If a temperature increase from 19.0 C to 33.0 C triples the rate constant for a reaction, what is the value of the activation barrier for the reaction?
The activation energy barrier is 57.1 kJ/mol.
The Arrhenius equation gives the relation between temperature and reaction rates:
#color(blue)(|bar(ul(color(white)(a/a) k = Ae^(-E_"a"/(RT))color(white)(a/a)|)))" "#
If we take the logarithms of both sides, we get
#lnk = lnA - E_"a"/(RT)#
Finally, if we have the rates at two different temperatures, we can derive the expression
#color(blue)(|bar(ul(color(white)(a/a) ln(k_2/k_1) = E_"a"/R(1/T_1 -1/T_2)color(white)(a/a)|)))" "#
In your problem,
Now, let's insert the numbers.