第16章熱力学

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

A reaction has $\text{Δ}H\text{°}$ = 100 kJ/mol and $\text{Δ}S\text{°}=\text{250 J/mol·K.}$ Is the reaction spontaneous at room temperature? If not, under what temperature conditions will it become spontaneous?

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

Use the standard free energy of formation 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) ${\text{MnO}}_2(s)⟶\text{Mn}(s)+{\text{O}}_2(g)$

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

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

Given:
${\text{P}}_4(s)+{\text{5O}}_2(g)⟶{\text{P}}_4{\text{O}}_{10}(s)\text{Δ}G\text{°}=\text{−2697.0 kJ/mol}$
${\text{2H}}_2(g)+{\text{O}}_2(g)⟶{\text{2H}}_2\text{O}(g)\text{Δ}G\text{°}=\text{−457.18 kJ/mol}$
${\text{6H}}_2\text{O}(g)+{\text{P}}_4{\text{O}}_{10}(s)⟶{\text{4H}}_3{\text{PO}}_4(l)\text{Δ}G\text{°}=\text{−428.66 kJ/mol}$

(a) Determine the standard free energy of formation, $\text{Δ}{G}_{\text{f}}^{°},$ for phosphoric acid.

(b) How does your calculated result compare to the value in Appendix G? Explain.

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

Consider the decomposition of red mercury(II) oxide under standard state conditions.
$\text{2HgO}(s,\text{red})⟶\text{2Hg}(l)+{\text{O}}_2(g)$

(a) Is the decomposition spontaneous under standard state conditions?

(b) Above what temperature does the reaction become spontaneous?

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.

(a) ${\text{N}}_2(g)+{\text{O}}_2(g)⟶\text{2NO}(g)\text{T}=2000\text{°C}{K}_p=4.1\times {10}^{\text{−4}}$

(b) ${\text{H}}_2(g)+{\text{I}}_2(g)⟶\text{2HI}(g)\text{T}=400\text{°C}{K}_p=50.0$

(c) ${\text{CO}}_2(g)+{\text{H}}_2(g)⟶\text{CO}(g)+{\text{H}}_2\text{O}(g)\text{T}=980\text{°C}{K}_p=1.67$

(d) ${\text{CaCO}}_3(s)⟶\text{CaO}(s)+{\text{CO}}_2(g)\text{T}=900\text{°C}{K}_p=1.04$

(e) $\text{HF}(aq)+{\text{H}}_2\text{O}(l)⟶{\text{H}}_3{\text{O}}^{\text{+}}(aq)+{\text{F}}^{\text{−}}(aq)\text{T}=25\text{°C}{K}_a=7.2\times {10}^{\text{−4}}$

(f) $\text{AgBr}(s)⟶{\text{Ag}}^{\text{+}}(aq)+{\text{Br}}^{\text{−}}(aq)\text{T}=25\text{°C}{K}_{\mathrm{sp}}=3.3\times {10}^{\text{−13}}$

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

(a) ${\text{Cl}}_2(g)+{\text{Br}}_2(g)⟶\text{2BrCl}(g)\text{T}=25\text{°C}{K}_p=4.7\times {10}^{\text{−2}}$

(b) ${\text{2SO}}_2(g)+{\text{O}}_2(g)\rightleftharpoons {\text{2SO}}_3(g)\text{T}=500\text{°C}{K}_p=48.2$

(c) ${\text{H}}_2\text{O}(l)\rightleftharpoons {\text{H}}_2\text{O}(g)\text{T}=60\text{°C}{K}_p=\text{0.196}$

(d) $\text{CoO}(s)+\text{CO}(g)\rightleftharpoons \text{Co}(s)+{\text{CO}}_2(g)\text{T}=550\text{°C}{K}_p=4.90\times {10}^2$

(e) ${\text{CH}}_3{\text{NH}}_2(aq)+{\text{H}}_2\text{O}(l)⟶{\text{CH}}_3{\text{NH}}_3{}^{\text{+}}(aq)+{\text{OH}}^{\text{−}}(aq)\text{T}=25\text{°C}{K}_b=4.4\times {10}^{\text{−4}}$

(f) ${\text{PbI}}_2(s)⟶{\text{Pb}}^{\mathrm{2+}}(aq)+{\text{2I}}^{\text{−}}(aq)\text{T}=25\text{°C}{K}_{\mathrm{sp}}=8.7\times {10}^{\text{−9}}$

Calculate the equilibrium constant at 25 °C for each of the following reactions from the value of ΔG° given.

