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Chapter 17: Problem 46

Ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\) dissolves spontaneously and endothermically in water. What can you deduce about the sign of \(\Delta S\) for the solution process?

Short Answer

Expert verified
The sign of \(\Delta S\) (change in entropy) for the dissolution process of ammonium nitrate in water is positive.

Step by step solution

01

Understanding the Dissolution Process

In the process of dissolution, solid particles of ammonium nitrate disperse into individual ions when mixed with water. Since these particles were in a more ordered state when in solid form and are now in a less ordered (more chaotic) state after dissolution, the overall disorder of the system has increased.
02

Analyzing the Energy Transfer

The process is described as endothermic, which means it absorbs heat from its surroundings. While this alone does not directly determine the sign of \(\Delta S\), it's one part of the overall picture.
03

Interpreting Spontaneous Reactions

The reaction is described as spontaneous. Spontaneous reactions increase the entropy of the universe (\(\Delta S_{\text{universe}} > 0\)). As the process is endothermic, the surroundings lose heat and thus, entropy decreases in the surroundings (\(\Delta S_{\text{surroundings}} < 0\)). In order for the overall change in entropy of the universe to be positive, the system must increase its entropy by a greater amount, so \(\Delta S_{\text{system}}\) must be positive.
04

Final Deduction

Taking into account the increased disorder after dissolution and the nature of spontaneous reactions, we can deduce that the sign of \(\Delta S\) for the dissolution process of ammonium nitrate is positive. It means that the entropy, or disorder, of the system increases.

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Most popular questions from this chapter

Which of the following processes are spontaneous and which are nonspontaneous at a given temperature? (a) \(\mathrm{NaNO}_{3}(s) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{NaNO}_{3}(a q) \quad\) saturated soln (b) \(\mathrm{NaNO}_{3}(s) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{NaNO}_{3}(a q) \quad\) unsaturated soln (c) \(\mathrm{NaNO}_{3}(s) \stackrel{\mathrm{H}_{2} \mathrm{O}}{\longrightarrow} \mathrm{NaNO}_{3}(a q)\) supersaturated soln

How does the entropy of a system change for each of the following processes? (a) A solid melts. (b) A liquid freezes. (c) A liquid boils. (d) A vapor is converted to a solid. (e) A vapor condenses to a liquid. (f) A solid sublimes. (g) Urea dissolves in water.

As an approximation, we can assume that proteins exist either in the native (or physiologically functioning) state and the denatured state: $$ \text { native } \rightleftharpoons \text { denatured } $$ The standard molar enthalpy and entropy of the denaturation of a certain protein are \(512 \mathrm{~kJ} / \mathrm{mol}\) and \(1.60 \mathrm{~kJ} / \mathrm{K} \cdot \mathrm{mol},\) respectively. Comment on the signs and magnitudes of these quantities, and calculate the temperature at which the process favors the denatured state.

For the autoionization of water at \(25^{\circ} \mathrm{C}\), $$ \mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{OH}^{-}(a q) $$ \(K_{\mathrm{w}}\) is \(1.0 \times 10^{-14} .\) What is \(\Delta G^{\circ}\) for the process?

The molar heat of vaporization of ethanol is 39.3 kJ/mol and the boiling point of ethanol is \(78.3^{\circ} \mathrm{C}\). Calculate \(\Delta S\) for the vaporization of 0.50 mol ethanol.
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