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Chapter 18: Problem 9

For each pair of substances listed here, choose the one having the larger standard entropy value at \(25^{\circ} \mathrm{C}\). The same molar amount is used in the comparison. Explain the basis for your choice. (a) \(\operatorname{Li}(s)\) or \(\operatorname{Li}(l)\) (b) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\) or \(\mathrm{CH}_{3} \mathrm{OCH}_{3}(l)\) (c) \(\operatorname{Ar}(g)\) or \(\operatorname{Xe}(g)\) (d) \(\mathrm{CO}(g)\) or \(\mathrm{CO}_{2}(g)\) (e) \(\mathrm{O}_{2}(g)\) or \(\mathrm{O}_{3}(g)\) (f) \(\mathrm{NO}_{2}(g)\) or \(\mathrm{N}_{2} \mathrm{O}_{4}(g)\)

Short Answer

Expert verified
The substance with the larger standard entropy value for each pair are: (a) Li(l), (b) C2H5OH(l), (c) Xe(g), (d) CO2(g), (e) O3(g), and (f) N2O4(g).

Step by step solution

01

Understanding entropy of different states

Entropy is higher in substances that are in the liquid state than in the solid state and is highest in the gaseous state. Therefore, for (a), Li(l) has a larger standard entropy value than Li(s). In a similar way, it can be stated that all gaseous substances will have a higher standard entropy value than substances in the liquid or solid state because gases have more disorder and randomness.
02

Complexity of Molecular structure

Next, we look at the complexity of the molecular structure. More complex molecules with more atoms have higher entropy because there are more possible arrangements of the atoms. For (b), C2H5OH and CH3OCH3, both substances are in the same state. But, C2H5OH has more atoms and a more complex structure than CH3OCH3, therefore C2H5OH has a larger standard entropy value.
03

Size of the Atoms

When comparing monoatomic gases as in (c), the larger atoms have more entropy because they have more electronic energy levels and therefore more possible microstates. So Xe(g) has a larger standard entropy value than Ar(g).
04

Number of Atoms in the Molecule

For molecules in the same physical state, a molecule with more atoms will have higher entropy. In CO2 there are 3 atoms, while in CO there are only 2, therefore CO2(g) has a larger standard entropy value than CO(g). Similarly, for (e), O3(g) has more atoms than O2(g), therefore it has a larger standard entropy value. And in (f), N2O4(g) has more atoms than NO2(g), so it has a larger standard entropy value.

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Most popular questions from this chapter

For reactions carried out under standard-state conditions, Equation (18.10) takes the form \(\Delta G^{\circ}=\Delta H^{\circ}-\) \(T \Delta S^{\circ} .\) (a) Assuming \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) are independent of temperature, derive the equation $$\ln \frac{K_{2}}{K_{1}}=\frac{\Delta H^{\circ}}{R}\left(\frac{T_{2}-T_{1}}{T_{1} T_{2}}\right)$$ where \(K_{1}\) and \(K_{2}\) are the equilibrium constants at \(T_{1}\) and \(T_{2}\), respectively. (b) Given that at \(25^{\circ} \mathrm{C} K_{\mathrm{c}}\) is \(4.63 \times 10^{-3}\) for the reaction $$ \mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) \quad \Delta H^{\circ}=58.0 \mathrm{~kJ} / \mathrm{mol} $$ calculate the equilibrium constant at \(65^{\circ} \mathrm{C}\)

Explain the following nursery rhyme in terms of the second law of thermodynamics. Humpty Dumpty sat on a wall; Humpty Dumpty had a great fall. All the King's horses and all the King's men Couldn't put Humpty together again.

For a reaction with a negative \(\Delta G^{\circ}\) value, which of the following statements is false? (a) The equilibrium constant \(K\) is greater than one, (b) the reaction is spontaneous when all the reactants and products are in their standard states, and (c) the reaction is always exothermic.

State whether the sign of the entropy change expected for each of the following processes will be positive or negative, and explain your predictions. (a) \(\mathrm{PCl}_{3}(l)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{PCl}_{5}(s)\) (b) \(2 \mathrm{HgO}(s) \longrightarrow 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g)\) (c) \(\mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{H}(g)\) (d) \(\mathrm{U}(s)+3 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{UF}_{6}(s)\)

Define free energy. What are its units?
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