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Chapter 18: Problem 44

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 ΔS for the solution process will be positive, implying that the process of ammonium nitrate dissolving in water increases the system's disorder (solution).

Step by step solution

01

Understanding Thermodynamics Rules

The Second Law of Thermodynamics states that, in general, the total entropy of a system and its surroundings always increase for a spontaneous process. It means that ΔS_system + ΔS_surroundings > 0.
02

Analyzing the Given Process

The dissolving of ammonium nitrate in water is a spontaneous process, and the problem states it's also endothermic (ΔH > 0). An endothermic process means the system absorbs heat from the surroundings.
03

Deduction of ΔS_system

Since overall ΔS_total > 0 for a spontaneous process, and we know that the dissolving of ammonium nitrate in water is endothermic, it means that the surroundings become more ordered (ΔS_surroundings < 0). In order to still get ΔS_total > 0, it implies that ΔS_system must be positive, which means the system (solution) becomes more disordered when NH4NO3 dissolves in water.

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Most popular questions from this chapter

For a reaction with a negative \(\Delta G^{\circ}\) value, which of the following statements is false? (a) The equilibrium constant \(K\) is greater than one, (b) the reaction is spontaneous when all the reactants and products are in their standard states, and (c) the reaction is always exothermic.

Explain the following nursery rhyme in terms of the second law of thermodynamics. Humpty Dumpty sat on a wall; Humpty Dumpty had a great fall. All the King's horses and all the King's men Couldn't put Humpty together again.

Consider the following reaction at \(25^{\circ} \mathrm{C}\) : $$ \mathrm{Fe}(\mathrm{OH})_{2}(s) \rightleftharpoons \mathrm{Fe}^{2+}(a q)+2 \mathrm{OH}^{-}(a q) $$ Calculate \(\Delta G^{\circ}\) for the reaction. \(K_{\mathrm{sp}}\) for \(\mathrm{Fe}(\mathrm{OH})_{2}\) is \(1.6 \times 10^{-14}\).

Predict whether the entropy change is positive or negative for each of these reactions: (a) \(\mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g)\) (b) \(\mathrm{O}(g)+\mathrm{O}(g) \longrightarrow \mathrm{O}_{2}(g)\) (c) \(\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{N}_{2} \mathrm{O}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) (d) \(2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)\)

State whether the sign of the entropy change expected for each of the following processes will be positive or negative, and explain your predictions. (a) \(\mathrm{PCl}_{3}(l)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{PCl}_{5}(s)\) (b) \(2 \mathrm{HgO}(s) \longrightarrow 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\) (c) \(\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{H}(g)\) (d) \(\mathrm{U}(s)+3 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{UF}_{6}(s)\)
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