Question

Chlorine atoms react with methane, forming HCl and CH3. The rate constant for the reaction was determined to be 3.600×107 at 278 K and 3.050×108 at 317 K. Calculate the activation energy for the reaction. (in kJ mol^-1)

Answer 1

Answer: The activation energy for the reaction is 40.143 kJ/mol

Explanation:

To calculate activation energy of the reaction, we use Arrhenius equation for two different temperatures, which is:

$\ln(\frac{K_{317K}}{K_{278K}})=\frac{E_a}{R}[\frac{1}{T_1}-\frac{1}{T_2}]$

where,

$K_{317K}$ = equilibrium constant at 317 K = $3.050\times 10^{8}M^{-1}s^{-1}$

$K_{278K}$ = equilibrium constant at 278 K = $3.600\times 10^{7}M^{-1}s^{-1}$

$E_a$ = Activation energy = ?

R = Gas constant = 8.314 J/mol K

$T_1$ = initial temperature = 278 K

$T_2$ = final temperature = 317 K

Putting values in above equation, we get:

$\ln(\frac{3.050\times 10^8}{3.600\times 10^{7}})=\frac{E_a}{8.314J/mol.K}[\frac{1}{278}-\frac{1}{317}]\\\\E_a=40143.3J/mol=40.143kJ/mol$

Hence, the activation energy for the reaction is 40.143 kJ/mol