JEE PYQ: Chemical Kinetics Question 1
Question 1 - 2021 (16 Mar Shift 1)
The decomposition of formic acid on gold surface follows first order kinetics. If the rate constant at 300 K is $1.0 \times 10^{-3},\text{s}^{-1}$ and the activation energy $E_a = 11.488,\text{kJ mol}^{-1}$, the rate constant at 200 K is ____ $\times 10^{-5},\text{s}^{-1}$. (Round off to the Nearest Integer).
(Given: $R = 8.314,\text{J mol}^{-1}\text{K}^{-1}$)
Show Answer
Answer: 10
Solution
$K_{300} = 10^{-3}$, $K_{200} = ?$. Using Arrhenius equation: $\ln\left(\frac{K_{300}}{K_{200}}\right) = \frac{E_a}{R}\left(\frac{1}{200} - \frac{1}{300}\right)$. $\ln\left(\frac{K_{300}}{K_{200}}\right) = \frac{11.488 \times 1000 \times 100}{8.314 \times 200 \times 300} = 2.303 = \ln 10$. So $\frac{K_{300}}{K_{200}} = 10$. $K_{200} = \frac{1}{10} \times K_{300} = 10^{-4} = 10 \times 10^{-5},\text{s}^{-1}$.
BETA
