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HW07solutionsF11

# Fall 2011 p 37 code up the differential equations

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Unformatted text preview: minutes, so we could recover 30% yield of each if desired. Fall 2011 p. 3/7 Code up the differential equations for reaction extents in Matlab: function dx=deriv2(t,x) global ratek A0; dx1=ratek(1)*(A0-x(1)-x(2)); dx2=ratek(2)*(A0-x(1)-x(2)); dx3=ratek(3)*(x(1)-x(3)); dx=[dx1;dx2;dx3]; end Now use an m ­file to integrate them and calculate the species concentrations from the reaction extents: global ratek A0 ratek=[.00201,.000501,.000134]; % rates in s^-1 A0=0.16; % use mM to avoid small values and numerical sensitivity issues trange=[0,60*40]; % interval calculated in s out to 40 min = 240 s x0=[0,0,0]; % all reaction extents start at 0.0 [t,xlist]=ode23(@deriv2,trange,x0); tmin=t/60; % choose to label plot axis in minutes x1=xlist(:,1); x2=xlist(:,2); x3=xlist(:,3); Asoln=A0-x1-x2; Bsoln=x1-x3; Csoln=x1+x2; Fall 2011 p. 4/7 Dsoln=x2+x3; plot(tmin,Asoln,'--',tmin,Bsoln,'-',tmin,Csoln,':', tmin,Dsoln, '.-') title('Salicylate esters') xlabel('time (min)') ylabel('concentration (mM)') legend('phenyl salicylate (feed)','...
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