---
title: "A student dissolves a sample of solid ammonium nitrate, \\(\\text{NH}_4\\text{NO}_3\\text{(s)}\\), in distilled water in an insulated container at \\(298\\text{ K}\\) according to the equation below.  \\[ \\text{NH}_4\\text{NO}_3\\text{(s)} \\rightarrow \\text{NH}_4^+\\text{(aq)} + \\text{NO}_3^-\\text{(aq)} \\]  The student observes that all the solid dissolves completely and the temperature of the mixture decreases from \\(25.0^\\circ\\text{C}\\) to \\(15.0^\\circ\\text{C}\\). Based on these observations, which of the following correctly predicts the sign of \\(\\Delta S^\\circ_{\\text{soln}}\\) and provides the correct justification?"
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url: "https://nerd-notes.com/ubq/120328/"
date_modified: "2026-08-23T04:23:09+00:00"
---

# A student dissolves a sample of solid ammonium nitrate, \(\text{NH}_4\text{NO}_3\text{(s)}\), in distilled water in an insulated container at \(298\text{ K}\) according to the equation below.

\[ \text{NH}_4\text{NO}_3\text{(s)} \rightarrow \text{NH}_4^+\text{(aq)} + \text{NO}_3^-\text{(aq)} \]

The student observes that all the solid dissolves completely and the temperature of the mixture decreases from \(25.0^\circ\text{C}\) to \(15.0^\circ\text{C}\). Based on these observations, which of the following correctly predicts the sign of \(\Delta S^\circ_{\text{soln}}\) and provides the correct justification?

A student dissolves a sample of solid ammonium nitrate, \(\text{NH}_4\text{NO}_3\text{(s)}\), in distilled water in an insulated container at \(298\text{ K}\) according to the equation below.

\[ \text{NH}_4\text{NO}_3\text{(s)} \rightarrow \text{NH}_4^+\text{(aq)} + \text{NO}_3^-\text{(aq)} \]

The student observes that all the solid dissolves completely and the temperature of the mixture decreases from \(25.0^\circ\text{C}\) to \(15.0^\circ\text{C}\). Based on these observations, which of the following correctly predicts the sign of \(\Delta S^\circ_{\text{soln}}\) and provides the correct justification?

- **A.** \(\Delta S^\circ_{\text{soln}} < 0\), because the decrease in solution temperature indicates that thermal energy is lost from the system to the surroundings.
- **B.** \(\Delta S^\circ_{\text{soln}} > 0\), because the process is thermodynamically favorable (\(\Delta G^\circ_{\text{soln}} < 0\)) despite being endothermic (\(\Delta H^\circ_{\text{soln}} > 0\)), requiring \(-T\Delta S^\circ_{\text{soln}} < 0\).
- **C.** \(\Delta S^\circ_{\text{soln}} > 0\), because the decrease in the temperature of the water causes an increase in the average kinetic energy of the dissolved ions.
- **D.** \(\Delta S^\circ_{\text{soln}} < 0\), because water molecules form structured hydration shells around \(\text{NH}_4^+\) and \(\text{NO}_3^-\) ions, which prevents the process from being entropy-driven.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120328/*