---
title: "A student investigates the kinetics of the gas-phase decomposition of sulfuryl chloride, \\(\\text{SO}_2\\text{Cl}_2\\text{(g)}\\), at \\(590\\text{ K}\\) according to the following balanced equation:  \\[ \\text{SO}_2\\text{Cl}_2\\text{(g)} \\rightarrow \\text{SO}_2\\text{(g)} + \\text{Cl}_2\\text{(g)} \\]  The student measures the concentration of \\(\\text{SO}_2\\text{Cl}_2\\) at various times during the reaction and constructs the plot of \\(\\ln[\\text{SO}_2\\text{Cl}_2]\\) versus time shown below.  Based on the graph, which of the following is the correct rate law and value of the rate constant, \\(k\\), for the reaction?"
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url: "https://nerd-notes.com/ubq/119777/"
date_modified: "2026-08-21T08:12:19+00:00"
---

# A student investigates the kinetics of the gas-phase decomposition of sulfuryl chloride, \(\text{SO}_2\text{Cl}_2\text{(g)}\), at \(590\text{ K}\) according to the following balanced equation:

\[ \text{SO}_2\text{Cl}_2\text{(g)} \rightarrow \text{SO}_2\text{(g)} + \text{Cl}_2\text{(g)} \]

The student measures the concentration of \(\text{SO}_2\text{Cl}_2\) at various times during the reaction and constructs the plot of \(\ln[\text{SO}_2\text{Cl}_2]\) versus time shown below.

Based on the graph, which of the following is the correct rate law and value of the rate constant, \(k\), for the reaction?

A student investigates the kinetics of the gas-phase decomposition of sulfuryl chloride, \(\text{SO}_2\text{Cl}_2\text{(g)}\), at \(590\text{ K}\) according to the following balanced equation:

\[ \text{SO}_2\text{Cl}_2\text{(g)} \rightarrow \text{SO}_2\text{(g)} + \text{Cl}_2\text{(g)} \]

The student measures the concentration of \(\text{SO}_2\text{Cl}_2\) at various times during the reaction and constructs the plot of \(\ln[\text{SO}_2\text{Cl}_2]\) versus time shown below.

Based on the graph, which of the following is the correct rate law and value of the rate constant, \(k\), for the reaction?

![A two-dimensional Cartesian graph displayed in grayscale on bare axes without background gridlines. The horizontal axis is labeled as Time (s) with evenly spaced numeric tick marks at 0, 100, 200, 300, 400, and 500. The vertical axis is labeled as ln[SO2Cl2] with evenly spaced numeric tick marks at 0.0, -1.0, -2.0, -3.0, -4.0, and -5.0. A single solid black trendline with a constant negative slope extends across the plot area. Two discrete filled black circular data markers are placed on the trendline at coordinates (0, -2.0) and (400, -4.0). No other points, curves, legends, text, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787299939-a0vRwQ.jpg)

- **A.** \(\text{Rate} = k[\text{SO}_2\text{Cl}_2]\), and \(k = -5.0 \times 10^{-3}\text{ s}^{-1}\)
- **B.** \(\text{Rate} = k[\text{SO}_2\text{Cl}_2]\), and \(k = 5.0 \times 10^{-3}\text{ s}^{-1}\)
- **C.** \(\text{Rate} = k[\text{SO}_2\text{Cl}_2]^2\), and \(k = 5.0 \times 10^{-3}\text{ M}^{-1}\text{s}^{-1}\)
- **D.** \(\text{Rate} = k[\text{SO}_2\text{Cl}_2]^2\), and \(k = 200\text{ M}^{-1}\text{s}^{-1}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119777/*