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4-Participant

Need help. Mathcad prime 7.0 : Parameter Estimation in Chemical Kinetics.

Help to sort out the problems. I have been using the program recently; I need to solve the estimation of parameters in chemical kinetics. Help to understand what the error is and how to solve it.

K4L3KT0R
1 ACCEPTED SOLUTION

Accepted Solutions
23-Emerald I
(To:K4L3KT0R)

To start:

Your first of 14 expressions regarding C0(t) is simple. C0(t)=C_0*e^(-k0*t), where C_0 is a constant that can be found with the initial condition C0(0)=0.013, if t=0 then C0(t)=C_0*e^0 = C_0, so C_0 = 0.013. Thus:

C0(t)=0.013*e^(-k0*t)

Your third expression says that C2'(t)=k0*C0(t) = k0*0.013*e^(-k0*t). So you can find C2(t) by integrating k0*0.013*e^(-k0*t), and the integration constant is found through the initial condition C2(0)=0.

Problems start to occur with your initial condition for C6(t). You state that C6(0)=C6e0, which is found from the data array. Now that makes C6(0) an array, where it can/should have only a single value. Besides it has a unit (mol/l) whereas none of the other initial conditions have a unit. That again may not be a problem, as long as they are 0, but the non-zero initial conditions might get you into unbalanced units.

Going further, I see that C9 and C10 are exactly equal. They're both defined with the same rhs, and their initial conditions are both 0. This will not help to solve the set of functions.

So: make sure your units are balanced, sort out the initial condition for C6(t), such that it is a single value. You may want to make it a parameter. And check your equations.

Success!
Luc

4 REPLIES 4
23-Emerald I
(To:K4L3KT0R)

What error are you concerned with?

Success!
Luc

4-Participant
(To:LucMeekes)

This

K4L3KT0R
4-Participant
(To:LucMeekes)

And do you see any other errors?If yes, please tell me which ones, I will be very grateful!

K4L3KT0R
23-Emerald I
(To:K4L3KT0R)

To start:

Your first of 14 expressions regarding C0(t) is simple. C0(t)=C_0*e^(-k0*t), where C_0 is a constant that can be found with the initial condition C0(0)=0.013, if t=0 then C0(t)=C_0*e^0 = C_0, so C_0 = 0.013. Thus:

C0(t)=0.013*e^(-k0*t)

Your third expression says that C2'(t)=k0*C0(t) = k0*0.013*e^(-k0*t). So you can find C2(t) by integrating k0*0.013*e^(-k0*t), and the integration constant is found through the initial condition C2(0)=0.

Problems start to occur with your initial condition for C6(t). You state that C6(0)=C6e0, which is found from the data array. Now that makes C6(0) an array, where it can/should have only a single value. Besides it has a unit (mol/l) whereas none of the other initial conditions have a unit. That again may not be a problem, as long as they are 0, but the non-zero initial conditions might get you into unbalanced units.

Going further, I see that C9 and C10 are exactly equal. They're both defined with the same rhs, and their initial conditions are both 0. This will not help to solve the set of functions.

So: make sure your units are balanced, sort out the initial condition for C6(t), such that it is a single value. You may want to make it a parameter. And check your equations.

Success!
Luc

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