---
title: "A student investigates the kinetics of the gas-phase decomposition of \\(\\text{N}_2\\text{O}_5(g)\\) at a constant temperature according to the following balanced equation:  \\[2\\text{N}_2\\text{O}_5(g) \\rightarrow 4\\text{NO}_2(g) + \\text{O}_2(g)\\]  The student measures the concentration of \\(\\text{N}_2\\text{O}_5(g)\\) over time and plots the data shown in the graph. A dashed line tangent to the curve is drawn at \\(t = 200\\text{ s}\\).  Based on the graph, what is the instantaneous rate of reaction at \\(t = 200\\text{ s}\\)?"
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url: "https://nerd-notes.com/ubq/120023/"
date_modified: "2026-08-21T08:31:59+00:00"
---

# A student investigates the kinetics of the gas-phase decomposition of \(\text{N}_2\text{O}_5(g)\) at a constant temperature according to the following balanced equation:

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

The student measures the concentration of \(\text{N}_2\text{O}_5(g)\) over time and plots the data shown in the graph. A dashed line tangent to the curve is drawn at \(t = 200\text{ s}\).

Based on the graph, what is the instantaneous rate of reaction at \(t = 200\text{ s}\)?

A student investigates the kinetics of the gas-phase decomposition of \(\text{N}_2\text{O}_5(g)\) at a constant temperature according to the following balanced equation:

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

The student measures the concentration of \(\text{N}_2\text{O}_5(g)\) over time and plots the data shown in the graph. A dashed line tangent to the curve is drawn at \(t = 200\text{ s}\).

Based on the graph, what is the instantaneous rate of reaction at \(t = 200\text{ s}\)?

![A line graph with gridlines plotting the concentration of \(\text{N}_2\text{O}_5\) versus time. The vertical y-axis is labeled \([\text{N}_2\text{O}_5]\text{ (M)}\) with values marked from \(0.000\) to \(0.200\) in increments of \(0.040\). The horizontal x-axis is labeled \(\text{Time (s)}\) with values marked from \(0\) to \(500\) in increments of \(100\). Light gray gridlines extend from each axis tick mark across the plot. A solid smooth curve starts at \((0, 0.200)\) and curves downward asymptotically toward the x-axis, passing through \((200, 0.080)\). A straight dashed line is tangent to the curve at the point \((200, 0.080)\). The dashed line extends from the y-intercept at \((0, 0.160)\) to the x-intercept at \((400, 0.000)\). A solid black dot highlights the point of tangency at \((200, 0.080)\). No other curves, points, labels, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-graph-1-1787301119-KgnMnG.jpg)

- **A.** \(2.0 \times 10^{-4}\text{ M}\cdot\text{s}^{-1}\)
- **B.** \(4.0 \times 10^{-4}\text{ M}\cdot\text{s}^{-1}\)
- **C.** \(8.0 \times 10^{-4}\text{ M}\cdot\text{s}^{-1}\)
- **D.** \(1.6 \times 10^{-3}\text{ M}\cdot\text{s}^{-1}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120023/*