# 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?

##### 1 Answer

The activation energy barrier is 57.1 kJ/mol.

#### Explanation:

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)|)))" "#

where

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.