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

Correct Answer: 3

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).