How to solve Arrhenius equation: k=Ae^-E/(RTa)

The temperature dependence of chemical reactions can be computed with the Arrhenius equation: k=Ae^-E/(RTa)^^

Where k=reaction rate (s−1), A=the pre exponential (or frequency) factor, E=activation energy (J/mol),

R=gas constant [8.314 J/(mole · K)], and Ta = absolute temperature (K). A compound has E=1 ×105 J/mol

and A=7 ×1016.

A. Create three MATLAB FUNCTION file to calculate the reaction rate.

B. Use MATLAB script file to generate a vector of Ta for temperatures ranging from 253 to 325 K.

C. Generate MATLAB plot of the reaction rate (k) versus Ta. Also include axis labels and titles for

the plot.

D. Calculate the reaction rate at Ta = 295 K and write the result here.

Answer 1

[Rahul]

Below given MATLAB script can solve the required Arrheieius equation. If different values are required, then those values can be replaced with those of variables, T_min,T_max, A,E,R.

% B

T_min = 253;
T_max = 325;

Ta_vec = linspace(T_min, T_max, 1000);

% C

A = 7e16; 
E = 1e5;
R = 8.314; 

k_vec = zeros(1, length(Ta_vec));
for i = 1:length(Ta_vec)
    
    Ta = Ta_vec(i);
    k_vec(i) = calculate_k(A, E, R, Ta);
end

plot(Ta_vec, k_vec);
title('Reaction Rate vs. Temperature');
xlabel('Temperature (K)');
ylabel('Reaction Rate (s^{-1})');

% D

A = 7e16; 
E = 1e5; 
R = 8.314; 

Ta = 295;
k = calculate_k(A, E, R, Ta);

fprintf('Reaction rate at Ta = %d K: %e s^-1\n', Ta, k);

% A
function k = calculate_k(A, E, R, Ta)

k = A * exp(-E / (R * Ta));

end