Reaction A(g) - 2B(g) + C(g) is a first order reaction. It was started with pure A. | t/min | Pressure of system at…

Step 1: Set up pressure relationships

$\ce{A(g) -> 2B(g) + C(g)}$

At $t=0$: $P_0$, 0, 0 → Total = $P_0$

At $t=\infty$: 0, $2P_0$, $P_0$ → Total = $3P_0$

Given: $P_\infty = 240$ mm Hg → $P_0 = 80$ mm Hg ✓ (option a is correct)

Step 2: Find $P_A$ at t = 10 min

At time $t$: $P_A = P_0 - x$, $P_B = 2x$, $P_C = x$

Total $= P_0 - x + 2x + x = P_0 + 2x$

At $t = 10$: $80 + 2x = 160 \Rightarrow x = 40$

$P_A = 80 - 40 = 40$ mm Hg ✓ (option d is correct)

Step 3: Calculate rate constant

For first order: $k = \tfrac{1}{t}\ln\tfrac{P_0}{P_A}$

$k = \frac{1}{10}\ln\frac{80}{40} = \frac{\ln 2}{10} = \frac{0.693}{10} = 0.0693\ \text{min}^{-1}$

Option (c) states $k = 1.693\ \text{min}^{-1}$ — this is INCORRECT ✗

Step 4: Check option (b)

First order reactions theoretically never reach 100% completion (exponential decay). ✓ Correct.

Answer: (c) — the rate constant $1.693\ \text{min}^{-1}$ is wrong; correct value is $0.0693\ \text{min}^{-1}$