Question

The rate at which a certain Australian tree cricket chirps is 194/min at 28°C, but only 47.6/min at 5°C, From these data calculate the energy of activation for the chirping process. (Hint: the ratio of the rates is equal to the ratio of the rate constants.) Enter in units of kJ/mol.

Answer 1

Answer: The energy of activation for the chirping process is 283.911 kJ/mol

Explanation:

According to the Arrhenius equation,

$K=A\times e^{\frac{-Ea}{RT}}$

The expression used with catalyst and without catalyst is,

$\log (\frac{K_2}{K_1})=\frac{Ea}{2.303\times R}[\frac{1}{T_1}-\frac{1}{T_2}]$

where,

$K_2$ = rate of reaction at $28^0C$ = 194/min

$K_1$ = rate of reaction at  $5^0C$ = 47.6 /min

$Ea$ = activation energy

R = gas constant = 8.314 J/Kmol

tex]T_1[/tex] = initial temperature = $5^oC=273+5=278K$

tex]T_1[/tex] = final temperature = $28^oC=273+28=301K$

Now put all the given values in this formula, we get

$\frac{194}{47.6}=\frac{E_a}{2.303\times 8.314}[\frac{1}{278}-\frac{1}{301}]$

${E_a}=283911J/mol=283.911kJ/mol$

Thus the energy of activation for the chirping process is 283.911 kJ/mol