---
title: "A sample of \\(\\text{N}_2\\text{O}_4(g)\\) is placed in a rigid, sealed container and allowed to decompose according to the equation below.  \\[ \\text{N}_2\\text{O}_4(g) \\rightleftharpoons 2\\,\\text{NO}_2(g) \\]  The reaction is allowed to reach equilibrium at two different temperatures. The equilibrium partial pressures of each gas at both temperatures are recorded in the table below.  | Temperature | \\(P_{\\text{N}_2\\text{O}_4}\\) (atm) | \\(P_{\\text{NO}_2}\\) (atm) | | :— | :— | :— | | \\(300\\text{ K}\\) | \\(4.0\\) | \\(2.0\\) | | \\(400\\text{ K}\\) | \\(0.50\\) | \\(4.0\\) |  Based on the data, which of the following correctly identifies the sign of \\(\\Delta H^\\circ\\) for the forward reaction and provides the correct justification using the equilibrium constant, \\(K_p\\)?"
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url: "https://nerd-notes.com/ubq/123827/"
date_modified: "2026-09-28T12:30:28+00:00"
---

# A sample of \(\text{N}_2\text{O}_4(g)\) is placed in a rigid, sealed container and allowed to decompose according to the equation below.

\[ \text{N}_2\text{O}_4(g) \rightleftharpoons 2\,\text{NO}_2(g) \]

The reaction is allowed to reach equilibrium at two different temperatures. The equilibrium partial pressures of each gas at both temperatures are recorded in the table below.

| Temperature | \(P_{\text{N}_2\text{O}_4}\) (atm) | \(P_{\text{NO}_2}\) (atm) |
| :— | :— | :— |
| \(300\text{ K}\) | \(4.0\) | \(2.0\) |
| \(400\text{ K}\) | \(0.50\) | \(4.0\) |

Based on the data, which of the following correctly identifies the sign of \(\Delta H^\circ\) for the forward reaction and provides the correct justification using the equilibrium constant, \(K_p\)?

A sample of \(\text{N}_2\text{O}_4(g)\) is placed in a rigid, sealed container and allowed to decompose according to the equation below.

\[ \text{N}_2\text{O}_4(g) \rightleftharpoons 2\,\text{NO}_2(g) \]

The reaction is allowed to reach equilibrium at two different temperatures. The equilibrium partial pressures of each gas at both temperatures are recorded in the table below.

| Temperature | \(P_{\text{N}_2\text{O}_4}\) (atm) | \(P_{\text{NO}_2}\) (atm) |
| :--- | :--- | :--- |
| \(300\text{ K}\) | \(4.0\) | \(2.0\) |
| \(400\text{ K}\) | \(0.50\) | \(4.0\) |

Based on the data, which of the following correctly identifies the sign of \(\Delta H^\circ\) for the forward reaction and provides the correct justification using the equilibrium constant, \(K_p\)?

- **A.** \(\Delta H^\circ > 0\), because \(K_p = 32\) at \(400\text{ K}\), which is greater than \(K_p = 1.0\) at \(300\text{ K}\).
- **B.** \(\Delta H^\circ > 0\), because \(K_p = 8.0\) at \(400\text{ K}\), which is greater than \(K_p = 0.50\) at \(300\text{ K}\).
- **C.** \(\Delta H^\circ < 0\), because \(K_p = \dfrac{1}{32}\) at \(400\text{ K}\), which is less than \(K_p = 1.0\) at \(300\text{ K}\).
- **D.** \(\Delta H^\circ < 0\), because \(K_p = 32\) at \(400\text{ K}\), which indicates that higher temperatures favor an exothermic process.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123827/*