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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 螖S 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 螖S_system + 螖S_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 (螖H > 0). An endothermic process means the system absorbs heat from the surroundings.
03

Deduction of 螖S_system

Since overall 螖S_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 (螖S_surroundings < 0). In order to still get 螖S_total > 0, it implies that 螖S_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

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.

A student placed \(1 \mathrm{~g}\) of each of three compounds \(\mathrm{A}\) \(\mathrm{B},\) and \(\mathrm{C}\) in a container and found that after 1 week no change had occurred. Offer some possible explanations for the fact that no reactions took place. Assume that \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{C}\) are totally miscible liquids.

Crystallization of sodium acetate from a supersaturated solution occurs spontaneously (see p. 426). What can you deduce about the signs of \(\Delta S\) and \(\Delta H ?\)

Consider the reaction $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) $$ Given that \(\Delta G^{\circ}\) for the reaction at \(25^{\circ} \mathrm{C}\) is 173.4 \(\mathrm{kJ} / \mathrm{mol}\), (a) calculate the standard free energy of formation of \(\mathrm{NO},\) and (b) calculate \(K_{P}\) of the reaction. (c) One of the starting substances in smog formation is NO. Assuming that the temperature in a running automobile engine is \(1100^{\circ} \mathrm{C},\) estimate \(K_{P}\) for the above reaction. (d) As farmers know, lightning helps to produce a better crop. Why?

Describe two ways that you could measure \(\Delta G^{\circ}\) of a reaction.
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