Question

The half life for a reaction between fixed concentration of reactants varies with temperature as follows:
$\begin{array}{ccccc}{T}^{o}C& 520& 533& 555& 574\\ t_{1/2}\left(sec\right)& 1288& 813& 562& 477\end{array}$
Calculate the activation energy of this reaction.

Answer 1

For a fixed concentration of reactants we have

$t_{1/2}\propto \frac{1}{k}$

$\Rightarrow t_{1/2}\propto \frac{1}{{Ae}^{{-E}_A/RT}}$ {Using Arrhenius Equation}

$\Rightarrow t_{1/2}\propto e^{E_A/RT}$

For two different data we can write

$\Rightarrow \frac{{\left(t_{1/2}\right)}_1}{{\left(t_{1/2}\right)}_2}=e^{\frac{E_A}{R}[\frac{1}{T_1}-\frac{1}{T_2}]}$

Puuting two data from the question, we get

$\Rightarrow \frac{1288}{813}=e^{\frac{E_A}{8.314}[\frac{1}{520}-\frac{1}{533}]}$

$\Rightarrow \frac{E_A}{8.314}[\frac{1}{520}-\frac{1}{533}]=0.4599$

${\Rightarrow E}_A=81.519KJ/mol$