(a) ${\text{O}}_2(g)+{\text{2F}}_2(g)⟶{\text{2OF}}_2(g)\text{Δ}G\text{°}=\text{−9.2 kJ}$

(b) ${\text{I}}_2(s)+{\text{Br}}_2(l)⟶\text{2IBr}(g)\text{Δ}G\text{°}=\text{7.3 kJ}$

(c) $\text{2LiOH}(s)+{\text{CO}}_2(g)⟶{\text{Li}}_2{\text{CO}}_3(s)+{\text{H}}_2\text{O}(g)\text{Δ}G\text{°}=\text{−79 kJ}$

(d) ${\text{N}}_2{\text{O}}_3(g)⟶\text{NO}(g)+{\text{NO}}_2(g)\text{Δ}G\text{°}=\text{−1.6 kJ}$

(e) ${\text{SnCl}}_4(l)⟶{\text{SnCl}}_4(l)\text{Δ}G\text{°}=\text{8.0 kJ}$

Calculate the equilibrium constant at 25 °C for each of the following reactions from the value of ΔG° given.

(a) ${\text{I}}_2(s)+{\text{Cl}}_2(g)⟶\text{2ICl}(g)\text{Δ}G\text{°}=\text{−10.88 kJ}$

(b) ${\text{H}}_2(g)+{\text{I}}_2(s)⟶\text{2HI}(g)\text{Δ}G\text{°}=\text{3.4 kJ}$

(c) ${\text{CS}}_2(g)+{\text{3Cl}}_2(g)⟶{\text{CCl}}_4(g)+{\text{S}}_2{\text{Cl}}_2(g)\text{Δ}G\text{°}=\text{−39 kJ}$

(d) ${\text{2SO}}_2(g)+{\text{O}}_2(g)⟶{\text{2SO}}_3(g)\text{Δ}G\text{°}=\text{−141.82 kJ}$

(e) ${\text{CS}}_2(g)⟶{\text{CS}}_2(l)\text{Δ}G\text{°}=\text{−1.88 kJ}$

Calculate the equilibrium constant at the temperature given.

(a) ${\text{O}}_2(g)+{\text{2F}}_2(g)⟶{\text{2F}}_2\text{O}(g)(\text{T}=100\text{°C})$

(b) ${\text{I}}_2(s)+{\text{Br}}_2(l)⟶\text{2IBr}(g)(\text{T}=0.0\text{°C})$

(c) $\text{2LiOH}(s)+{\text{CO}}_2(g)⟶{\text{Li}}_2{\text{CO}}_3(s)+{\text{H}}_2\text{O}(g)(\text{T}=575\text{°C})$

(d) ${\text{N}}_2{\text{O}}_3(g)⟶\text{NO}(g)+{\text{NO}}_2(g)(\text{T}=\mathrm{-10.0}\text{°C})$

(e) ${\text{SnCl}}_4(l)⟶{\text{SnCl}}_4(g)(\text{T}=200\text{°C})$

Calculate the equilibrium constant at the temperature given.

(a) ${\text{I}}_2(s)+{\text{Cl}}_2(g)⟶\text{2ICl}(g)(\text{T}=100\text{°C})$

(b) ${\text{H}}_2(g)+{\text{I}}_2(s)⟶\text{2HI}(g)(\text{T}=0.0\text{°C})$

(c) ${\text{CS}}_2(g)+{\text{3Cl}}_2(g)⟶{\text{CCl}}_4(g)+{\text{S}}_2{\text{Cl}}_2(g)(\text{T}=125\text{°C})$

(d) ${\text{2SO}}_2(g)+{\text{O}}_2(g)⟶{\text{2SO}}_3(g)(\text{T}=675\text{°C})$

(e) ${\text{CS}}_2(g)⟶{\text{CS}}_2(l)(\text{T}=90\text{°C})$

Consider the following reaction at 298 K:
${\text{N}}_2{\text{O}}_4(g)\rightleftharpoons {\text{2NO}}_2(g)K_P=0.142$

What is the standard free energy change at this temperature? Describe what happens to the initial system, where the reactants and products are in standard states, as it approaches equilibrium.

Determine the normal boiling point (in kelvin) of dichloromethane, CH₂Cl₂. Find the actual boiling point using the Internet or some other source, and calculate the percent error in the temperature. Explain the differences, if any, between the two values.

Under what conditions is ${\text{N}}_2{\text{O}}_3(g)⟶\text{NO}(g)+{\text{NO}}_2(g)$ spontaneous?

At room temperature, the equilibrium constant (K_w) for the self-ionization of water is 1.00 $\times$ 10⁻¹⁴. Using this information, calculate the standard free energy change for the aqueous reaction of hydrogen ion with hydroxide ion to produce water. (Hint: The reaction is the reverse of the self-ionization reaction.)

Hydrogen sulfide is a pollutant found in natural gas. Following its removal, it is converted to sulfur by the reaction ${\text{2H}}_2\text{S}(g)+{\text{SO}}_2(g)\rightleftharpoons \frac{3}{8}{\text{S}}_8(s,\text{rhombic})+{\text{2H}}_2\text{O}(l).$ What is the equilibrium constant for this reaction? Is the reaction endothermic or exothermic?

Consider the decomposition of CaCO₃(s) into CaO(s) and CO₂(g). What is the equilibrium partial pressure of CO₂ at room temperature?

