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title: "A student studies the kinetics of two gaseous decomposition reactions carried out in separate rigid containers at constant temperature:  Reaction 1: \\(\\text{A(g)} \\xrightarrow{\\text{catalyst}} 2\\,\\text{C(g)}\\), which follows zero-order kinetics with rate constant \\(k_1\\).  Reaction 2: \\(\\text{B(g)} \\rightarrow \\text{D(g)} + \\text{E(g)}\\), which follows first-order kinetics with rate constant \\(k_2\\).  In an initial experiment with \\([\\text{A}]_0 = 0.10 \\text{ M}\\) and \\([\\text{B}]_0 = 0.10 \\text{ M}\\), the half-life of Reaction 1 and the half-life of Reaction 2 are both measured to be \\(60 \\text{ s}\\). If the experiment is repeated at the same temperature with \\([\\text{A}]_0 = 0.20 \\text{ M}\\) and \\([\\text{B}]_0 = 0.20 \\text{ M}\\), what is the value of the ratio \\(\\dfrac{t_{1/2}\\text{ of Reaction 1}}{t_{1/2}\\text{ of Reaction 2}}\\) in the second experiment?"
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url: "https://nerd-notes.com/ubq/123692/"
date_modified: "2026-09-28T12:02:00+00:00"
---

# A student studies the kinetics of two gaseous decomposition reactions carried out in separate rigid containers at constant temperature:

Reaction 1: \(\text{A(g)} \xrightarrow{\text{catalyst}} 2\,\text{C(g)}\), which follows zero-order kinetics with rate constant \(k_1\).

Reaction 2: \(\text{B(g)} \rightarrow \text{D(g)} + \text{E(g)}\), which follows first-order kinetics with rate constant \(k_2\).

In an initial experiment with \([\text{A}]_0 = 0.10 \text{ M}\) and \([\text{B}]_0 = 0.10 \text{ M}\), the half-life of Reaction 1 and the half-life of Reaction 2 are both measured to be \(60 \text{ s}\). If the experiment is repeated at the same temperature with \([\text{A}]_0 = 0.20 \text{ M}\) and \([\text{B}]_0 = 0.20 \text{ M}\), what is the value of the ratio \(\dfrac{t_{1/2}\text{ of Reaction 1}}{t_{1/2}\text{ of Reaction 2}}\) in the second experiment?

A student studies the kinetics of two gaseous decomposition reactions carried out in separate rigid containers at constant temperature:

Reaction 1: \(\text{A(g)} \xrightarrow{\text{catalyst}} 2\,\text{C(g)}\), which follows zero-order kinetics with rate constant \(k_1\).

Reaction 2: \(\text{B(g)} \rightarrow \text{D(g)} + \text{E(g)}\), which follows first-order kinetics with rate constant \(k_2\).

In an initial experiment with \([\text{A}]_0 = 0.10 \text{ M}\) and \([\text{B}]_0 = 0.10 \text{ M}\), the half-life of Reaction 1 and the half-life of Reaction 2 are both measured to be \(60 \text{ s}\). If the experiment is repeated at the same temperature with \([\text{A}]_0 = 0.20 \text{ M}\) and \([\text{B}]_0 = 0.20 \text{ M}\), what is the value of the ratio \(\dfrac{t_{1/2}\text{ of Reaction 1}}{t_{1/2}\text{ of Reaction 2}}\) in the second experiment?

- **A.** \(0.25\)
- **B.** \(0.50\)
- **C.** \(1.0\)
- **D.** \(2.0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123692/*