Question

5. The gas-phase decomposition of ethyl iodide to give ethylene and hydrogen iodide is a first-order reaction. C2H5I  C2H4 + HI At 600 K, the value of k is 1.60 × 10– 5 s– 1. When the temperature is raised to 700 K, the value of k increases to 6.36 × 10– 3 s– 1. What is the activation energy for this reaction?

Answer 1

Answer: The activation energy for the reaction is 209 kJ

Explanation:

According to the Arrhenius equation,

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

or,

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

where,

$K_1$ = rate constant at $600K$ = $1.60\time 10^{-5}s^{-1}$

$K_2$ = rate constant at $700K$ = $6.36\times 10^{-3}s^{-1}$

$E_a$ = activation energy for the reaction = ?

R = gas constant = 8.314 J/mole.K

$T_1$ = initial temperature = $600K$

$T_2$ = final temperature = $700K$

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

$\log (\frac{6.36\times 10^{-3}s^{-1}}{1.60\times 10^{-5}s^{-1}})=\frac{E_a}{2.303\times 8.314J/mole.K}[\frac{1}{600K}-\frac{1}{700K}]$

$2.60=\frac{E_a}{2.303\times 8.314J/mole.K}[\frac{1}{600K}-\frac{1}{700K}]$

$E_a=209087J/mole=209 kJ$

Therefore, the activation energy for the reaction is 209 kJ