Exercises

What is a nonspontaneous reaction?

A helium-filled balloon spontaneously deflates overnight as He atoms diffuse through the wall of the balloon. Describe the redistribution of matter and/or energy that accompanies this process.

In Figure 12.8 all possible distributions and microstates are shown for four different particles shared between two boxes. Determine the entropy change, ΔS, if the particles are initially evenly distributed between the two boxes, but upon redistribution all end up in Box (b).

How does the process described in the previous item relate to the system shown in Figure 12.4?

Consider the system shown in Figure 12.9. What is the change in entropy for the process where the energy is initially associated only with particle A, but in the final state the energy is distributed between two different particles?

Arrange the following sets of systems in order of increasing entropy. Assume one mole of each substance and the same temperature for each member of a set.

(a) H₂(g), HBrO₄(g), HBr(g)

(b) H₂O(l), H₂O(g), H₂O(s)

(c) He(g), Cl₂(g), P₄(g)

Consider two processes: sublimation of I₂(s) and melting of I₂(s) (Note: the latter process can occur at the same temperature but somewhat higher pressure).

${\text{I}}_2(s)⟶{\text{I}}_2(g)$

${\text{I}}_2(s)⟶{\text{I}}_2(l)$

Is ΔS positive or negative in these processes? In which of the processes will the magnitude of the entropy change be greater?

Predict the sign of the entropy change for the following processes.

(a) An ice cube is warmed to near its melting point.

(b) Exhaled breath forms fog on a cold morning.

(c) Snow melts.

Write the balanced chemical equation for the combustion of methane, CH₄(g), to give carbon dioxide and water vapor. Explain why it is difficult to predict whether ΔS is positive or negative for this chemical reaction.

What is the difference between ΔS and ΔS° for a chemical change?

Determine the entropy change for the combustion of liquid ethanol, C₂H₅OH, under the standard conditions to give gaseous carbon dioxide and liquid water.

“Thermite” reactions have been used for welding metal parts such as railway rails and in metal refining. One such thermite reaction is ${\text{Fe}}_2{\text{O}}_3(s)+2\text{Al}(s)⟶{\text{Al}}_2{\text{O}}_3(s)+2\text{Fe}(s).$ Is the reaction spontaneous at room temperature under standard conditions? During the reaction, the surroundings absorb 851.8 kJ/mol of heat.

From the following information, determine $\text{Δ}S\text{°}$ for the following:

$\text{N}(g)+\text{O}(g)⟶\text{NO}(g)\text{Δ}S\text{°}=?$

${\text{N}}_2(g)+{\text{O}}_2(g)⟶2\text{NO}(g)\text{Δ}S\text{°}=\text{24.8 J/K}$

${\text{N}}_2(g)⟶2\text{N}(g)\text{Δ}S\text{°}=\text{115.0 J/K}$

${\text{O}}_2(g)⟶2\text{O}(g)\text{Δ}S\text{°}=\text{117.0 J/K}$

Use the standard entropy data in Appendix G to determine the change in entropy for each of the following reactions. All the processes occur at the standard conditions and 25 °C.

(a) ${\text{MnO}}_2(s)⟶\text{Mn}(s)+{\text{O}}_2(g)$

(b) ${\text{H}}_2(g)+{\text{Br}}_2(l)⟶\text{2HBr}(g)$

(c) $\text{Cu}(s)+\text{S}(g)⟶\text{CuS}(s)$

(d) $\text{2LiOH}(s)+{\text{CO}}_2(g)⟶{\text{Li}}_2{\text{CO}}_3(s)+{\text{H}}_2\text{O}(g)$

(e) ${\text{CH}}_4(g)+{\text{O}}_2(g)⟶\text{C}(s,\text{graphite})+{\text{2H}}_2\text{O}(g)$

(f) ${\text{CS}}_2(g)+{\text{3Cl}}_2(g)⟶{\text{CCl}}_4(g)+{\text{S}}_2{\text{Cl}}_2(g)$

What is the difference between ΔG and ΔG° for a chemical change?

Explain what happens as a reaction starts with ΔG < 0 (negative) and reaches the point where ΔG = 0.

Use the standard free energy data in Appendix G to determine the free energy change for each of the following reactions, which are run under standard state conditions and 25 °C. Identify each as either spontaneous or nonspontaneous at these conditions.

(a) $\text{C}(s\text{, graphite})+{\text{O}}_2(g)⟶{\text{CO}}_2(g)$

(b) ${\text{O}}_2(g)+{\text{N}}_2(g)⟶\text{2NO}(g)$

(c) $\text{2Cu}(s)+\text{S}(g)⟶{\text{Cu}}_2\text{S}(s)$

(d) $\text{CaO}(s)+{\text{H}}_2\text{O}(l)⟶\text{Ca}{(\text{OH})}_2(s)$

(e) ${\text{Fe}}_2{\text{O}}_3(s)+\text{3CO}(g)⟶\text{2Fe}(s)+{\text{3CO}}_2(g)$

(f) ${\text{CaSO}}_4\text{·}{\text{2H}}_2\text{O}(s)⟶{\text{CaSO}}_4(s)+{\text{2H}}_2\text{O}(g)$

Is the formation of ozone (O₃(g)) from oxygen (O₂(g)) spontaneous at room temperature under standard state conditions?

