Question

Consider the following first-order gas phase reaction at constant temperature $\text{A(g)} \rightarrow 2\text{B(g)} + \text{C(g)}$ If the total pressure of the gases is found to be 200 torr after 23 sec. and 300 torr upon the complete decomposition of $\text{A}$ after a very long time, then the rate constant of the given reaction is $\dots \dots \times 10^{-2} \, \text{s}^{-1}$ (nearest integer). $\text{[Given: } \log_{10}(2) = 0.301 \text{]}$

Answer 1

The reaction is: $\text{A(g)} \rightarrow 2\text{B(g)} + \text{C(g)}$
Given:
$P_{23} = P_0 + 2x = 200 \\\ P_\infty = 3P_0 = 300 \\\ P_0 = 100$
The rate constant $K$ is calculated using:
$K = \frac{1}{t} \ln \frac{P_\infty - P_0}{P_\infty - P_t}$
Substituting the values:
$K = \frac{2.3}{23} \log \frac{300 - 100}{300 - 200}$ $K = \frac{2.3 \times 0.301}{23} = 0.0301 = 3.01 \times 10^{-2} \, \text{s}^{-1}$
The correct answer is (3).

Answer 2

The reaction is: $\text{A(g)} \rightarrow 2\text{B(g)} + \text{C(g)}$
Given:
$P_{23} = P_0 + 2x = 200 \\\ P_\infty = 3P_0 = 300 \\\ P_0 = 100$
The rate constant $K$ is calculated using:
$K = \frac{1}{t} \ln \frac{P_\infty - P_0}{P_\infty - P_t}$
Substituting the values:
$K = \frac{2.3}{23} \log \frac{300 - 100}{300 - 200}$ $K = \frac{2.3 \times 0.301}{23} = 0.0301 = 3.01 \times 10^{-2} \, \text{s}^{-1}$
The correct answer is (3).