---
title: "A student investigates the kinetics of the reaction represented by the equation below.  \\[ \\text{A}\\text{(aq)} + 2\\,\\text{B}\\text{(aq)} \\rightarrow \\text{C}\\text{(aq)} \\]  To determine the rate law, the student performs three trials at \\(298\\text{ K}\\) in which \\(\\text{B}\\text{(aq)}\\) is present in large excess (\\([\\text{B}]_0 \\gg [\\text{A}]_0\\)), so that \\([\\text{B}]\\) remains essentially constant throughout each trial. Under these conditions, the rate law is given by:  \\[ \\text{Rate} = k'[\\text{A}]^m \\]  where \\(k’ = k[\\text{B}]_0^n\\). In each trial, a plot of \\(\\ln[\\text{A}]\\) versus time yields a straight line. The experimental data collected are shown in the following table.  | Trial | \\([\\text{A}]_0\\text{ (M)}\\) | \\([\\text{B}]_0\\text{ (M)}\\) | \\(k’\\text{ (s}^{-1}\\text{)}\\) | | :—: | :—: | :—: | :—: | | 1 | \\(1.0 \\times 10^{-4}\\) | \\(0.10\\) | \\(2.0 \\times 10^{-3}\\) | | 2 | \\(2.0 \\times 10^{-4}\\) | \\(0.10\\) | \\(2.0 \\times 10^{-3}\\) | | 3 | \\(1.0 \\times 10^{-4}\\) | \\(0.20\\) | \\(8.0 \\times 10^{-3}\\) |  Which of the following is the rate law for the reaction and the calculated value of the rate constant, \\(k\\)?"
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url: "https://nerd-notes.com/ubq/123686/"
date_modified: "2026-09-28T12:01:59+00:00"
---

# A student investigates the kinetics of the reaction represented by the equation below.

\[ \text{A}\text{(aq)} + 2\,\text{B}\text{(aq)} \rightarrow \text{C}\text{(aq)} \]

To determine the rate law, the student performs three trials at \(298\text{ K}\) in which \(\text{B}\text{(aq)}\) is present in large excess (\([\text{B}]_0 \gg [\text{A}]_0\)), so that \([\text{B}]\) remains essentially constant throughout each trial. Under these conditions, the rate law is given by:

\[ \text{Rate} = k'[\text{A}]^m \]

where \(k’ = k[\text{B}]_0^n\). In each trial, a plot of \(\ln[\text{A}]\) versus time yields a straight line. The experimental data collected are shown in the following table.

| Trial | \([\text{A}]_0\text{ (M)}\) | \([\text{B}]_0\text{ (M)}\) | \(k’\text{ (s}^{-1}\text{)}\) |
| :—: | :—: | :—: | :—: |
| 1 | \(1.0 \times 10^{-4}\) | \(0.10\) | \(2.0 \times 10^{-3}\) |
| 2 | \(2.0 \times 10^{-4}\) | \(0.10\) | \(2.0 \times 10^{-3}\) |
| 3 | \(1.0 \times 10^{-4}\) | \(0.20\) | \(8.0 \times 10^{-3}\) |

Which of the following is the rate law for the reaction and the calculated value of the rate constant, \(k\)?

A student investigates the kinetics of the reaction represented by the equation below.

\[ \text{A}\text{(aq)} + 2\,\text{B}\text{(aq)} \rightarrow \text{C}\text{(aq)} \]

To determine the rate law, the student performs three trials at \(298\text{ K}\) in which \(\text{B}\text{(aq)}\) is present in large excess (\([\text{B}]_0 \gg [\text{A}]_0\)), so that \([\text{B}]\) remains essentially constant throughout each trial. Under these conditions, the rate law is given by:

\[ \text{Rate} = k'[\text{A}]^m \]

where \(k' = k[\text{B}]_0^n\). In each trial, a plot of \(\ln[\text{A}]\) versus time yields a straight line. The experimental data collected are shown in the following table.

| Trial | \([\text{A}]_0\text{ (M)}\) | \([\text{B}]_0\text{ (M)}\) | \(k'\text{ (s}^{-1}\text{)}\) |
| :---: | :---: | :---: | :---: |
| 1 | \(1.0 \times 10^{-4}\) | \(0.10\) | \(2.0 \times 10^{-3}\) |
| 2 | \(2.0 \times 10^{-4}\) | \(0.10\) | \(2.0 \times 10^{-3}\) |
| 3 | \(1.0 \times 10^{-4}\) | \(0.20\) | \(8.0 \times 10^{-3}\) |

Which of the following is the rate law for the reaction and the calculated value of the rate constant, \(k\)?

- **A.** \(\text{Rate} = k[\text{A}][\text{B}]\), and \(k = 0.020\text{ M}^{-1}\text{ s}^{-1}\)
- **B.** \(\text{Rate} = k[\text{A}][\text{B}]\), and \(k = 0.20\text{ M}^{-1}\text{ s}^{-1}\)
- **C.** \(\text{Rate} = k[\text{A}][\text{B}]^2\), and \(k = 0.20\text{ M}^{-2}\text{ s}^{-1}\)
- **D.** \(\text{Rate} = k[\text{A}][\text{B}]^2\), and \(k = 2.0\text{ M}^{-2}\text{ s}^{-1}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123686/*