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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> (<Image height="29" width="185" zoomable="false">[encoded data, 5096 characters]<Drawing-Root>LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIlNVQhIiItJSlCT1VORFNfWUc2IyQiJF0iRiotJS1CT1VORFNfV0lEVEhHNiMkIiVdPUYqLSUuQk9VTkRTX0hFSUdIVEc2IyQiJCFIRiotJSlDSElMRFJFTkc2Ig==</Drawing-Root></Image>).  The governing equations for this reaction scheme can be written as</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="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtaUdGJDYlUSJrRicvJSdpdGFsaWNHRjRGLy1GRzYmUSIxRidGSi8lKnN1YnNjcmlwdEdRJXRydWVGJ0YvLUZHNiVRIkNGJ0ZKRi8tRkc2JlEiQUYnRkpGT0YvRitGRi1GRzYmUSIyRidGSkZPRi9GUi1GRzYmUSJCRidGSkZPRi9GLw==">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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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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkiQ0c2IjYjSSJBR0YqNiNJInRHRipGLiwkKiZJI2sxR0YqIiIiRidGMiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<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>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtJkkiQ0c2IjYjSSJCR0YqNiNJInRHRipGLiwmKiZJI2sxR0YqIiIiLSZGKTYjSSJBR0YqRi1GMkYyKiZJI2syR0YqRjJGJ0YyISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=[C[A](t),C[B](t)];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NyQtJkkiQ0c2IjYjSSJBR0YmNiNJInRHRiYtJkYlNiNJIkJHRiZGKQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, store the right hand sides of equations 1 and 2 in eqs.</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<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="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkZXFzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JKG1mZW5jZWRHRiQ2Ji1GIzYnLUYjNiYtRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORlotRiM2Ji1GLDYlUSNrMUYnRi9GMi1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORl9vLUYjNictSSVtc3ViR0YkNiUtRiw2JVEiQ0YnRi9GMi1GIzYlLUYsNiVRIkFGJ0YvRjIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRjkvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkhGXm9GYG8tRlA2JC1GIzYlLUYsNiVRInRGJ0YvRjJGXnBGOUY5Rl5wRjlGOUZecEY5LUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkhGXm8vRk5RLDAuMzMzMzMzM2VtRictRiM2JkZmbi1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRllGZW4tRiM2Ji1GLDYlUSNrMkYnRi9GMkZbby1GIzYnLUZkbzYlRmZvLUYjNiUtRiw2JVEiQkYnRi9GMkZecEY5RmFwRmRwRmdwRl5wRjlGOUY5Rl5wRjlGOS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZecEY5">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="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">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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="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">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</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="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">[encoded data, 4836 characters]</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="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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">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="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">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="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">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="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">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 the indpendent variable, t.<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="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">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="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">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="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEjQ2JGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSM6PUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYjNiYtRiM2Ji1JI21uR0YkNiRRIjJGJ0Y5LUY2Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GZW4tSSVtc3VwR0YkNiUtRjY2LVEvJkV4cG9uZW50aWFsRTtGJ0Y5RjtGPkZARkJGREZGRkhGWi9GTlEsMC4xMTExMTExZW1GJy1GIzYmLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZlby1GLDYlUSJ0RidGL0YyLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Y5LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y5LUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkhGZG9GZm8tRiM2JkZTRlctRmhuNiVGam4tRiM2JkZhby1GIzYmRlNGV0Znb0Y5RmpvRjlGXXBGOUY5RmpvRjk=">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="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">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>
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<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, 28156 characters]</Plot></Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>.  We can use Maple's limit command to find a new expression for the concentration of B when <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>.  First, let's set k<Font mathsize="12" mathvariant="normal" subscript="true" mathbackground="[255,255,255]" mathcolor="[0,0,0]" fontfamily="Times New Roman">1</Font> = 1 min<Font superscript="true" encoding="UTF-8">\342\210\2221</Font>, and then we will find the limit of the expression for the concentration of B as <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"></Text-field>
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<Group labelreference="L192" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
</Input>
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<Group labelreference="L157" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=subs(k1=1,ca);</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>
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<Group labelreference="L144" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cb:=subs(k1=1,cb);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJiwmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComSSNrMkdGKiIiIkkidEdGKkYvISIiRjEtRiY2IywkRjBGMUYvRi8sJkYuRjFGL0YvRjFGMQ==</Equation></Text-field>
</Output>
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<Group labelreference="L194" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cc:=subs(k1=1,cc);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgiIiJGIy1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCRJInRHRikhIiJGLSomLCYtRiU2IywkKiZJI2syR0YpRiNGLEYjRi1GLUYkRiNGIywmRjRGLUYjRiNGLUYj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, the 'limit' command is applied  for <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>:              </Text-field>
</Input>
</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="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">KiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kidEdGKCEiIkYqIiIi</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="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">KiYsKC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSJ0R0YpIiIiRiwhIiJGK0YtRixGJEYt</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[A]'):</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, 27772 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="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">LCQqKEkjazFHNiIiIiIsJiomSSNrMkdGJUYmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJComRilGJkkidEdGJUYmISIiRiZGJiomRiRGJi1GKzYjLCQqJkYkRiZGMkYmRjNGJkYzRiYsJkYpRjNGJEYmRjNGMw==</Equation></Text-field>
</Output>
</Group>
<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="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">LCQqJi1JI2xuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJkkjazJHRikiIiJJI2sxR0YpISIiRi0sJkYsRi9GLkYtRi9GLw==</Equation></Text-field>
</Output>
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<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="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">LCQqKEkjazFHNiIiIiIsJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjKihJI2syR0YlRiYtSSNsbkdGKjYjKiZGL0YmRiQhIiJGJiwmRi9GNEYkRiZGNEY0LUYpNiMqKEYkRiZGMEYmRjVGNEYmRiZGNUY0RjQ=</Equation></Text-field>
</Output>
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<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="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">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="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">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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>
</Input>
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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>