# 18.6: Spontaneity and Equilibrium

= 1, and the system is at equilibrium. We can use the measured equilibrium constant K at one temperature and ΔH° to estimate the equilibrium constant for a reaction at any other temperature.

## Conceptual Problems

1. Do you expect products or reactants to dominate at equilibrium in a reaction for which ΔG° is equal to
1. 1.4 kJ/mol?
2. 105 kJ/mol?
3. −34 kJ/mol?
1. The change in free energy enables us to determine whether a reaction will proceed spontaneously. How is this related to the extent to which a reaction proceeds?
1. What happens to the change in free energy of the reaction N2(g) + 3F2(g) → 2NF3(g) if the pressure is increased while the temperature remains constant? if the temperature is increased at constant pressure? Why are these effects not so important for reactions that involve liquids and solids?
1. Compare the expressions for the relationship between the change in free energy of a reaction and its equilibrium constant where the reactants are gases versus liquids. What are the differences between these expressions?

## Numerical Problems

1. Carbon monoxide, a toxic product from the incomplete combustion of fossil fuels, reacts with water to form CO2 and H2, as shown in the equation CO(g)+H2O(g)⇌CO2(g)+H2(g), for which ΔH° = −41.0 kJ/mol and ΔS° = −42.3 J cal/(mol·K) at 25°C and 1 atm.
1. What is ΔG° for this reaction?
2. What is ΔG if the gases have the following partial pressures: PCO = 1.3 atm, $$P_{\mathrm{H_2O}}$$ = 0.8 atm, $$P_{\mathrm{CO_2}}$$ = 2.0 atm, and $$P_{\mathrm{H_2}}$$ = 1.3 atm?
3. What is ΔG if the temperature is increased to 150°C assuming no change in pressure?
1. Methane and water react to form carbon monoxide and hydrogen according to the equation CH4(g) + H2O(g) ⇌ CO(g) + 3H2(g).
1. What is the standard free energy change for this reaction?
2. What is Kp for this reaction?
3. What is the carbon monoxide pressure if 1.3 atm of methane reacts with 0.8 atm of water, producing 1.8 atm of hydrogen gas?
4. What is the hydrogen gas pressure if 2.0 atm of methane is allowed to react with 1.1 atm of water?
5. At what temperature does the reaction become spontaneous?
1. Calculate the equilibrium constant at 25°C for each equilibrium reaction and comment on the extent of the reaction.
1. CCl4(g)+6H2O(l)⇌CO2(g)+4HCl(aq); ΔG° = −377 kJ/mol
2. Xe(g)+2F2(g)⇌XeF4(s); ΔH° = −66.3 kJ/mol, ΔS° = −102.3 J/(mol·K)
3. PCl3(g)+S⇌PSCl3(l); ΔGf(PCl3) = −272.4 kJ/mol, ΔGf (PSCl3) = −363.2 kJ/mol
1. Calculate the equilibrium constant at 25°C for each equilibrium reaction and comment on the extent of the reaction.
1. 2KClO3(s)⇌2KCl(s)+3O2(g); ΔG° = −225.8 kJ/mol
2. CoCl2(s)+6H2O(g)⇌CoCl2⋅6H2O(s); ΔHrxn = −352 kJ/mol, ΔSrxn = −899 J/(mol·K)
3. 2PCl3(g)+O2(g)⇌2POCl3(g); ΔGf(PCl3) = −272.4 kJ/mol, ΔGf (POCl3) = −558.5 kJ/mol
1. The gas-phase decomposition of N2O4 to NO2 is an equilibrium reaction with Kp = 4.66 × 10−3. Calculate the standard free-energy change for the equilibrium reaction between N2O4 and NO2.
1. The standard free-energy change for the dissolution K4Fe(CN)6⋅H2O(s)⇌4K+(aq)+Fe(CN)64−(aq)+H2O(l) is 26.1 kJ/mol. What is the equilibrium constant for this process at 25°C?
1. Ammonia reacts with water in liquid ammonia solution (am) according to the equation NH3(g) + H2O(am) ⇌ NH4+(am) + OH(am). The change in enthalpy for this reaction is 21 kJ/mol, and ΔS° = −303 J/(mol·K). What is the equilibrium constant for the reaction at the boiling point of liquid ammonia (−31°C)?
1. At 25°C, a saturated solution of barium carbonate is found to have a concentration of [Ba2+] = [CO32−] = 5.08 × 10−5 M. Determine ΔG° for the dissolution of BaCO3.
1. Lead phosphates are believed to play a major role in controlling the overall solubility of lead in acidic soils. One of the dissolution reactions is Pb3(PO4)2(s)+4H+(aq)⇌3Pb2+(aq)+2H2PO4(aq), for which log K = −1.80. What is ΔG° for this reaction?
1. The conversion of butane to 2-methylpropane is an equilibrium process with ΔH° = −2.05 kcal/mol and ΔG° = −0.89 kcal/mol.
1. What is the change in entropy for this conversion?
2. Based on structural arguments, are the sign and magnitude of the entropy change what you would expect? Why?
3. What is the equilibrium constant for this reaction?
1. The reaction of CaCO3(s) to produce CaO(s) and CO2(g) has an equilibrium constant at 25°C of 2 × 10−23. Values of ΔHf are as follows: CaCO3, −1207.6 kJ/mol; CaO, −634.9 kJ/mol; and CO2, −393.5 kJ/mol.
1. What is ΔG° for this reaction?
2. What is the equilibrium constant at 900°C?
3. What is the partial pressure of CO2(g) in equilibrium with CaO and CaCO3 at this temperature?
4. Are reactants or products favored at the lower temperature? at the higher temperature?
1. In acidic soils, dissolved Al3+ undergoes a complex formation reaction with SO42− to form [AlSO4+]. The equilibrium constant at 25°C for the reaction Al3+(aq)+SO42−(aq)⇌AlSO4+(aq) is 1585.
1. What is ΔG° for this reaction?
2. How does this value compare with ΔG° for the reaction Al3+(aq)+F(aq)⇌AlF2+(aq), for which K = 107 at 25°C?
3. Which is the better ligand to use to trap Al3+ from the soil?

1. −28.4 kJ/mol
2. −26.1 kJ/mol
3. −19.9 kJ/mol
1. 1.21 × 1066; equilibrium lies far to the right.
2. 1.89 × 106; equilibrium lies to the right.
3. 5.28 × 1016; equilibrium lies far to the right.
1. 13.3 kJ/mol
1. 5.1 × 10−21
1. 10.3 kJ/mol
1. 129.5 kJ/mol
2. 6
3. 6.0 atm
4. Products are favored at high T; reactants are favored at low T.