Question

1. Consider the decomposition of barium carbonate: BaCO3(s)←−→BaO(s)+CO2(g)

a. Using data from Appendix C in the textbook, calculate the equilibrium pressure of CO2 at 1200 K .

2.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. Calculate the equilibrium constant Kp for the reaction at a temperature of 298 K .

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

Answer 1

(1) BaCO3(s)←−→BaO(s)+CO2(g)

ΔG = ΔG⁰_{f  products} – ΔG⁰_{f  reactants}

ΔG = [( ΔG⁰_f  BaO(s) )+ ( ΔG⁰_{f  CO2 (g)} )]- [( ΔG⁰_fBaCO3(s) )]

= [ -520.4 + (-394.4)] - [-1137.62]

= 222.82 kJ

We know that ΔG = -RT ln K

Where

R = gas constant = 8.314x10^-3 kJ/(mol-K)

T = Temperature = 298 K

K = Equilibrium constant = ?

Plug the values we get

lnK = -ΔG /(RT)

= -89.93

K = e^-89.93 = 8.74x10^-40

^{K = pCO2 =} 8.74x10^{-40 atm}

(2)SO2(g)+2H2S(g) ⇌ 3 S(s)+2H2O(g)  

ΔG = ΔG⁰_fproducts – ΔG⁰_freactants

ΔG = [(3x ΔG⁰_fS(s) )+ (2 x ΔG⁰_{fH2O (g)} )]- [( ΔG⁰_fSO2(g) )+ (2x ΔG⁰_{fH2S (g)} )]

    = [(3x0) + ( 2x (-228.6))] - [ -300.4 + (2x(-33.01))]

= -90.78 kJ/mol

= -90.78x103 J

We know that ΔG = -RT ln K

Where

R = gas constant = 8.314x10-3 kJ/(mol-K)

T = Temperature = 298 K

K = Equilibrium constant = ?

Plug the values we get

lnK = -ΔG /(RT)

= 36.64

K = e^36.64 = 8.18x10¹⁵