Question

The rate constant for a certain reaction is measured at two different temperatures:

Answer 1

Answer: The activation energy Ea for this reaction is 22689.8 J/mol

Explanation:

According to Arrhenius equation with change in temperature, the formula is as follows.

$ln \frac{k_{2}}{k_{1}} = \frac{-E_{a}}{R}[\frac{1}{T_{2}} - \frac{1}{T_{1}}]$

$k_1$ = rate constant at temperature $T_1$ = $2.3\times 10^8$

$k_2$ = rate constant at temperature $T_2$ = $4.8\times 10^8$

$E_a$= activation energy = ?

R= gas constant = 8.314 J/kmol

$T_1$ = temperature = $280.0^0C=(273+280)=553K$

$T_2$ = temperature = $376.0^0C=(273+376)=649K$

Putting in the values ::

$ln \frac{4.8\times 10^8}{2.3\times 10^8} = \frac{-E_{a}}{8.314}[\frac{1}{649} - \frac{1}{553}]$

$E_a=22689.8J/mol$

The activation energy Ea for this reaction is 22689.8 J/mol