Question

The reaction SO2(g)+2H2S(g) ⇌ 3 S(s)+2H2O(g) is the basis of a suggested method for removal of SO2 , a pollutant that irritates airways causing coughing, from power-plant stack gases. The values below may be helpful when answering questions about the process. Substance ΔG∘f (kJ/mol) ΔH∘f (kJ/mol) H2O(g) − 228.6 − 241.8 H2O(l) − 237.1 − 285.8 SO2(g) − 300.4 − 296.9 SO3(g) − 370.4 − 395.2 H2S(g) − 33.01 − 20.17 S(s) 0 0

Assume that the partial pressure of sulfur dioxide, PSO2, is equal to the partial pressure of dihydrogen sulfide, PH2S, and therefore PSO2=PH2S. If the vapor pressure of water is 22 torr , calculate the equilibrium partial pressure of SO2 (PSO2) in the system at 298 K.

Express the pressure in atmospheres to two significant figures.

Answer 1

Calculate ΔG⁰_rxn as below.

ΔG⁰_rxn = ∑n.ΔG⁰_f(products) - ∑n.ΔG⁰_f(reactants)

where n denotes the number of mol(s) of reactant and product molecules. Therefore,

ΔG⁰_rxn = [(3 mol S)*ΔG⁰_f(S, s) + (2 mol H₂O)*ΔG⁰_f(H₂O, g)] – [(1 mol SO₂)*ΔG⁰_f(SO₂, g) + (2 mol H₂S)*ΔG⁰_f(H₂S)]

= [(3 mol)*(0 kJ/mol) + (2 mol)*(-228.6 kJ/mol)] – [(1 mol)*(-300.4 kJ/mol) + (2 mol)*(-33.01 kJ/mol)]

= (-457.2 kJ) – (-300.4 kJ – 66.02 kJ)

= (-457.2 kJ) – (-366.42 kJ)

= -90.78 kJ

Determine the equilibrium constant for the reaction as

ΔG⁰_rxn = -RTln K_p

where T = 298 K is the temperature of the reaction and K_p is the equilibrium constant for the reaction.

Plug in values and obtain

-90.78 kJ = -(8.314 J/mol.K)*(298 K)*ln K_p

======> (-90.78 kJ)*(1000 J)/(1 kJ) = -(2477.572 J/mol )*ln K_p

======> -9078 J = -(2477.572 J/mol)*ln K_p

======> ln K_p =(-9078 J)/(-2477.572 J/mol)

======> ln K_p = 3.6641 (ignore units)

======> K_p = exp(3.6641)

======> K_p = 39.02

Write down the expression for K_p as

K_p = (P_H2O)²/(P_SO2)(P_H2S)²

Given the relation and P_H2O = 22 torr (ignore units), we can write

39.02 = (22)²/(P)(P)² (denote P_SO2 = P_H2S = P)

=====> 39.02 = (484)/(P)³

=====> P³ = 484/39.02 = 12.40

=====> P = 2.314 ≈ 2.3 (correct to 2 sig. figs)

The partial pressure of SO₂ is 2.3 torr (ans).