---
title: "A student investigates the gas-phase decomposition reaction represented below:  \\[ \\text{XY}(g) \\rightleftharpoons \\text{X}(g) + \\text{Y}(g) \\quad K_c = 4.0 \\times 10^{-5} \\]  The student performs two separate trials in rigid containers at the same temperature, each starting with pure \\(\\text{XY}(g)\\): – Trial 1: \\([\\text{XY}]_0 = 0.40 \\text{ M}\\) – Trial 2: \\([\\text{XY}]_0 = 1.0 \\times 10^{-4} \\text{ M}\\)  To calculate \\([\\text{X}]_{\\text{eq}}\\) without solving a quadratic equation, the student assumes that \\([\\text{XY}]_{\\text{eq}} \\approx [\\text{XY}]_0\\). Which of the following correctly evaluates the validity of this approximation for Trial 2 and the direction of error in the calculated value of \\([\\text{X}]_{\\text{eq}}\\)?"
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url: "https://nerd-notes.com/ubq/123801/"
date_modified: "2026-09-28T12:30:21+00:00"
---

# A student investigates the gas-phase decomposition reaction represented below:

\[ \text{XY}(g) \rightleftharpoons \text{X}(g) + \text{Y}(g) \quad K_c = 4.0 \times 10^{-5} \]

The student performs two separate trials in rigid containers at the same temperature, each starting with pure \(\text{XY}(g)\):
– Trial 1: \([\text{XY}]_0 = 0.40 \text{ M}\)
– Trial 2: \([\text{XY}]_0 = 1.0 \times 10^{-4} \text{ M}\)

To calculate \([\text{X}]_{\text{eq}}\) without solving a quadratic equation, the student assumes that \([\text{XY}]_{\text{eq}} \approx [\text{XY}]_0\). Which of the following correctly evaluates the validity of this approximation for Trial 2 and the direction of error in the calculated value of \([\text{X}]_{\text{eq}}\)?

A student investigates the gas-phase decomposition reaction represented below:

\[ \text{XY}(g) \rightleftharpoons \text{X}(g) + \text{Y}(g) \quad K_c = 4.0 \times 10^{-5} \]

The student performs two separate trials in rigid containers at the same temperature, each starting with pure \(\text{XY}(g)\):
- Trial 1: \([\text{XY}]_0 = 0.40 \text{ M}\)
- Trial 2: \([\text{XY}]_0 = 1.0 \times 10^{-4} \text{ M}\)

To calculate \([\text{X}]_{\text{eq}}\) without solving a quadratic equation, the student assumes that \([\text{XY}]_{\text{eq}} \approx [\text{XY}]_0\). Which of the following correctly evaluates the validity of this approximation for Trial 2 and the direction of error in the calculated value of \([\text{X}]_{\text{eq}}\)?

- **A.** The approximation is invalid because the ratio \(\dfrac{[\text{XY}]_0}{K_c}\) is too small, resulting in a calculated \([\text{X}]_{\text{eq}}\) that is greater than the actual \([\text{X}]_{\text{eq}}\).
- **B.** The approximation is invalid because the ratio \(\dfrac{[\text{XY}]_0}{K_c}\) is too small, resulting in a calculated \([\text{X}]_{\text{eq}}\) that is less than the actual \([\text{X}]_{\text{eq}}\).
- **C.** The approximation is valid because \(K_c \ll 1\), ensuring that a negligible fraction of \(\text{XY}(g)\) dissociates regardless of its initial concentration.
- **D.** The approximation is valid because lower initial reactant concentration decreases the percent dissociation of \(\text{XY}(g)\), keeping the amount of reactant consumed negligible.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123801/*