(This question comes from a Chemical Engineering background, I hope it still falls in the scope of engineering.stackexchange.com If not, please move.)

I am trying to calculate and plot fractional yield as a function of temperature for a parallel reaction of first-order reactions forming 3 products R, S and P from reactant A.

enter image description here

I know the highest possible reaction temperature is 500k. S is the desirable product and I am trying to find the reaction temperature to maximize its production and calculate reactor outlet concentration of S for XA = 100%. Thus far, I have tried to construct the respective rate equations and thus corresponding Arrhenius equations (which I have data for), what I'm not sure is if I am plotting this equation against temperature, is this a valid solution to evaluate the fractional yield?

Here is my MATLAB code and corresponding graph:

CA0 = 100; % Initial concentration of A (mol/m^3)

V_reactor = 1; % Reactor volume (for example, 1 m^3)

T_range = linspace(0, 1000, 10); % Temperature range from 0 K to 500 K

YieldS = zeros(size(T_range));

for i = 1:length(T_range)
    T = T_range(i); % Temperature at this iteration
    R = 8.314; % Universal gas constant (J/(mol*K))

k1 = 5*10^8 * exp(-65000 / (R * T)); % Adjust activation energy (kJ/mol) as needed
k2 = 10^9 * exp(-50000 / (R * T)); % Adjust activation energy (kJ/mol) as needed
k3 = 10^7 * exp(-45000 / (R * T)); % Adjust activation energy (kJ/mol) as needed

dC = @(V, C) [-k1 * C(1) - k2 * C(1) - k3 * C(1); % dCA/dV
               k1 * C(1); % dCR/dV
               k2 * C(1); % dCS/dV
               k3 * C(1)]; % dCP/dV

% Initial conditions (at V = 0)
C0 = [CA0; 0; 0; 0]; % Initial concentrations of A, R, S, and P

[V, C] = ode45(dC, [0, V_reactor], C0);

CA_outlet = C(end, 1);
CS_outlet = C(end, 3);

YieldS(i) = (CS_outlet / CA0) * 100;

enter image description here

  • $\begingroup$ Does a Chemistry Stack exist? $\endgroup$
    – Solar Mike
    Commented Oct 8, 2023 at 14:18

1 Answer 1


The Method used is Correct Approach ,till finding the Arrhenius Rate Equation and plotting the Graph. But rather than using this method, we can calculate the Fractional Yield, using the conversion factor or using the Concentrations of Reactant and Desired Product.


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