Question

The activation energy of a reaction is zero. Its rate constant at $280K$ is $1.6\times 10^{-6}{s}^{-1}$ the rate constant at $300K$ is

• A. $3.2\times 10^{-6}{s}^{-1}$
• B. zero
• C. $1.6\times 10^{-6}{s}^{-1}$
• D. $1.6\times 10^{-5}{s}^{-1}$

Answer 1

Answer: (C)

Key Idea Arrhenius equation is given as:

$\log \frac{k_2}{k_1}=\frac{E_a}{2.303R}\left[\frac{1}{T_1}-\frac{1}{T_2}\right]$

Given,

Activation energy of a reaction, $E_A=0$

Rate constant, $k_1=1.6\times 10^{-6}{s}^{-1}$

Temperature, $T_1=280K,T_2=300K$

According to Arrhenius equation

$log\frac{k_2}{1.6\times 10^{-6}}=\frac{0}{2.303R}\left[\frac{1}{280}-\frac{1}{300}\right]$

$log\frac{k_2}{1.6\times 10^{-6}}=0$

$\frac{k_2}{1.6\times 10^{-6}}=$ antilog 0

$\frac{k_2}{1.6\times 10^{-6}}=1$

$\therefore k_2=1.6\times 10^{-6}{s}^{-1}$