
</Input>
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<Group labelreference="L62" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cbmax:=subs(t=tmax,cb);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmY2JtYXhHNiIsJCooSSNrMUdGJCIiIiwmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMqKEkjazJHRiRGKC1JI2xuR0YsNiMqJkYxRihGJyEiIkYoLCZGMUY2RidGKEY2RjYtRis2IyooRidGKEYyRihGN0Y2RihGKEY3RjZGNg==">LCQqKEkjazFHNiIiIiIsJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjKihJI2syR0YlRiYtSSNsbkdGKjYjKiZGL0YmRiQhIiJGJiwmRi9GNEYkRiZGNEY0LUYpNiMqKEYkRiZGMEYmRjVGNEYmRiZGNUY0RjQ=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L63" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The equation for 'cbmax' can be simplified further by using Maple's 'simplify' command.</Text-field>
</Input>
</Group>
<Group labelreference="L64" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cbmax:=simplify(cbmax);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmY2JtYXhHNiIqKEkjazFHRiQiIiIsJikqJkkjazJHRiRGJ0YmISIiKiZGK0YnLCZGK0YsRiZGJ0YsRicpRioqJkYmRidGLkYsRixGJ0YuRiw=">KihJI2sxRzYiIiIiLCYpKiZJI2syR0YkRiVGIyEiIiomRilGJSwmRilGKkYjRiVGKkYlKUYoKiZGI0YlRixGKkYqRiVGLEYq</Equation></Text-field>
</Output>
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<Group labelreference="L65" drawlabel="true">
<Input>
<Text-field style="Normal" layout="Normal"><Font style="Text">A maximum for the concentration of B(cbmax) for the special case of </Font><Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY2LUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiYtRiw2JVEia0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1JI21uR0YkNiRRIjFGJ0Y4RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnLUkjbW9HRiQ2LVEifkYnRjgvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0Zlbi1GSDYtUSI9RidGOEZLRk1GT0ZRRlNGVUZXL0ZaUSwwLjI3Nzc3NzhlbUYnL0ZnbkZcb0ZHLUYwNiZGMi1GIzYkLUY+NiRRIjJGJ0Y4RjhGQUZERkctRiw2JVEkY2FuRidGNUY4RkctRiw2JVEjYmVGJ0Y1RjhGRy1GLDYlUSZmb3VuZEYnRjVGOEZHLUYsNiVRI2FzRidGNUY4RkctRiw2JVEoZm9sbG93c0YnRjVGOC1GSDYtUSI6RidGOEZLRk1GT0ZRRlNGVUZXRltvRl1vRkdGR0Y4">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</Equation></Text-field>
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<Group labelreference="L66" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="2D Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">LUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMhIiI=</Equation></Text-field>
</Output>
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<Group labelreference="L67" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The time needed for the concentration of B to reach a maximum, for the case when k<Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiZGKy1GIzYkLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJ0YrRjg=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiZGKy1GIzYkLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJ0YrRjg=</Equation>= k<Equation executable="false" style="Text" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiZGKy1GIzYkLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJ0YrRjg=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3ViR0YkNiZGKy1GIzYkLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSdhdG9taWNGJ0YrRjg=</Equation> can be found as</Text-field>
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<Group labelreference="L68" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">limit(tmax,k2=k1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkmbWZyYWNHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSVtcm93R0YkNiUtSSNtaUdGJDYlUSNrMUYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGLy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRi8lKWJldmVsbGVkR1EmZmFsc2VGJw==">KiRJI2sxRzYiISIi</Equation></Text-field>
</Output>
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<Group labelreference="L86" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Note that when k<Font subscript="true">1 </Font>= k<Font subscript="true">2</Font>, 'cbmax' is independent of the rate constants, the time taken to reach this maximum value e<Font superscript="true">-1</Font> is inversely proportional to the rate constant k<Font subscript="true">1</Font>.</Text-field>
</Input>
</Group>
</Worksheet>