Question

A(g) → 2B(g) + C(g) is a first order reaction. The initial pressure of the system was found to be 800 mm Hg which increased to 1600 mm Hg after 10 min. The total pressure of the system after 30 min will be ___mm Hg. (Nearest integer)

Answer 1

Correct Answer: 2200

1. Initial Condition: At \(t = 0\): \[ P_A = 800 \, \text{mm Hg}, \quad P_B = 0, \quad P_C = 0. \] 2. First-order Kinetics Relation: For a first-order reaction: \[ (P_A)_t = (P_A)_0 \left(\frac{1}{2}\right)^{t/t_{1/2}}. \] Here: \((P_A)_0 = 800 \, \text{mm Hg}\), At \(t = 10 \, \text{min}\), \((P_A)_t = 1600 \, \text{mm Hg}\). Half-life (\(t_{1/2}\)) of the reaction is \(10 \, \text{min}\). 3. Pressure after 30 minutes: At \(t = 30 \, \text{min}\): \[ t = 3 \cdot t_{1/2}. \] The pressure of \(P_A\) will be: \[ (P_A)_t = 800 \cdot \left(\frac{1}{2}\right)^3 = 800 \cdot \frac{1}{8} = 100 \, \text{mm Hg}. \] 4. Total Pressure Contribution: The pressure due to products \(2B + C\): For \(2B\): \(P_B = 2 \cdot (800 - 100) = 1400 \, \text{mm Hg}\), For \(C\): \(P_C = 800 - 100 = 700 \, \text{mm Hg}\). Total pressure: \[ P_{\text{total}} = (P_A) + (P_B) + (P_C). \] Substituting values: \[ P_{\text{total}} = 100 + 1400 + 700 = 2200 \, \text{mm Hg}. \] % Final Answer Final Answer: \( \boxed{2200} \, \text{mm Hg} \)