Arrhenius type fit without taking the log(y) and inverse of x

Hi all, I have a group of data.

x= 0 7.2 12 16.7 19.4 20.8 21.5

y= 0.02526 0.02604 0.02678 0.02752 0.02822 0.02913 0.02963

And I want to fit the data using a arrhenius type fit with x as the x axis instead of log(x), please tell me how to solve this, thank you.

[Manikanta Aditya]

Try out this:

% Define the Arrhenius function
arrhenius = @(A, Ea, R, x) A .* exp(-Ea ./ (R .* x));

% Data
x = [0, 7.2, 12, 16.7, 19.4, 20.8, 21.5];
y = [0.02526, 0.02604, 0.02678, 0.02752, 0.02822, 0.02913, 0.02963];

% Gas constant in J/(mol*K)
R = 8.314;

% Initial guess for A and Ea
A0 = 1;
Ea0 = 1;

% Fit the data
f = fit(x', y', fittype(@(A, Ea, x) arrhenius(A, Ea, R, x)), 'StartPoint', [A0, Ea0]);

% Print the optimal parameters
fprintf('A = %.5f, Ea = %.5f\n', f.A, f.Ea);

A = 0.03044, Ea = 10.31241

[John D'Errico]

@Manikanta Aditya - your choice of course, but your comment surely should have been an answer, since it solves the question directly as asked. Then you would get credit for the answer. It could then get the upvotes it deserves.

[Manikanta Aditya]

@John D'Errico, Sure will post as answer, Thanks.

[Torsten]

@Lifu

Note that your x-values have to be specified in [K], not in [degC] !!!

[Lifu]

Thank you!

Answer 1

[Manikanta Aditya]

Hi,

Check this to get answer to your query:

% Define the Arrhenius function
arrhenius = @(A, Ea, R, x) A .* exp(-Ea ./ (R .* x));
% Data
x = [0, 7.2, 12, 16.7, 19.4, 20.8, 21.5];
y = [0.02526, 0.02604, 0.02678, 0.02752, 0.02822, 0.02913, 0.02963];
% Gas constant in J/(mol*K)
R = 8.314;
% Initial guess for A and Ea
A0 = 1;
Ea0 = 1;
% Fit the data
f = fit(x', y', fittype(@(A, Ea, x) arrhenius(A, Ea, R, x)), 'StartPoint', [A0, Ea0]);
% Print the optimal parameters
fprintf('A = %.5f, Ea = %.5f\n', f.A, f.Ea);

A = 0.03044, Ea = 10.31241

Thank you.

[Lifu]

Thank you!

[Lifu]

Is it possible to draw the curve using Matlab?

[Torsten]

% Define the Arrhenius function
arrhenius = @(A, Ea, R, x) A .* exp(-Ea ./ (R .* x));
% Data
x = [0, 7.2, 12, 16.7, 19.4, 20.8, 21.5];
x = x + 273.15;
y = [0.02526, 0.02604, 0.02678, 0.02752, 0.02822, 0.02913, 0.02963];
% Gas constant in J/(mol*K)
R = 8.314;
%Compute initial guesses for A and Ea solving log(y) = log(A) - Ea/R * 1/x
xt = 1./x;
yt = log(y);
A = [ones(numel(x),1),xt.'];
b = yt.';
sol = A\b;
% Set initial guess for A and Ea
A0 = exp(sol(1))

A0 = 0.1965

Ea0 = -R*sol(2)

Ea0 = 4.6930e+03

% Fit the data
f = fit(x', y', fittype(@(A, Ea, x) arrhenius(A, Ea, R, x)), 'StartPoint', [A0, Ea0]);
% Print the optimal parameters
fprintf('A = %.5f, Ea = %.5f\n', f.A, f.Ea);

A = 0.19735, Ea = 4702.95547

hold on
plot(x,y,'o')
plot(x,arrhenius(A0,Ea0,R,x),'g')
plot(x,arrhenius(f.A,f.Ea,R,x),'r')
hold off

[Lifu]

That works, thank you.

[Lifu]

I also wanted to fit the same data with Arrhenius function + a linear function, could you please show me how to do that? Also how do I check the R square for the fit? Thank you.

[Sam Chak]

Is R-square formula unavailable? Also, if you already learn how to fit using the Arrhenius function, what obstacles are you facing with the Arrhenius plus linear function?