---
title: "A student investigates the kinetics of the gas-phase decomposition of dinitrogen pentoxide represented by the following equation:  \\[ 2\\text{ N}_2\\text{O}_5\\text{(g)} \\rightarrow 4\\text{ NO}_2\\text{(g)} + \\text{O}_2\\text{(g)} \\]  The rate constant \\(k\\) is measured at several different temperatures, and the data are plotted as \\(\\ln k\\) versus \\(1/T\\), where \\(T\\) is temperature in kelvins (\\(\\text{K}\\)). A linear regression of the data yields the best-fit line shown in the graph below, with the equation \\(y = -1.20 \\times 10^4 x + 30.5\\).  Based on these data, what is the activation energy, \\(E_a\\), for the decomposition reaction? (Use \\(R = 8.314\\text{ J}/(\\text{mol}\\cdot\\text{K})\\))"
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date_modified: "2026-09-28T12:02:05+00:00"
---

# A student investigates the kinetics of the gas-phase decomposition of dinitrogen pentoxide represented by the following equation:

\[ 2\text{ N}_2\text{O}_5\text{(g)} \rightarrow 4\text{ NO}_2\text{(g)} + \text{O}_2\text{(g)} \]

The rate constant \(k\) is measured at several different temperatures, and the data are plotted as \(\ln k\) versus \(1/T\), where \(T\) is temperature in kelvins (\(\text{K}\)). A linear regression of the data yields the best-fit line shown in the graph below, with the equation \(y = -1.20 \times 10^4 x + 30.5\).

Based on these data, what is the activation energy, \(E_a\), for the decomposition reaction? (Use \(R = 8.314\text{ J}/(\text{mol}\cdot\text{K})\))

A student investigates the kinetics of the gas-phase decomposition of dinitrogen pentoxide represented by the following equation:

\[ 2\text{ N}_2\text{O}_5\text{(g)} \rightarrow 4\text{ NO}_2\text{(g)} + \text{O}_2\text{(g)} \]

The rate constant \(k\) is measured at several different temperatures, and the data are plotted as \(\ln k\) versus \(1/T\), where \(T\) is temperature in kelvins (\(\text{K}\)). A linear regression of the data yields the best-fit line shown in the graph below, with the equation \(y = -1.20 \times 10^4 x + 30.5\).

Based on these data, what is the activation energy, \(E_a\), for the decomposition reaction? (Use \(R = 8.314\text{ J}/(\text{mol}\cdot\text{K})\))

![The diagram shows an Arrhenius plot with bare grayscale axes and no gridlines. The vertical y-axis is labeled '\(\ln k\)' and has values decreasing downward. The horizontal x-axis is labeled '\(1/T\text{ (K}^{-1}\text{)}\)'. A single solid straight line slopes downward from left to right across the quadrant, representing the linear regression fit to experimental data points shown as four small solid black dots along the line. Adjacent to the line, a text box displays the regression equation: '\(y = -1.20 \times 10^4 x + 30.5\)'. The y-intercept occurs above the origin, and the slope is negative throughout. No other particles, labels, text, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596925-xZOPE2.jpg)

- **A.** \(1.4\text{ kJ/mol}\)
- **B.** \(12\text{ kJ/mol}\)
- **C.** \(100\text{ kJ/mol}\)
- **D.** \(1.0 \times 10^5\text{ kJ/mol}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123710/*