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Chapter 19: Problem 88

For each of the following processes, indicate whether the signs of \(\Delta S\) and \(\Delta H\) are expected to be positive, negative, or about zero. (a) A solid sublimes. (b) The temperature of a sample of \(\mathrm{Co}(s)\) is lowered from \(60^{\circ} \mathrm{C}\) to \(25^{\circ} \mathrm{C}\) . ( ) Ethyl alcohol evaporates from a beaker. (d) A diatomic molecule dissociates into atoms. (e) A piece of charcoal is combusted to form \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g)\)

Short Answer

Expert verified
(a) \(\Delta S > 0\), \(\Delta H > 0\). (b) \(\Delta S < 0\), \(\Delta H < 0\). (c) \(\Delta S > 0\), \(\Delta H > 0\). (d) \(\Delta S > 0\), \(\Delta H > 0\). (e) \(\Delta S > 0\), \(\Delta H < 0\).

Step by step solution

01

(a) A solid sublimes.

In the process of sublimation, a solid directly turns into a gas, without passing through the liquid phase. This process results in an increase in disorder, as the substance moves from a more ordered solid state to a less ordered gas state. Hence, the entropy change \(\Delta S\) is expected to be positive. Sublimation is an endothermic process, meaning that the system absorbs energy from its surroundings. This absorbed energy increases the heat content of the system. Therefore, the enthalpy change \(\Delta H\) is expected to be positive.
02

(b) The temperature of a sample of \(\mathrm{Co}(s)\) is lowered from \(60^{\circ} \mathrm{C}\) to \(25^{\circ} \mathrm{C}\).

Lowering the temperature of a system leads to a decrease in its molecular motion or the kinetic energy, which results in a decrease in disorder. Therefore, \(\Delta S\) is expected to be negative in this case. Lowering the temperature of a substance decreases its energy content as heat is released into the surroundings. Hence, the enthalpy change \(\Delta H\) is expected to be negative in this case.
03

(c) Ethyl alcohol evaporates from a beaker.

When a liquid evaporates, it turns into a gas. This process increases the disorder or randomness of the molecules, as they move from a more ordered liquid phase to a less ordered gas phase. Therefore, the entropy change \(\Delta S\) is expected to be positive. Evaporation is an endothermic process, as the liquid absorbs energy from its surroundings to change into a gas. Thus, the enthalpy change \(\Delta H\) is expected to be positive in this case.
04

(d) A diatomic molecule dissociates into atoms.

When a diatomic molecule dissociates into atoms, it breaks a chemical bond, which increases the disorder of the system. Therefore, the entropy change \(\Delta S\) is expected to be positive. Dissociation requires energy to break the chemical bond between the atoms, making it an endothermic process. Thus, the enthalpy change \(\Delta H\) is expected to be positive in this case.
05

(e) A piece of charcoal is combusted to form \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2}\mathrm{O}(g)\).

Combustion is an exothermic process, meaning that heat is released into the surroundings. In this process, the piece of charcoal undergoes a chemical reaction, and as a result, the change in entropy depends on the balance between the decrease in entropy due to the combustion reaction and the increase in entropy as the products are formed in the gas phase. Overall, the entropy change \(\Delta S\) is positive due to the greater number of gas product molecules compared to the solid reactants. Because the combustion process releases heat into the surroundings, the enthalpy change \(\Delta H\) is expected to be negative.

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Most popular questions from this chapter

Free Energy and Equilibrium (Section) Consider the reaction 2 \(\mathrm{NO} 2(g) \rightarrow \mathrm{N} 2 \mathrm{O} 4(g) .\) (a) Using data from Appendix C, calculate \(\Delta G^{\circ}\) at 298 \(\mathrm{K}\) (b) Calculate \(\Delta G\) at 298 \(\mathrm{K}\) if the partial pressures of \(\mathrm{NO} 2\) and \(\mathrm{N} 2 \mathrm{O} 4\) are 0.40 atm and 1.60 atm, respectively.

In each of the following pairs, which compound would you expect to have the higher standard molar entropy: (a) \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\) or \(\mathrm{C}_{2} \mathrm{H}_{6}(g),(\mathbf{b}) \mathrm{CO}_{2}(g)\) or \(\mathrm{CO}(g) ?\)

(a) What is the difference between a state and a microstate of a system? (b) As a system goes from state A to state \(B,\) its entropy decreases. What can you say about the number of microstates corresponding to each state? (c) In a particular spontaneous process, the number of microstates available to the system decreases. What can you conclude about the sign of \(\Delta S_{\text { surr }}\) ?

Using data from Appendix \(\mathrm{C}\) , calculate \(\Delta G^{\circ}\) for the following reactions. Indicate whether each reaction is spontaneous at 298 \(\mathrm{K}\) under standard conditions. $$ \begin{array}{l}{\text { (a) } 2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AgCl}(s)} \\ {\text { (b) } \mathrm{P}_{4} \mathrm{O}_{10}(s)+16 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)} \\ {\text { (c) } \mathrm{CH}_{4}(g)+4 \mathrm{F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)} \\ {\text { (d) } 2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)}\end{array} $$

Indicate whether each statement is true or false. (a) The third law of thermodynamics says the entropy of a perfect, pure crystal at absolute zero increases with the mass of the crystal. (b) "Translational motion" of molecules refers to their change in spatial location as a func-tion of time. ( c ) "Rotational" and "vibrational" motions contribute to the entropy in atomic gases like He and Xe.(d) The larger the number of atoms in a molecule, the more degrees of freedom of rotational and vibrational motion it likely has.
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