---
title: "A reaction coordinate diagram for two competing pathways of a reactant \\(\\text{R}\\) forming products \\(\\text{P}_1\\) and \\(\\text{P}_2\\) is shown below.  Three identical sealed containers each initially receive \\(0.10 \\text{ mol}\\) of \\(\\text{R}\\) and are allowed to react for \\(15 \\text{ min}\\). Sample 1 is maintained at \\(220 \\text{ K}\\), Sample 2 is maintained at \\(350 \\text{ K}\\), and Sample 3 is maintained at \\(550 \\text{ K}\\).  Which of the following correctly ranks the samples from least to greatest in terms of the mole fraction of \\(\\text{P}_2\\) present after \\(15 \\text{ min}\\), and provides the correct justification?"
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url: "https://nerd-notes.com/ubq/123948/"
date_modified: "2026-09-28T12:32:27+00:00"
---

# A reaction coordinate diagram for two competing pathways of a reactant \(\text{R}\) forming products \(\text{P}_1\) and \(\text{P}_2\) is shown below.

Three identical sealed containers each initially receive \(0.10 \text{ mol}\) of \(\text{R}\) and are allowed to react for \(15 \text{ min}\). Sample 1 is maintained at \(220 \text{ K}\), Sample 2 is maintained at \(350 \text{ K}\), and Sample 3 is maintained at \(550 \text{ K}\).

Which of the following correctly ranks the samples from least to greatest in terms of the mole fraction of \(\text{P}_2\) present after \(15 \text{ min}\), and provides the correct justification?

A reaction coordinate diagram for two competing pathways of a reactant \(\text{R}\) forming products \(\text{P}_1\) and \(\text{P}_2\) is shown below.

Three identical sealed containers each initially receive \(0.10 \text{ mol}\) of \(\text{R}\) and are allowed to react for \(15 \text{ min}\). Sample 1 is maintained at \(220 \text{ K}\), Sample 2 is maintained at \(350 \text{ K}\), and Sample 3 is maintained at \(550 \text{ K}\).

Which of the following correctly ranks the samples from least to greatest in terms of the mole fraction of \(\text{P}_2\) present after \(15 \text{ min}\), and provides the correct justification?

![A reaction energy profile graph plotted on Cartesian axes with a vertical axis labeled Potential Energy and a horizontal axis labeled Reaction Coordinate without gridlines. A horizontal line segment at the left represents reactant \(\text{R}\). From \(\text{R}\), two distinct reaction pathways branch. Pathway 1, drawn as a solid curve, rises to a lower activation energy peak labeled \(\text{TS}_1\) and descends to a product plateau labeled \(\text{P}_1\), which lies below \(\text{R}\). Pathway 2, drawn as a dashed curve, rises to a higher activation energy peak labeled \(\text{TS}_2\) and descends to a product plateau labeled \(\text{P}_2\), which lies significantly lower in energy than \(\text{P}_1\). A double-headed arrow indicates that the activation energy barrier to \(\text{TS}_1\) is smaller than the activation energy barrier to \(\text{TS}_2\). No other curves, gridlines, labels, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790598746-Y9Zh38.jpg)

- **A.** \(\text{Sample 1} < \text{Sample 3} < \text{Sample 2}\), because the rate of formation of \(\text{P}_2\) reaches a maximum at intermediate temperatures before thermal decomposition occurs at higher temperatures.
- **B.** \(\text{Sample 1} < \text{Sample 2} < \text{Sample 3}\), because higher temperatures provide a greater fraction of molecules with sufficient kinetic energy to overcome the larger activation barrier to form \(\text{P}_2\) and facilitate equilibration toward the more stable product.
- **C.** \(\text{Sample 3} < \text{Sample 2} < \text{Sample 1}\), because \(\text{P}_2\) is the kinetic product and is favored at low temperatures where reactant molecules have insufficient energy to reach \(\text{TS}_2\).
- **D.** \(\text{Sample 3} < \text{Sample 1} < \text{Sample 2}\), because the overall formation of \(\text{P}_2\) from \(\text{R}\) is exothermic, so increasing the temperature decreases the equilibrium yield of \(\text{P}_2\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123948/*