---
title: "A student investigates the kinetics of the first-order decomposition of hydrogen peroxide at a constant temperature of \\(298\\text{ K}\\):  \\[ 2\\text{H}_2\\text{O}_2\\text{(aq)} \\rightarrow 2\\text{H}_2\\text{O(l)} + \\text{O}_2\\text{(g)} \\]  The concentration of \\(\\text{H}_2\\text{O}_2\\text{(aq)}\\) is monitored over time, producing the curve shown in the graph. The student identifies the following four reaction rate values:  \\(r_0\\): the instantaneous rate of decomposition at \\(t = 0\\text{ s}\\) \\(r_1\\): the instantaneous rate of decomposition at \\(t = 100\\text{ s}\\) \\(r_2\\): the instantaneous rate of decomposition at \\(t = 200\\text{ s}\\) \\(r_{\\text{avg}}\\): the average rate of decomposition over the time interval from \\(t = 0\\text{ s}\\) to \\(t = 100\\text{ s}\\)  Which of the following correctly ranks these four rates from greatest to least?"
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url: "https://nerd-notes.com/ubq/123719/"
date_modified: "2026-09-28T12:02:08+00:00"
---

# A student investigates the kinetics of the first-order decomposition of hydrogen peroxide at a constant temperature of \(298\text{ K}\):

\[ 2\text{H}_2\text{O}_2\text{(aq)} \rightarrow 2\text{H}_2\text{O(l)} + \text{O}_2\text{(g)} \]

The concentration of \(\text{H}_2\text{O}_2\text{(aq)}\) is monitored over time, producing the curve shown in the graph. The student identifies the following four reaction rate values:

\(r_0\): the instantaneous rate of decomposition at \(t = 0\text{ s}\)
\(r_1\): the instantaneous rate of decomposition at \(t = 100\text{ s}\)
\(r_2\): the instantaneous rate of decomposition at \(t = 200\text{ s}\)
\(r_{\text{avg}}\): the average rate of decomposition over the time interval from \(t = 0\text{ s}\) to \(t = 100\text{ s}\)

Which of the following correctly ranks these four rates from greatest to least?

A student investigates the kinetics of the first-order decomposition of hydrogen peroxide at a constant temperature of \(298\text{ K}\):

\[ 2\text{H}_2\text{O}_2\text{(aq)} \rightarrow 2\text{H}_2\text{O(l)} + \text{O}_2\text{(g)} \]

The concentration of \(\text{H}_2\text{O}_2\text{(aq)}\) is monitored over time, producing the curve shown in the graph. The student identifies the following four reaction rate values:

\(r_0\): the instantaneous rate of decomposition at \(t = 0\text{ s}\)
\(r_1\): the instantaneous rate of decomposition at \(t = 100\text{ s}\)
\(r_2\): the instantaneous rate of decomposition at \(t = 200\text{ s}\)
\(r_{\text{avg}}\): the average rate of decomposition over the time interval from \(t = 0\text{ s}\) to \(t = 100\text{ s}\)

Which of the following correctly ranks these four rates from greatest to least?

![A grayscale Cartesian coordinate graph showing a single smooth, solid curve representing reactant concentration over time. The horizontal axis is labeled 'Time (s)' with tick marks at 0, 100, 200, and 300. The vertical axis is labeled '[H2O2] (M)' with tick marks at 0.00, 0.25, 0.50, 0.75, and 1.00. The solid curve starts at the coordinate (0, 1.00) and decreases monotonically with a decreasing slope (concave upward), passing through (100, 0.50) and (200, 0.25), approaching 0 at longer times. No other curves, data points, or annotations appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596928-GqeoLB.jpg)

- **A.** \(r_0 > r_1 > r_{\text{avg}} > r_2\)
- **B.** \(r_0 > r_{\text{avg}} > r_1 > r_2\)
- **C.** \(r_{\text{avg}} > r_0 > r_1 > r_2\)
- **D.** \(r_2 > r_1 > r_{\text{avg}} > r_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123719/*