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Chapter 19: Problem 25

Indicate whether each statement is true or false. (a) The second law of thermodynamics says that entropy can only be produced but cannot not be destroyed. (b) In a certain process the entropy of the system changes by $1.2 \mathrm{~J} / \mathrm{K}\( (increase) and the entropy of the surroundings changes by \)-1.2 \mathrm{~J} / \mathrm{K}$ (decrease). Thus, this process must be spontaneous. (c) In a certain process the entropy of the system changes by $1.3 \mathrm{~J} / \mathrm{K}\( (increase) and the entropy of the surroundings changes by \)-1.2 \mathrm{~J} / \mathrm{K}$ (decrease). Thus, this process must be reversible.

Short Answer

Expert verified
(a) True (b) False (c) False

Step by step solution

01

Statement (a)

The second law of thermodynamics states that the total entropy in a closed system can only increase but cannot decrease. In other words, entropy can be created but not destroyed. So, the statement is true.
02

Statement (b)

To determine if this process is spontaneous, we need to consider the overall entropy change in the system and the surroundings. If the total entropy change is positive, the process is spontaneous according to the second law of thermodynamics. Total entropy change is the sum of the entropy change of the system and the surroundings, which is: \(1.2 J/K + (-1.2 J/K) = 0 J/K\). Since the total entropy change is zero, the process is not spontaneous, and the statement is false.
03

Statement (c)

To determine if this process is reversible, we can again consider the overall entropy change in the system and the surroundings. For a process to be reversible, the total entropy change must be zero. In this case, the total entropy change is: \(1.3 J/K + (-1.2 J/K) = 0.1 J/K\), which is not zero. Thus, the process is not reversible, and the statement is false.

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Most popular questions from this chapter

The \(K_{b}\) for methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)\) at \(25^{\circ} \mathrm{C}\) is given in Appendix \(D\). (a) Write the chemical equation for the equilibrium that corresponds to \(K_{b}\). (b) By using the value of \(K_{b}\), calculate \(\Delta G^{\circ}\) for the equilibrium in part (a). (c) What is the value of \(\Delta G\) at equilibrium? (d) What is the value of \(\Delta G\) when $\left[\mathrm{H}^{+}\right]=6.7 \times 10^{-9} \mathrm{M},\left[\mathrm{CH}_{3} \mathrm{NH}_{3}^{+}\right]=2.4 \times 10^{-3} \mathrm{M}$ and \(\left[\mathrm{CH}_{3} \mathrm{NH}_{2}\right]=0.098 \mathrm{M} ?\)

The value of \(K_{a}\) for nitrous acid \(\left(\mathrm{HNO}_{2}\right)\) at \(25^{\circ} \mathrm{C}\) is given in Appendix D. (a) Write the chemical equation for the equilibrium that corresponds to \(K_{a}\). (b) By using the value of \(K_{a}\) calculate \(\Delta G^{\circ}\) for the dissociation of nitrous acid in aqueous solution. (c) What is the value of \(\Delta G\) at equilibrium? (d) What is the value of \(\Delta G\) when $\left[\mathrm{H}^{+}\right]=5.0 \times 10^{-2} \mathrm{M}\(, \)\left[\mathrm{NO}_{2}^{-}\right]=6.0 \times 10^{-4} \mathrm{M},\( and \)\left[\mathrm{HNO}_{2}\right]=0.20 \mathrm{M} ?$

(a) In a chemical reaction, two gases combine to form a solid. What do you expect for the sign of \(\Delta S ?\) (b) How does the entropy of the system change in the processes described in Exercise \(19.12 ?\)

Indicate whether each of the following statements is trueor false. If it is false, correct it. (a) The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends entirely on the value of $\Delta H\( for the process \)\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) .$ (b) The reaction of \(\mathrm{Na}(s)\) with \(\mathrm{Cl}_{2}(g)\) to form \(\mathrm{NaCl}(s)\) is a spontaneous process. (c) A spontaneous process can in principle be conducted reversibly. (d) Spontaneous processes in general require that work be done to force them to proceed. (e) Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system.

The reaction $$ \mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{~S}(g) \rightleftharpoons 3 \mathrm{~S}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) $$ is the basis of a suggested method for removal of \(\mathrm{SO}_{2}\) from power-plant stack gases. The standard free energy of each substance is given in Appendix C. (a) What is the equilibrium constant for the reaction at $298 \mathrm{~K} ?(\mathbf{b})$ In principle, is this reaction a feasible method of removing \(\mathrm{SO}_{2}\) ? (c) If \(P_{5 \mathrm{O}_{2}}=P_{\mathrm{H}_{2}}\) s and the vapor pressure of water is \(3.33 \mathrm{kPa}\), calculate the equilibrium \(\mathrm{SO}_{2}\) pressure in the system at \(298 \mathrm{~K}\). (d) Would you expect the process to be more or less effective at higher temperatures?
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