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Chapter 17: Problem 23

Which of the following processes are spontaneous? a. Salt dissolves in \(\mathrm{H}_{2} \mathrm{O}\). b. A clear solution becomes a uniform color after a few drops of dye are added. c. Iron rusts. d. You clean your bedroom.

Short Answer

Expert verified
Processes a, b, and c (salt dissolves in \(\mathrm{H}_2 \mathrm{O}\), a clear solution becomes a uniform color after adding dye, and iron rusts) are spontaneous as they occur naturally without external intervention and increase the entropy of the system. Process d (cleaning your bedroom) is non-spontaneous, as it requires external intervention and decreases entropy.

Step by step solution

01

Process a: Salt dissolves in \(\mathrm{H}_2 \mathrm{O}\)

Salt dissolving in water is a spontaneous process because it occurs naturally without any external intervention. In this process, the salt ions interact with water molecules, and the dissolution takes place based on the electrostatic attraction between them. This process increases the entropy (disorder) of the system, making it spontaneous.
02

Process b: A clear solution becomes a uniform color after a few drops of dye are added

When a few drops of dye are added to a clear solution, the dye molecules spread throughout the solution to give a uniform color. This process is also a spontaneous process, as it occurs naturally without external intervention. The molecules of dye are distributed evenly in the solution by diffusion, and this process increases the overall entropy of the system, contributing to its spontaneity.
03

Process c: Iron rusts

Iron rusting is a spontaneous process because it occurs naturally in the presence of air and moisture. When iron comes in contact with air and water, it forms iron oxide or rust. This process is a slow chemical reaction, known as oxidation, and it leads to an increase in entropy. This increase in entropy makes the process of iron rusting spontaneous.
04

Process d: You clean your bedroom

Cleaning your bedroom is a non-spontaneous process because it requires external intervention (in this case, your effort) to organize and decrease the overall entropy of the system (your bedroom). The natural tendency of things is towards an increase in entropy, which is opposite to the result of cleaning your bedroom. As the process relies on external intervention and decreases entropy, it is considered non-spontaneous.

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Most popular questions from this chapter

Two crystalline forms of white phosphorus are known. Both forms contain \(\mathrm{P}_{4}\) molecules, but the molecules are packed together in different ways. The \(\alpha\) form is always obtained when the liquid freezes. However, below \(-76.9^{\circ} \mathrm{C}\), the \(\alpha\) form spontaneously converts to the \(\beta\) form: $$\mathrm{P}_{4}(s, \alpha) \longrightarrow \mathrm{P}_{4}(s, \beta)$$ a. Predict the signs of \(\Delta H\) and \(\Delta S\) for this process. b. Predict which form of phosphorus has the more ordered crystalline structure (has the smaller positional probability).

Using data from Appendix 4, calculate \(\Delta H^{\circ}, \Delta G^{\circ}\), and \(K\) (at 298 K) for the production of ozone from oxygen: $$3 \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{O}_{3}(g)$$ At \(30 \mathrm{~km}\) above the surface of the earth, the temperature is about 230\. \(\mathrm{K}\) and the partial pressure of oxygen is about \(1.0 \times 10^{-3}\) atm. Estimate the partial pressure of ozone in equilibrium with oxygen at \(30 \mathrm{~km}\) above the earth's surface. Is it reasonable to assume that the equilibrium between oxygen and ozone is maintained under these conditions? Explain.

Consider the reaction $$2 \mathrm{POCl}_{3}(g) \longrightarrow 2 \mathrm{PCl}_{3}(g)+\mathrm{O}_{2}(g)$$ a. Calculate \(\Delta G^{\circ}\) for this reaction. The \(\Delta G_{\mathrm{f}}^{\circ}\) values for \(\mathrm{POCl}_{3}(g)\) and \(\mathrm{PCl}_{3}(g)\) are \(-502 \mathrm{~kJ} / \mathrm{mol}\) and \(-270 . \mathrm{kJ} / \mathrm{mol}\), respectively. b. Is this reaction spontaneous under standard conditions at \(298 \mathrm{~K} ?\) c. The value of \(\Delta S^{\circ}\) for this reaction is \(179 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\). At what temperatures is this reaction spontaneous at standard conditions? Assume that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not depend on temperature.

For ammonia \(\left(\mathrm{NH}_{3}\right.\) ), the enthalpy of fusion is \(5.65 \mathrm{~kJ} / \mathrm{mol}\) and the entropy of fusion is \(28.9 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\). a. Will \(\mathrm{NH}_{3}(s)\) spontaneously melt at \(200 . \mathrm{K}\) ? b. What is the approximate melting point of ammonia?

Consider two reactions for the production of ethanol: $$\begin{array}{l}\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(l) \\\ \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(l)+\mathrm{H}_{2}(g) \end{array}$$ Which would be the more thermodynamically feasible at standard conditions? Why?
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