---
title: "A student investigates the kinetics of the gas-phase decomposition of \\(\\text{NO}_2\\text{(g)}\\) at a constant temperature of \\(573\\text{ K}\\) according to the following equation:  \\[ 2\\text{NO}_2\\text{(g)} \\rightarrow 2\\text{NO(g)} + \\text{O}_2\\text{(g)} \\]  The student measures the concentration of \\(\\text{NO}_2\\text{(g)}\\) over time and plots \\(\\dfrac{1}{[\\text{NO}_2]}\\) as a function of time, as shown in the graph below.  Based on the graph, what is the value of the rate constant, \\(k\\), for the reaction?"
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url: "https://nerd-notes.com/ubq/119890/"
date_modified: "2026-08-21T08:17:02+00:00"
---

# A student investigates the kinetics of the gas-phase decomposition of \(\text{NO}_2\text{(g)}\) at a constant temperature of \(573\text{ K}\) according to the following equation:

\[ 2\text{NO}_2\text{(g)} \rightarrow 2\text{NO(g)} + \text{O}_2\text{(g)} \]

The student measures the concentration of \(\text{NO}_2\text{(g)}\) over time and plots \(\dfrac{1}{[\text{NO}_2]}\) as a function of time, as shown in the graph below.

Based on the graph, what is the value of the rate constant, \(k\), for the reaction?

A student investigates the kinetics of the gas-phase decomposition of \(\text{NO}_2\text{(g)}\) at a constant temperature of \(573\text{ K}\) according to the following equation:

\[ 2\text{NO}_2\text{(g)} \rightarrow 2\text{NO(g)} + \text{O}_2\text{(g)} \]

The student measures the concentration of \(\text{NO}_2\text{(g)}\) over time and plots \(\dfrac{1}{[\text{NO}_2]}\) as a function of time, as shown in the graph below.

Based on the graph, what is the value of the rate constant, \(k\), for the reaction?

![A line graph displayed on a two-dimensional Cartesian plane with a white background and light gray gridlines. The horizontal axis is labeled 'Time (s)' and has major tick marks with numerical labels at 0, 20, 40, 60, 80, and 100. The vertical axis is labeled '1/[NO2] (M^-1)' and has major tick marks with numerical labels at 0, 20, 40, 60, and 80. A single solid black linear trendline begins on the vertical axis at the coordinate (0, 20) and extends with a constant positive slope upward to the coordinate (100, 70). Two distinct solid black circular data points are plotted on the line: one at (0, 20) and one at (100, 70). No other lines, curves, data points, or text annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787300222-b2vhdR.jpg)

- **A.** \(0.50\text{ M}^{-1}\cdot\text{s}^{-1}\)
- **B.** \(0.70\text{ M}^{-1}\cdot\text{s}^{-1}\)
- **C.** \(2.0\text{ M}^{-1}\cdot\text{s}^{-1}\)
- **D.** \(50\text{ M}^{-1}\cdot\text{s}^{-1}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/119890/*