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Chapter 19: Problem 48

Predict which member of each of the following pairs has the greater standard entropy at \(25^{\circ} \mathrm{C}:\) (a) \(\mathrm{C}_{6} \mathrm{H}_{6}(l)\) or \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\), (b) \(\mathrm{CO}(g)\) or \(\mathrm{CO}_{2}(g)\) (c) \(1 \mathrm{~mol} \mathrm{~N}_{2} \mathrm{O}_{4}(g)\) or $2 \mathrm{~mol} \mathrm{NO}_{2}(g)$ (d) \(\mathrm{HCl}(g)\) or \(\mathrm{HCl}(a q) .\) Use Appendix \(\mathrm{C}\) to find the standard entropy of each substance.

Short Answer

Expert verified
In summary, the substances with greater standard entropy at $25^{\circ} \mathrm{C}$ in each pair are: (a) \( C_6H_6(g) \) (b) \( CO_2(g) \) (c) \( 2 \thinspace mol \thinspace NO_2(g) \) (d) \( HCl(g) \)

Step by step solution

01

Examine phase changes

In general, the gas phase of a substance has a higher standard entropy than the liquid or solid phase, as gas particles are more spread out and have more potential to move freely. (a) C6H6(l) or C6H6(g) Since C6H6(g) is in the gas phase and C6H6(l) is in liquid phase, the standard entropy of C6H6(g) will be greater.
02

Compare molecular complexity

When comparing molecules, more complex or larger molecules tend to have a greater standard entropy due to increased molecular vibration. (b) CO(g) or CO2(g) CO2(g) is a larger and more complex molecule than CO(g). Therefore, the standard entropy of CO2(g) will be greater.
03

Consider stoichiometry

If a reaction involves more moles of gaseous products than reactants, the products will generally have a greater standard entropy. (c) 1 mol N2O4(g) or 2 mol NO2(g) The reaction involves the decomposition of N2O4(g) to form 2 moles of NO2(g). Since there are more moles of gas in the products, the standard entropy of 2 mol NO2(g) will be greater.
04

Examine a combination of phase change and dissociation in solution

When a gaseous substance dissolves in a liquid, the standard entropy will generally decrease due to increased intermolecular interactions and a decrease in randomness. (d) HCl(g) or HCl(aq) HCl(aq) involves the dissociation of HCl(g) in water. Since the gas particles become restrained in the solution, the standard entropy of HCl(g) will be greater. In summary, the substances with greater standard entropy in each pair are: (a) C6H6(g) (b) CO2(g) (c) 2 mol NO2(g) (d) HCl(g)

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Most popular questions from this chapter

Consider a system consisting of an ice cube. (a) Under what conditions can the ice cube melt reversibly? (b) If the ice cube melts reversibly, is \(\Delta H\) zero for the process?

For a certain chemical reaction, $\Delta H^{\circ}=-40.0 \mathrm{k} \mathrm{J}\( and \)\Delta S^{\circ}=-150.0 \mathrm{~J} / \mathrm{K}$. (a) Does the reaction lead to an increase or decrease in the randomness or disorder of the system? (b) Does the reaction lead to an increase or decrease in the randomness or disorder of the surroundings? (c) Calculate \(\Delta G^{\circ}\) for the reaction at \(298 \mathrm{~K}\). (d) Is the reaction spontaneous at $298 \mathrm{~K}$ under standard conditions?

Consider the reaction $2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$ (a) Using data from Appendix \(\mathrm{C},\) calculate \(\Delta G^{\circ}\) at \(298 \mathrm{~K}\). (b) Calculate \(\Delta G\) at \(298 \mathrm{~K}\) if the partial pressures of all gases are \(33.4 \mathrm{kPa}\).

Using \(S^{\circ}\) values from Appendix \(\mathrm{C}\), calculate $\Delta S^{\circ}$ values for the following reactions. In each case, account for the sign of \(\Delta S\). (a) $\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow \mathrm{NH}_{4}^{+}(a q)+\mathrm{Cl}^{-}(a q)$ (b) $\mathrm{CH}_{3} \mathrm{OH}(g) \longrightarrow \mathrm{CO}(g)+2 \mathrm{H}_{2}(g)$ (c) $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$ (d) $\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$

(a) What do you expect for the sign of \(\Delta S\) in a chemical reaction in which 3 mol of gaseous reactants are converted to 2 mol of gaseous products? (b) For which of the processes in Exercise 19.11 does the entropy of the system increase?
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