---
title: "A student investigates the catalytic removal of a hypothetical dissolved contaminant, \\(\\text{R(aq)}\\), by \\(\\text{H}_2\\text{O}_2\\text{(aq)}\\). The temperature is maintained at \\(298\\ \\text{K}\\), and the same catalyst surface area is used in each trial. The student obtains the following initial-rate data.  | Trial | \\([\\text{R}]\\) \\((\\text{M})\\) | \\([\\text{H}_2\\text{O}_2]\\) \\((\\text{M})\\) | Initial disappearance rate of \\(\\text{R}\\) \\((\\text{M}\\,\\text{s}^{-1})\\) | |——-|————————|————————————–|——————————————————————| | \\(1\\) | \\(0.010\\) | \\(0.010\\) | \\(5.0\\times10^{-5}\\) | | \\(2\\) | \\(0.040\\) | \\(0.010\\) | \\(1.0\\times10^{-4}\\) | | \\(3\\) | \\(0.010\\) | \\(0.040\\) | \\(4.0\\times10^{-4}\\) | | \\(4\\) | \\(0.040\\) | \\(0.040\\) | \\(8.0\\times10^{-4}\\) |  Which of the following gives both the differential rate law and the units of the rate constant, \\(k\\), that are consistent with the data?"
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url: "https://nerd-notes.com/ubq/120043/"
date_modified: "2026-08-21T08:40:55+00:00"
---

# A student investigates the catalytic removal of a hypothetical dissolved contaminant, \(\text{R(aq)}\), by \(\text{H}_2\text{O}_2\text{(aq)}\). The temperature is maintained at \(298\ \text{K}\), and the same catalyst surface area is used in each trial. The student obtains the following initial-rate data.

| Trial | \([\text{R}]\) \((\text{M})\) | \([\text{H}_2\text{O}_2]\) \((\text{M})\) | Initial disappearance rate of \(\text{R}\) \((\text{M}\,\text{s}^{-1})\) |
|——-|————————|————————————–|——————————————————————|
| \(1\) | \(0.010\) | \(0.010\) | \(5.0\times10^{-5}\) |
| \(2\) | \(0.040\) | \(0.010\) | \(1.0\times10^{-4}\) |
| \(3\) | \(0.010\) | \(0.040\) | \(4.0\times10^{-4}\) |
| \(4\) | \(0.040\) | \(0.040\) | \(8.0\times10^{-4}\) |

Which of the following gives both the differential rate law and the units of the rate constant, \(k\), that are consistent with the data?

A student investigates the catalytic removal of a hypothetical dissolved contaminant, \(\text{R(aq)}\), by \(\text{H}_2\text{O}_2\text{(aq)}\). The temperature is maintained at \(298\ \text{K}\), and the same catalyst surface area is used in each trial. The student obtains the following initial-rate data.

| Trial | \([\text{R}]\) \((\text{M})\) | \([\text{H}_2\text{O}_2]\) \((\text{M})\) | Initial disappearance rate of \(\text{R}\) \((\text{M}\,\text{s}^{-1})\) |
|-------|------------------------|--------------------------------------|------------------------------------------------------------------|
| \(1\) | \(0.010\) | \(0.010\) | \(5.0\times10^{-5}\) |
| \(2\) | \(0.040\) | \(0.010\) | \(1.0\times10^{-4}\) |
| \(3\) | \(0.010\) | \(0.040\) | \(4.0\times10^{-4}\) |
| \(4\) | \(0.040\) | \(0.040\) | \(8.0\times10^{-4}\) |

Which of the following gives both the differential rate law and the units of the rate constant, \(k\), that are consistent with the data?

- **A.** \(\text{rate}=k[\text{R}]^{1/2}[\text{H}_2\text{O}_2]^{3/2}\); \(k\) has units of \(\text{M}\,\text{s}^{-1}\).
- **B.** \(\text{rate}=k[\text{R}]^{1/2}[\text{H}_2\text{O}_2]^{3/2}\); \(k\) has units of \(\text{M}^{-1}\,\text{s}^{-1}\).
- **C.** \(\text{rate}=k[\text{R}][\text{H}_2\text{O}_2]^3\); \(k\) has units of \(\text{M}^{-3}\,\text{s}^{-1}\).
- **D.** \(\text{rate}=k[\text{R}]^2[\text{H}_2\text{O}_2]^{2/3}\); \(k\) has units of \(\text{M}^{-5/3}\,\text{s}^{-1}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120043/*