Among other things, an ideal fuel for the control thrusters of a space vehicle should decompose in a spontaneous exothermic reaction when exposed to the appropriate catalyst. Evaluate the following substances under standard state conditions as suitable candidates for fuels.

(a) Ammonia: ${\text{2NH}}_3(g)⟶{\text{N}}_2(g)+{\text{3H}}_2(g)$

(b) Diborane: ${\text{B}}_2{\text{H}}_6(g)⟶\text{2B}(g)+{\text{3H}}_2(g)$

(c) Hydrazine: ${\text{N}}_2{\text{H}}_4(g)⟶{\text{N}}_2(g)+{\text{2H}}_2(g)$

(d) Hydrogen peroxide: ${\text{H}}_2{\text{O}}_2(l)⟶{\text{H}}_2\text{O}(g)+\frac{1}{2}{\text{O}}_2(g)$

Calculate ΔG° for each of the following reactions from the equilibrium constant at the temperature given.

$\begin{array}{ccccccc}\text{(a)}{\text{Cl}}_2(g)+{\text{Br}}_2(g)⟶\text{2BrCl}(g)\hfill & & & \text{T}=25\text{°C}\hfill & & & K_p=4.7\times {10}^{\text{−2}}\hfill \\ \text{(b)}{\text{2SO}}_2(g)+{\text{O}}_2(g)\rightleftharpoons {\text{2SO}}_3(g)\hfill & & & \text{T}=500\text{°C}\hfill & & & K_p=48.2\hfill \\ \text{(c)}{\text{H}}_2\text{O}(l)\rightleftharpoons {\text{H}}_2\text{O}(g)\hfill & & & \text{T}=60\text{°C}\hfill & & & K_p=\text{0.196}\hfill \\ \text{(d)}\text{CoO}(s)+\text{CO}(g)\rightleftharpoons \text{Co}(s)+{\text{CO}}_2(g)\hfill & & & \text{T}=550\text{°C}\hfill & & & K_p=4.90\times {10}^2\hfill \\ \text{(e)}{\text{CH}}_3{\text{NH}}_2(aq)+{\text{H}}_2\text{O}(l)⟶{\text{CH}}_3{\text{NH}}_3{}^{\text{+}}(aq)+{\text{OH}}^{\text{−}}(aq)\hfill & & & \text{T}=25\text{°C}\hfill & & & K_p=4.4\times {10}^{\text{−4}}\hfill \\ \text{(f)}{\text{PbI}}_2(s)⟶{\text{Pb}}^{\mathrm{2+}}(aq)+{\text{2I}}^{\text{−}}(aq)\hfill & & & \text{T}=25\text{°C}\hfill & & & K_p=8.7\times {10}^{\text{−9}}\hfill \end{array}$

Given that the $\text{Δ}{G}_{\text{f}}^{°}$ for Pb²⁺(aq) and Cl⁻(aq) is −24.3 kJ/mole and −131.2 kJ/mole respectively, determine the solubility product, K_sp, for PbCl₂(s).

Determine the standard enthalpy change, entropy change, and free energy change for the conversion of diamond to graphite. Discuss the spontaneity of the conversion with respect to the enthalpy and entropy changes. Explain why diamond spontaneously changing into graphite is not observed.

In glycolysis, the reaction of glucose (Glu) to form glucose-6-phosphate (G6P) requires ATP to be present as described by the following equation:
$\text{Glu}+\text{ATP}⟶\text{G6P}+\text{ADP}\text{Δ}G\text{°}=\text{−17 kJ}$

In this process, ATP becomes ADP summarized by the following equation:
$\text{ATP}⟶\text{ADP}\text{Δ}G\text{°}=\text{−30 kJ}$

Determine the standard free energy change for the following reaction, and explain why ATP is necessary to drive this process:
$\text{Glu}⟶\text{G6P}\text{Δ}G\text{°}=?$

Without doing a numerical calculation, determine which of the following will reduce the free energy change for the reaction, that is, make it less positive or more negative, when the temperature is increased. Explain.

(a) ${\text{N}}_2(g)+{\text{3H}}_2(g)⟶{\text{2NH}}_3(g)$

(b) $\text{HCl}(g)+{\text{NH}}_3(g)⟶{\text{NH}}_4\text{Cl}(s)$

(c) ${({\text{NH}}_4)}_2{\text{Cr}}_2{\text{O}}_7(s)⟶{\text{Cr}}_2{\text{O}}_3(s)+{\text{4H}}_2\text{O}(g)+{\text{N}}_2(g)$

(d) $\text{2Fe}(s)+{\text{3O}}_2(g)⟶{\text{Fe}}_2{\text{O}}_3(s)$

An important source of copper is from the copper ore, chalcocite, a form of copper(I) sulfide. When heated, the Cu₂S decomposes to form copper and sulfur described by the following equation:
${\text{Cu}}_2\text{S}(s)⟶\text{Cu}(s)+\text{S}(s)$

(a) Determine $\text{Δ}G\text{°}$ for the decomposition of Cu₂S(s).

(b) The reaction of sulfur with oxygen yields sulfur dioxide as the only product. Write an equation that describes this reaction, and determine $\text{Δ}G\text{°}$ for the process.

(c) The production of copper from chalcocite is performed by roasting the Cu₂S in air to produce the Cu. By combining the equations from Parts (a) and (b), write the equation that describes the roasting of the chalcocite, and explain why coupling these reactions together makes for a more efficient process for the production of the copper.