Question

The rate constant of a reaction at temperature 200 K is 10 times less than the rate constant at 400 K. What is the activation energy $ E_a$ of the reaction? (R = Gas constant)

• A. 1842.4 R
• B. 921.2 R
• C. 460.6 R
• D. 230.3 R

Answer 1

Answer: (B)

Activation energy can be calculated with Arrhenius equation
log $ \frac{ k_2 }{ k_1 } = \frac{ E_a }{ 2.303 R } \bigg [ \frac{ T_2 = T_1 }{ T_1 T_2 } \bigg ] $
where, $ k_1$ = rate constant at $ T_1$ temperature
$k_2$ = rate constant at $ T_2 $ temperature
$E_a$ = activation energy
R = gas constant
$ T_1, \, T_2$ = temperatures in keivin
log $ \frac{ 10 }{ I } = \frac{ E_a }{ 2.303 R } \bigg [ \frac{ 400 - 200 }{ 400 \times 200 } \bigg ] $
i = $ \frac{ E_a }{ 2.303 R } \bigg [ \frac{ 200 }{ 400 \times 200 } \bigg ] $
$ E_a = 2.303 \times T \times 400 $
$ E_a = 921.2 \, R$