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Chapter 19: Problem 53

Using \(S^{\circ}\) values from Appendix C, calculate \(\Delta S^{\circ}\) values for the following reactions. In each case account for the sign of \(\Delta S^{\circ} .\) (a) \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)\) (b) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) (c) \(\mathrm{Be}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{BeO}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) (d) \(2 \mathrm{CH}_{3} \mathrm{OH}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\)

Short Answer

Expert verified
The calculated \(\Delta S^{\circ}\) values for the reactions are: (a) \(\Delta S^{\circ}_{1} = S^{\circ}(C_2H_6) - [S^{\circ}(C_2H_4) + S^{\circ}(H_2)]\) (b) \(\Delta S^{\circ}_{2} = 2 \cdot S^{\circ}(NO_2) - S^{\circ}(N_2O_4)\) (c) \(\Delta S^{\circ}_{3} = [S^{\circ}(BeO) + S^{\circ}(H_2O_{(g)})] - S^{\circ}(Be(OH)_2_{(s)})\) (d) \(\Delta S^{\circ}_{4} = [2 \cdot S^{\circ}(CO_2) + 4 \cdot S^{\circ}(H_2O_{(g)})] - [2 \cdot S^{\circ}(CH_3OH_{(g)}) + 3 \cdot S^{\circ}(O_2)]\) Substitute the standard entropy values from Appendix C for each species and calculate the sum of entropies for reactants and products. The sign of \(\Delta S^{\circ}\) depends on whether the sum of the products' entropy is greater or lesser than the sum of the reactants' entropy.

Step by step solution

01

(a) Calculate \(\Delta S^{\circ}\) for the first reaction.

For the first reaction, we have: C2H4(g) + H2(g) → C2H6(g) To calculate the \(\Delta S^{\circ}\), substitute the standard entropy values of each species from Appendix C into the formula, then calculate the sum of entropies for reactants and products, and find the difference. \(\Delta S^{\circ}_{1} = S^{\circ}(C_2H_6) - [S^{\circ}(C_2H_4) + S^{\circ}(H_2)]\)
02

(b) Calculate \(\Delta S^{\circ}\) for the second reaction.

For the second reaction, we have: N2O4(g) → 2NO2(g) To calculate the \(\Delta S^{\circ}\), substitute the standard entropy values of each species from Appendix C into the formula, then calculate the sum of entropies for reactants and products, and find the difference. \(\Delta S^{\circ}_{2} = 2 \cdot S^{\circ}(NO_2) - S^{\circ}(N_2O_4)\)
03

(c) Calculate \(\Delta S^{\circ}\) for the third reaction.

For the third reaction, we have: Be(OH)2(s) → BeO(s) + H2O(g) To calculate the \(\Delta S^{\circ}\), substitute the standard entropy values of each species from Appendix C into the formula, then calculate the sum of entropies for reactants and products, and find the difference. \(\Delta S^{\circ}_{3} = [S^{\circ}(BeO) + S^{\circ}(H_2O_{(g)})] - S^{\circ}(Be(OH)_2_{(s)})\)
04

(d) Calculate \(\Delta S^{\circ}\) for the fourth reaction.

For the fourth reaction, we have: 2CH3OH(g) + 3O2(g) → 2CO2(g) + 4H2O(g) To calculate the \(\Delta S^{\circ}\), substitute the standard entropy values of each species from Appendix C into the formula, then calculate the sum of entropies for reactants and products, and find the difference. \(\Delta S^{\circ}_{4} = [2 \cdot S^{\circ}(CO_2) + 4 \cdot S^{\circ}(H_2O_{(g)})] - [2 \cdot S^{\circ}(CH_3OH_{(g)}) + 3 \cdot S^{\circ}(O_2)]\) Now, refer to Appendix C to substitute the \(S^{\circ}\) values and then calculate \(\Delta S^{\circ}\) for each reaction. The sign of \(\Delta S^{\circ}\) will be determined by whether the entropy of the products is greater or lesser than the entropy of the reactants.

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Most popular questions from this chapter

For the isothermal expansion of a gas into a vacuum, \(\Delta E=0, q=0\), and \(w=0\). (a) Is this a spontaneous process? (b) Explain why no work is done by the system during this process. (c) In thermodynamics, what is the "driving force" for the expansion of the gas?

About \(86 \%\) of the world's electrical energy is produced by using steam turbines, a form of heat engine. In his analysis of an ideal heat engine, Sadi Carnot concluded that the maximum possible efficiency is defined by the total work that could be done by the engine, divided by the quantity of heat available to do the work (for example, from hot steam produced by combustion of a fuel such as coal or methane). This efficiency is given by the ratio \(\left(T_{\text {high }}-T_{\text {low }}\right) / T_{\text {high }}\), where \(T_{\text {high }}\) is the temperature of the heat going into the engine and \(T_{\text {low }}\) is that of the heat leaving the engine. (a) What is the maximum possible efficiency of a heat engine operating between an input temperature of \(700 \mathrm{~K}\) and an exit temperature of \(288 \mathrm{~K} ?\) (b) Why is it important that electrical power plants be located near bodies of relatively cool water? (c) Under what conditions could a heat engine operate at or near \(100 \%\) efficiency? (d) It is often said that if the energy of combustion of a fuel such as methane were captured in an electrical fuel cell instead of by burning the fuel in a heat engine, a greater fraction of the energy could be put to useful work. Make a qualitative drawing like that in Figure 5.10 that illustrates the fact that in principle the fuel cell route will produce more useful work than the heat engine route from combustion of methane.

As shown here, one type of computer keyboard cleaner contains liquefied 1,1 -difluoroethane \(\left(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{~F}_{2}\right),\) which is a gas at atmospheric pressure. When the nozzle is squeezed, the 1,1 -difluoroethane vaporizes out of the nozzle at high pressure, blowing dust out of objects. (a) Based on your experience, is the vaporization a spontaneous process at room temperature? (b) Defining the 1,1 -difluoroethane as the system, do you expect \(q_{\mathrm{sys}}\) for the process to be positive or negative? Explain. (c) Predict whether \(\Delta S\) is positive or negative for this process. (d) Given your answers to (a), (b), and (c), do you think the operation of this product depends more on heat flow or more on entropy change?

Consider the reaction $$ \mathrm{PbCO}_{3}(s) \rightleftharpoons \mathrm{PbO}(s)+\mathrm{CO}_{2}(g) $$ Using data in Appendix C, calculate the equilibrium pressure of \(\mathrm{CO}_{2}\) in the system at (a) \(400^{\circ} \mathrm{C}\) and (b) \(180^{\circ} \mathrm{C}\).

Acetylene gas, \(\mathrm{C}_{2} \mathrm{H}_{2}(g),\) is used in welding. (a) Write a balanced equation for the combustion of acetylene gas to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\). (b) How much heat is produced in burning \(1 \mathrm{~mol}\) of \(\mathrm{C}_{2} \mathrm{H}_{2}\) under standard conditions if both reactants and products are brought to \(298 \mathrm{~K}\) ? (c) What is the maximum amount of useful work that can be accomplished under standard conditions by this reaction?
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