Question

Ethyl chloride vapor decomposes by the first-order reaction C2H5Cl → C2H4 + HCl The activation energy is 249 kJ/mol and the frequency factor is 1.60 × 1014 s−1. Find the value of the specific rate constant at 896 K . Enter your answer numerically (to 4 decimal places) and in terms of the appropriate units for a first order reaction.

Answer 1

Answer : The value of rate constant is, $0.3607s^{-1}$

Explanation :

The Arrhenius equation is written as:

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

Taking logarithm on both the sides, we get:

$\ln k=-\frac{Ea}{RT}+\ln A$             ............(1)

where,

k = rate constant

Ea = activation energy  = 249 kJ/mol = 249000 kJ/mol

T = temperature  = 896 K

R = gas constant  = 8.314 J/K.mole

A = pre-exponential factor  or frequency factor = $1.60\times 10^{14}s^{-1}$

Now we have to calculate the value of rate constant by putting the given values in equation 1, we get:

$\ln k=-\frac{249000J/mol}{8.314J/K.mol\times 896K}+\ln (1.60\times 10^{14}s^{-1})$

$\ln k=-1.0198$

$k=0.3607s^{-1}$

Therefore, the value of rate constant is, $0.3607s^{-1}$