---
title: "A student studies the first-order decomposition of reactant \\(\\text{A}\\) at two temperatures. The student obtains the following data.  | \\(T\\) | \\(t\\) | \\([\\text{A}]\\) | |—|—|—| | \\(300\\ \\text{K}\\) | \\(0\\ \\text{s}\\) | \\(0.100\\ \\text{M}\\) | | \\(300\\ \\text{K}\\) | \\(3465\\ \\text{s}\\) | \\(0.0500\\ \\text{M}\\) | | \\(330\\ \\text{K}\\) | \\(0\\ \\text{s}\\) | \\(0.100\\ \\text{M}\\) | | \\(330\\ \\text{K}\\) | \\(346.5\\ \\text{s}\\) | \\(0.0250\\ \\text{M}\\) |  For the calculations, use \\(R=8.31\\ \\text{J mol}^{-1}\\text{K}^{-1}\\), \\(\\ln 2=0.693\\), and \\(\\ln 20=3.00\\). What is the estimated activation energy, \\(E_a\\), for the decomposition?"
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url: "https://nerd-notes.com/ubq/120028/"
date_modified: "2026-08-21T08:40:38+00:00"
---

# A student studies the first-order decomposition of reactant \(\text{A}\) at two temperatures. The student obtains the following data.

| \(T\) | \(t\) | \([\text{A}]\) |
|—|—|—|
| \(300\ \text{K}\) | \(0\ \text{s}\) | \(0.100\ \text{M}\) |
| \(300\ \text{K}\) | \(3465\ \text{s}\) | \(0.0500\ \text{M}\) |
| \(330\ \text{K}\) | \(0\ \text{s}\) | \(0.100\ \text{M}\) |
| \(330\ \text{K}\) | \(346.5\ \text{s}\) | \(0.0250\ \text{M}\) |

For the calculations, use \(R=8.31\ \text{J mol}^{-1}\text{K}^{-1}\), \(\ln 2=0.693\), and \(\ln 20=3.00\). What is the estimated activation energy, \(E_a\), for the decomposition?

A student studies the first-order decomposition of reactant \(\text{A}\) at two temperatures. The student obtains the following data.

| \(T\) | \(t\) | \([\text{A}]\) |
|---|---|---|
| \(300\ \text{K}\) | \(0\ \text{s}\) | \(0.100\ \text{M}\) |
| \(300\ \text{K}\) | \(3465\ \text{s}\) | \(0.0500\ \text{M}\) |
| \(330\ \text{K}\) | \(0\ \text{s}\) | \(0.100\ \text{M}\) |
| \(330\ \text{K}\) | \(346.5\ \text{s}\) | \(0.0250\ \text{M}\) |

For the calculations, use \(R=8.31\ \text{J mol}^{-1}\text{K}^{-1}\), \(\ln 2=0.693\), and \(\ln 20=3.00\). What is the estimated activation energy, \(E_a\), for the decomposition?

- **A.** \(82.3\ \text{kJ mol}^{-1}\)
- **B.** \(90.5\ \text{kJ mol}^{-1}\)
- **C.** \(165\ \text{kJ mol}^{-1}\)
- **D.** \(550\ \text{kJ mol}^{-1}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120028/*