In the laboratory, hydrogen chloride (HCl(g)) and ammonia (NH₃(g)) often escape from bottles of their solutions and react to form the ammonium chloride (NH₄Cl(s)), the white glaze often seen on glassware. Assuming that the number of moles of each gas that escapes into the room is the same, what is the maximum partial pressure of HCl and NH₃ in the laboratory at room temperature? (Hint: The partial pressures will be equal and are at their maximum value when at equilibrium.)

Benzene can be prepared from acetylene. ${\text{3C}}_2{\text{H}}_2(g)\rightleftharpoons {\text{C}}_6{\text{H}}_6(g).$ Determine the equilibrium constant at 25 °C and at 850 °C. Is the reaction spontaneous at either of these temperatures? Why is all acetylene not found as benzene?

Carbon dioxide decomposes into CO and O₂ at elevated temperatures. What is the equilibrium partial pressure of oxygen in a sample at 1000 °C for which the initial pressure of CO₂ was 1.15 atm?

Carbon tetrachloride, an important industrial solvent, is prepared by the chlorination of methane at 850 K.
${\text{CH}}_4(g)+{\text{4Cl}}_2(g)⟶{\text{CCl}}_4(g)+\text{4HCl}(g)$

What is the equilibrium constant for the reaction at 850 K? Would the reaction vessel need to be heated or cooled to keep the temperature of the reaction constant?

Acetic acid, CH₃CO₂H, can form a dimer, (CH₃CO₂H)₂, in the gas phase.
${\text{2CH}}_3{\text{CO}}_2\text{H}(g)⟶{({\text{CH}}_3{\text{CO}}_2\text{H})}_2(g)$

The dimer is held together by two hydrogen bonds with a total strength of 66.5 kJ per mole of dimer.

At 25 °C, the equilibrium constant for the dimerization is 1.3 $\times$ 10³ (pressure in atm). What is ΔS° for the reaction?

Determine ΔGº for the following reactions.

(a) Antimony pentachloride decomposes at 448 °C. The reaction is:
${\text{SbCl}}_5(g)⟶{\text{SbCl}}_3(g)+{\text{Cl}}_2(g)$

An equilibrium mixture in a 5.00 L flask at 448 °C contains 3.85 g of SbCl₅, 9.14 g of SbCl₃, and 2.84 g of Cl₂.

(b) Chlorine molecules dissociate according to this reaction:
${\text{Cl}}_2(g)⟶2\text{Cl}(g)$

1.00% of Cl₂ molecules dissociate at 975 K and a pressure of 1.00 atm.

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 free energy change, $\text{Δ}{G}_{\text{f}}^{°},$ for the formation of S²⁻(aq) given that the $\text{Δ}{G}_{\text{f}}^{°}$ for Ag⁺(aq) and Ag₂S(s) are 77.1 kJ/mole and −39.5 kJ/mole respectively, and the solubility product for Ag₂S(s) is 8 $\times$ 10⁻⁵¹.

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.

The evaporation of one mole of water at 298 K has a standard free energy change of 8.58 kJ.
${\text{H}}_2\text{O}(l)\rightleftharpoons {\text{H}}_2\text{O}(g)\text{Δ}G\text{°}=\text{8.58 kJ}$

(a) Is the evaporation of water under standard thermodynamic conditions spontaneous?

(b) Determine the equilibrium constant, K_P, for this physical process.

(c) By calculating ∆G, determine if the evaporation of water at 298 K is spontaneous when the partial pressure of water, $P_{{\text{H}}_2\text{O}},$ is 0.011 atm.

(d) If the evaporation of water were always nonspontaneous at room temperature, wet laundry would never dry when placed outside. In order for laundry to dry, what must be the value of $P_{{\text{H}}_2\text{O}}$ in the air?

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:
$\text{Glu}⟶\text{G6P}\text{Δ}G\text{°}=?$

One of the important reactions in the biochemical pathway glycolysis is the reaction of glucose-6-phosphate (G6P) to form fructose-6-phosphate (F6P):
$\text{G6P}\rightleftharpoons \text{F6P}\text{Δ}G\text{°}=\text{1.7 kJ}$

(a) Is the reaction spontaneous or nonspontaneous under standard thermodynamic conditions?

(b) Standard thermodynamic conditions imply the concentrations of G6P and F6P to be 1 M, however, in a typical cell, they are not even close to these values. Calculate ΔG when the concentrations of G6P and F6P are 120 μM and 28 μM respectively, and discuss the spontaneity of the forward reaction under these conditions. Assume the temperature is 37 °C.

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

When ammonium chloride is added to water and stirred, it dissolves spontaneously and the resulting solution feels cold. Without doing any calculations, deduce the signs of ΔG, ΔH, and ΔS for this process, and justify your choices.

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.

What happens to $\text{Δ}G$ (becomes more negative or more positive) for the following chemical reactions when the partial pressure of oxygen is increased?

(a) $\text{S}(s)+{\text{O}}_2(g)⟶{\text{SO}}_2(g)$

(b) ${\text{2SO}}_2(g)+{\text{O}}_2(g)⟶{\text{2SO}}_3(g)$

(c) $\text{HgO}(s)⟶\text{Hg}(l)+{\text{O}}_2(g)$