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Chapter 19: Problem 40

For each of the following pairs, predict which substance possesses the larger entropy per mole: (a) \(1 \mathrm{~mol}\) of \(\mathrm{O}_{2}(g)\) at \(300^{\circ} \mathrm{C}, 1.013 \mathrm{kPa},\) or \(1 \mathrm{~mol}\) of \(\mathrm{O}_{3}(g)\) at \(300^{\circ} \mathrm{C}, 1.013 \mathrm{kPa} ;\) (b) \(1 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{O}(g)\) at $100^{\circ} \mathrm{C}, 101.3 \mathrm{kPa}\(, or \)1 \mathrm{~mol}\( of \)\mathrm{H}_{2} \mathrm{O}(l)$ at $100^{\circ} \mathrm{C}, 101.3 \mathrm{kPa} ;(\mathbf{c}) 0.5 \mathrm{~mol}\( of \)\mathrm{N}_{2}(g)\( at \)298 \mathrm{~K}, 20-\mathrm{L}$. vol- ume, or \(0.5 \mathrm{~mol} \mathrm{CH}_{4}(g)\) at $298 \mathrm{~K}, 20-\mathrm{L}$ volume; (d) \(100 \mathrm{~g}\) \(\mathrm{Na}_{2} \mathrm{SO}_{4}(s)\) at \(30^{\circ} \mathrm{C}\) or $100 \mathrm{~g} \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)\( at \)30^{\circ} \mathrm{C}$

Short Answer

Expert verified
(a) 1 mole of O3(g) at 300°C and 1.013kPa has the larger entropy per mole. (b) 1 mole of H2O(g) at 100°C and 101.3kPa has the larger entropy per mole. (c) 0.5 mole of CH4(g) at 298K and 20L volume has the larger entropy per mole. (d) 100g Na2SO4(aq) at 30°C has the larger entropy per mole.

Step by step solution

01

Compare the molecular complexity

Both O2 and O3 are gases. O3 molecule has a more complex structure than O2 molecule which results in a larger entropy per mole for O3. Therefore, 1 mole of O3(g) at 300°C and 1.013kPa has the larger entropy per mole. (b) Comparing 1 mole of H2O(g) and 1 mole of H2O(l)
02

Compare the molecular phase

Here, we have one mole of the same substance but in different phases. Gaseous phase has more entropy per mole than the liquid phase as the molecules are more disordered. Therefore, 1 mole of H2O(g) at 100°C and 101.3kPa has the larger entropy per mole. (c) Comparing 0.5 mole of N2(g) and 0.5 mole of CH4(g)
03

Compare the molecular complexity once again

Both N2 and CH4 are in gaseous phase and both have 0.5 mole under the same condition of temperature and volume. However, CH4 molecule is more complex than N2 molecule which results in a larger entropy per mole for CH4. Therefore, 0.5 mole of CH4(g) at 298K and 20L volume has the larger entropy per mole. (d) Comparing 100g Na2SO4(s) and 100g Na2SO4(aq)
04

Compare the ionic solvation and solution formation

In this case, Na2SO4 is in a solid-state and an aqueous solution. When a solute dissolves in a solvent forming a solution, the entropy of the solution gets increased. In the aqueous solution, the ions get hydrated and increase their entropy. Therefore, 100g Na2SO4(aq) at 30°C has the larger entropy per mole.

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Most popular questions from this chapter

Consider the following process: a system changes from state 1 (initial state) to state 2 (final state) in such a way that its temperature changes from $300 \mathrm{~K}\( to \)400 \mathrm{~K}$. (a) Is this process isothermal? (b) Does the temperature change depend on the particular pathway taken to carry out this change of state? (c) Does the change in the internal energy, \(\Delta E\), depend on whether the process is reversible or irreversible?

(a) What sign for \(\Delta S\) do you expect when the pressure on 0.600 mol of an ideal gas at \(350 \mathrm{~K}\) is increased isothermally from an initial pressure of \(76.0 \mathrm{kPa} ?(\mathbf{b})\) If the final pressure on the gas is \(121.6 \mathrm{kPa}\), calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change?

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} ?$

When most elastomeric polymers (e.g., a rubber band) are stretched, the molecules become more ordered, as illustrated here: Suppose you stretch a rubber band. (a) Do you expect the entropy of the system to increase or decrease? (b) If the rubber band were stretched isothermally, would heat need to be absorbed or emitted to maintain constant temperature? (c) Try this experiment: Stretch a rubber band and wait a moment. Then place the stretched rubber band on your upper lip, and let it return suddenly to its unstretched state (remember to keep holding on!). What do you observe? Are your observations consistent with your answer to part (b)?

Use data from Appendix \(C\) to calculate the equilibrium constant, \(K,\) and \(\Delta G^{\circ}\) at \(298 \mathrm{~K}\) for each of the following reactions: (a) \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{HI}(g)\) (b) $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g)$ (c) $3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{6}(g)$
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