---
title: "A student investigates the rate of the gas-phase decomposition of a compound \\(\\text{X}\\) at \\(300\\text{ K}\\) in a rigid container:  \\[ \\text{X(g)} \\rightarrow \\text{Y(g)} + \\text{Z(g)} \\]  The student monitors the concentration of \\(\\text{X}\\) over time and generates the three plots shown below.  Based on the graphs, what is the order of the reaction with respect to \\(\\text{X}\\), and what is the total time required for \\([\\text{X}]\\) to decrease from an initial concentration of \\(0.40\\text{ M}\\) to \\(0.050\\text{ M}\\)?"
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url: "https://nerd-notes.com/ubq/121521/"
date_modified: "2026-08-23T05:05:01+00:00"
---

# A student investigates the rate of the gas-phase decomposition of a compound \(\text{X}\) at \(300\text{ K}\) in a rigid container:

\[ \text{X(g)} \rightarrow \text{Y(g)} + \text{Z(g)} \]

The student monitors the concentration of \(\text{X}\) over time and generates the three plots shown below.

Based on the graphs, what is the order of the reaction with respect to \(\text{X}\), and what is the total time required for \([\text{X}]\) to decrease from an initial concentration of \(0.40\text{ M}\) to \(0.050\text{ M}\)?

A student investigates the rate of the gas-phase decomposition of a compound \(\text{X}\) at \(300\text{ K}\) in a rigid container:

\[ \text{X(g)} \rightarrow \text{Y(g)} + \text{Z(g)} \]

The student monitors the concentration of \(\text{X}\) over time and generates the three plots shown below.

Based on the graphs, what is the order of the reaction with respect to \(\text{X}\), and what is the total time required for \([\text{X}]\) to decrease from an initial concentration of \(0.40\text{ M}\) to \(0.050\text{ M}\)?

![A grayscale figure showing three side-by-side coordinate plots labeled Plot 1, Plot 2, and Plot 3 from left to right. Each plot has bare black axes with tick marks. Plot 1 has a vertical axis labeled [X] (M) with values 0.00, 0.10, 0.20, 0.30, 0.40, and a horizontal axis labeled Time (s) with values 0, 30, 60. A solid black curve begins at (0, 0.40), passes through (30, 0.20) and (60, 0.10), decaying smoothly toward the horizontal axis. Plot 2 has a vertical axis labeled ln[X] with values -2.5, -2.0, -1.5, -1.0, -0.5, and a horizontal axis labeled Time (s) from 0 to 60. A solid black line is strictly linear with a constant negative slope starting at (0, -0.92) and ending at (60, -2.30). Plot 3 has a vertical axis labeled 1/[X] (M^-1) from 0 to 12, and a horizontal axis labeled Time (s) from 0 to 60. A solid black curve begins at (0, 2.5) and curves upward with an increasing slope to (60, 10.0). No other particles, labels, text, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787461500-kf68Fi.jpg)

- **A.** First order, and \(90\text{ s}\)
- **B.** First order, and \(60\text{ s}\)
- **C.** Second order, and \(60\text{ s}\)
- **D.** Second order, and \(90\text{ s}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121521/*