Question

The time required for 5% completion of a reaction at 300 K is equal to that required for its 20% completion at 320 K. If the pre -exponential factor for the reaction is $3.56\times {10}^9$ $se{c}^{-1}$. Then which of the following is correct.(given log95 = 1.98, log80 = 1.90, log5 =0.7, R=$\frac{25}{3}J{K}^{-1}mo{l}^{-1}$)

• A. The reaction follows first order kinetics
• B. The activation energy of the reaction is 64.48 kJ/mol
• C. The activation energy for the reaction is 7.19 kJ/mol
• D. The reaction follows second order kinetics

Answer 1

Answer: (A), (B)

The activation energy of the reaction is 64.48 kJ/mol

a) Since unit of pre exponential factor is $se{c}^{-1}$, so it is a first order reaction.
b)We know that,
$k=\frac{2.303}{t}$$log\frac{a}{a-x}$
So at 300 K ,
$k_{300}=\frac{2.303}{t}$$log\frac{100}{95}$----(1)
At 320 K ,
$k_{320}=\frac{2.303}{t}$$log\frac{100}{80}$------(2)
Dividing equation (2) by (1),
$\frac{k_{320}}{k_{300}}$=5
From Arrhenius equation,
$log5=\frac{E_a\times 3}{2.303\times 25}$($\frac{1}{300}-\frac{1}{320}$)
$⟹$$0.7=\frac{E_a\times 3}{276360}$
$⟹$$E_a$= 64484J/mol = 64.48 kJ/mol