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Chapter 19: Problem 39

For each of the following pairs, predict which substance has the higher entropy per mole at a given temperature: (a) \(\mathrm{I}_{2}(s)\) or \(\mathrm{I}_{2}(g)\) (b) \(\mathrm{O}_{2}(g)\) at \(50.7 \mathrm{kPa}\) or \(\mathrm{O}_{2}\) at \(101.3 \mathrm{kPa}\) (c) 1 molof \(\mathrm{N}_{2}\) in 22.4 Lor \(1 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) in \(44.8 \mathrm{~L}\). (d) \(\mathrm{CH}_{3} \mathrm{OH}(I)\) or \(\mathrm{CH}_{3} \mathrm{OH}(s)\)

Short Answer

Expert verified
In summary: (a) \(\mathrm{I}_{2}(g)\) has higher entropy than \(\mathrm{I}_{2}(s)\). (b) \(\mathrm{O}_{2}(g)\) at \(50.7 \mathrm{kPa}\) has higher entropy than \(\mathrm{O}_{2}(g)\) at \(101.3 \mathrm{kPa}\). (c) \(\mathrm{N}_{2}\) in \(44.8 \mathrm{~L}\) has higher entropy than \(\mathrm{N}_{2}\) in \(22.4 \mathrm{~L}\). (d) \(\mathrm{CH}_{3}\mathrm{OH}(l)\) has higher entropy than \(\mathrm{CH}_{3}\mathrm{OH}(s)\).

Step by step solution

01

Pair (a) Analysis

For iodine, we have to compare the entropy of the solid phase and the gas phase. As mentioned, entropy is higher for gases than for solids.
02

Pair (a) Conclusion

In pair (a), Iodine gas (\(\mathrm{I}_{2}(g)\)) has the higher entropy per mole at a given temperature compared to solid iodine (\(\mathrm{I}_{2}(s)\)).
03

Pair (b) Analysis

In this case, we have to compare the entropy of oxygen gas at two different pressures. As pressure increases, entropy decreases.
04

Pair (b) Conclusion

In pair (b), oxygen gas (\(\mathrm{O}_{2}\)) at \(50.7 \mathrm{kPa}\) pressure has higher entropy per mole at a given temperature compared to oxygen gas at \(101.3 \mathrm{kPa}\).
05

Pair (c) Analysis

In this case, we have to compare the entropy of 1 mole of nitrogen gas in different volumes. As volume increases, entropy also increases.
06

Pair (c) Conclusion

In pair (c), 1 mole of nitrogen gas in 44.8 L (\(\mathrm{N}_{2}\) in \(44.8 \mathrm{~L}\)) has higher entropy per mole at a given temperature compared to 1 mole of nitrogen gas in 22.4 L (\(\mathrm{N}_{2}\) in 22.4 L).
07

Pair (d) Analysis

For methanol (\(\mathrm{CH}_{3}\mathrm{OH}\)), we have to compare the entropy of the liquid phase and the solid phase. As mentioned, entropy is higher for liquids than for solids.
08

Pair (d) Conclusion

In pair (d), liquid methanol (\(\mathrm{CH}_{3}\mathrm{OH}(l)\)) has higher entropy per mole at a given temperature compared to solid methanol (\(\mathrm{CH}_{3}\mathrm{OH}(s)\)).

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Most popular questions from this chapter

Most liquids follow Trouton's rule (see Exercise 19.93 ), which states that the molar entropy of vaporization is approximately $88 \pm 5 \mathrm{~J} / \mathrm{mol}-\mathrm{K}$. The normal boiling points and enthalpies of vaporization of several organic liquids are as follows: \begin{tabular}{lcc} \hline & Normal Boiling & \\ Substance & Point \(\left({ }^{\circ} \mathrm{C}\right)\) & $\Delta H_{\text {vap }}(\mathrm{k} / / \mathrm{mol})$ \\ \hline Acetone, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}\) & 56.1 & 29.1 \\\ Dimethyl ether, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{O}\) & -24.8 & 21.5 \\\ Ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) & 78.4 & 38.6 \\ Octane, \(\mathrm{C}_{\mathrm{s}} \mathrm{H}_{18}\) & 125.6 & 34.4 \\ Pyridine, \(\mathrm{C}_{5} \mathrm{H}_{\mathrm{S}} \mathrm{N}\) & 115.3 & 35.1 \\\ \hline \end{tabular} (a) Calculate \(\Delta S_{\text {vap }}\) for each of the liquids. Do all the liquids obey Trouton's rule? (b) With reference to intermolecular forces (Section 11.2), can you explain any exceptions to the rule? (c) Would you expect water to obey Trouton's rule? By using data in Appendix \(\mathrm{B}\), check the accuracy of your conclusion. (d) Chlorobenzene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Cl}\right)\) boils at \(131.8^{\circ} \mathrm{C}\). Use Trouton's rule to estimate $\Delta H_{\text {vap }}$ for this substance.

Consider a system that consists of two standard playing dice, with the state of the system defined by the sum of the values shown on the top faces. (a) The two arrangements of top faces shown here can be viewed as two possible microstates of the system. Explain. (b) To which state does each microstate correspond? (c) How many possible states are there for the system? (d) Which state or states have the highest entropy? Explain. (e) Which state or states have the lowest entropy? Explain. (f) Calculate the absolute entropy of the two-dice system.

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 \(\mathrm{H}_{2} \mathrm{O}(l) .(\mathbf{b})\) 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?

Consider what happens when a sample of the explosive TNT is detonated under atmospheric pressure. (a) Is the detonation a reversible process? (b) What is the sign of \(q\) for this process? (c) Is w positive, negative, or zero for the process?

Which of the following processes are spontaneous and which are nonspontaneous: (a) mixing of water and ethanol, \((\mathbf{b})\) dissolution of sugar in a cup of hot coffee, (c) formation of oxygen atoms from \(\mathrm{O}_{2}\) molecules at \(\mathrm{STP}\), (d) rusting of iron, (e) formation of glucose from \(\mathrm{CO}_{2}\) and $\mathrm{H}_{2} \mathrm{O}\( at \)\mathrm{STP} ?$
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