2017 H2 Chem P1 Q11 — Kinetics Solution

The answer is A (1, 2 and 3).
\(\text{X}_2(\text{g}) \rightarrow 2\text{X}(\text{g})\), starting with 1 mol of \(\text{X}_2\) at pressure \(p\).
• Statement 1 is true: when 75% of \(\text{X}_2\) has reacted, 25% remains. For a first-order reaction, 100% \(\rightarrow\) 50% \(\rightarrow\) 25% takes 2 half-lives, \(2 \times 30 = 60\) minutes.
• Statement 2 is true: \(n(\text{X}_2 \text{ reacted}) = 0.75 \times 1 = 0.75\) mol, so \(n(\text{X formed}) = 2 \times 0.75 = 1.5\) mol.
• Statement 3 is true: total amount of gas \(= n(\text{X}_2) + n(\text{X}) = 0.25 + 1.5 = 1.75\) mol. At constant volume and temperature, \(\dfrac{p_1}{n_1} = \dfrac{p_2}{n_2}\), so \(p_2 = \dfrac{p}{1} \times 1.75 = \dfrac{7p}{4}\).
• B is wrong: it leaves out the true statement 3.
• C is wrong: it leaves out the true statements 2 and 3.
• D is wrong: it leaves out the true statement 1.