Adv P Chem Final - Maggie Purvis
Rate Constants
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k1f=249918.96;k1r=4044.1996;k2f=43301953;k2r=7767323.4;k3f=0.134715;k3r=0.1899605;k4=kp*7.34928*10^-14;k5=kp*7.34928*10^-14;k6=kp*1.41293*10^-20;
Reaction Rate Equations
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c1f=k1f*Am[t];c1r=k1r*B1[t];c2f=k2f*B1[t];c2r=k2r*B2[t];c3f=k3f*Am[t];c3r=k3r*B3[t];p1f=kp*A[t]*KCO3[t];p1r=kp*Am[t]*KHCO3[t];{p2f,p3f,p4f}=kp*{B1[t],B2[t],B3[t]}*KHCO3[t];{p2r,p3r,p4r}={k4*Z5[t],k5*E5[t],k6*E6[t]}*KCO3[t];
Test Case 1 - Protonation/Deprotonation of A
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eqs1={KHCO3'[t]==p1f-p1r,KCO3'[t]==-p1f+p1r,A'[t]==-p1f+p1r,Am'[t]==p1f-p1r,B1KHCO3[0]==0,KCO3[0]==0.5,A[0]==0.5,Am[0]==0};
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vars1={KHCO3[t],KCO3[t],A[t],Am[t]};
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s1=NDSolve[eqs1/.kp10^11,vars1,{t,0,1}];
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Plot[Evaluate[A[t]/.s1],{t,0,.0000000002},PlotRange{0,0.5}]
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Test Case 2 - Include B1 and Z5
Test Case 2 - Include B1 and Z5
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eqs2={KHCO3'[t]==p1f-p1r-p2f+p2r,KCO3'[t]==-p1f+p1r+p2f-p2r,A'[t]==-p1f+p1r,Am'[t]==p1f-p1r-c1f+c1r,B1'[t]==-p2f+p2r+c1f-c1r,Z5'[t]==p2f-p2r,KHCO3[0]==0,KCO3[0]==0.5,A[0]==0.5,Am[0]==0,B1[0]==0,Z5[0]==0};
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vars2={KHCO3[t],KCO3[t],A[t],Am[t],B1[t],Z5[t]};
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s2=NDSolve[eqs2/.kp10^11,vars2,{t,0,1}];
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Plot[Evaluate[Z5[t]/.s2],{t,0,0.0001},PlotRange{0,0.5}]
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Test Case 3 - Include E5 and B2
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eqs3={KHCO3'[t]==p1f-p1r-p2f+p2r-p3f+p3r,KCO3'[t]==-p1f+p1r+p2f-p2r+p3f-p3r,A'[t]==-p1f+p1r,Am'[t]==p1f-p1r-c1f+c1r,B1'[t]==-p2f+p2r+c1f-c1r-c2f+c2r,Z5'[t]==p2f-p2r,E5'[t]==p3f-p3r,B2'[t]==-p3f+p3r+c2f-c2r,KHCO3[0]==0,KCO3[0]==0.5,A[0]==0.5,Am[0]==0,B1[0]==0,Z5[0]==0,E5[0]==0,B2[0]==0};
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vars3={KHCO3[t],KCO3[t],A[t],Am[t],B1[t],Z5[t],B2[t],E5[t]};
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s3=NDSolve[eqs3/.kp10^11,vars3,{t,0,1}];
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Plot[Evaluate[Z5[t]/.s3],{t,0,0.0001},PlotRange{0,0.5}]
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Final - Plot Z5 as a Function of Time for 2 Cases: kp=10^11 and kp=10^8
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eqs={KHCO3'[t]==(-p1f+p2f+p3f+p4f)-(-p1r+p2r+p3r+p4r),KCO3'[t]==-(-p1f+p2f+p3f+p4f)+(-p1r+p2r+p3r+p4r),A'[t]==-p1f+p1r,Am'[t]==p1f-p1r-c1f+c1r-c3f+c3r,B1'[t]==-p2f+p2r+c1f-c1r-c2f+c2r,B2'[t]==-p3f+p3r+c2f-c2r,B3'[t]==-p4f+p4r+c3f-c3r,Z5'[t]==p2f-p2r,E5'[t]==p3f-p3r,E6'[t]==p4f-p4r,KHCO3[0]==0,KCO3[0]==0.5,A[0]==0.5,Am[0]==0,B1[0]==0,B2[0]==0,B3[0]==0,Z5[0]==0,E5[0]==0,E6[0]==0};
Trial 2 - kp = .001*10^11 = 10^8