Question

One step in the commercial synthesis of sulfuric acid is the catalytic oxidation of sulfur dioxide:
2SO2(g)+O2(g)???2SO3(g)
A mixture of 192 g of SO2, 48.0 g of O2, and a V2O5 catalyst is heated to 800 K in a 15.0 L vessel.

Part A) asked to use the data in Appendix B in the textbook to calculate the partial pressures of SO3, SO2, and O2 at equilibrium. Assume that ?H? and ?S? are independent of temperature. And I found the answers to be:

pSO3, pSO2, pO2 =

13,0.63,0.32 atm  

I am having trouble with part C) calculate the total pressure (in atm) at 1000 K.

Thank you.

Answer 1

Sol :-

Total pressure (P₁) at 800 K = 13 + 0.63+ 0.32 = 13.95 atm

The given equation is :

2 SO₂ (g) + O₂ (g) <---------> 2 SO₃ (g) , ΔH⁰_rxn = ?

We know that

ΔH⁰_rxn = ∑Δ_fH⁰_Products - ∑Δ_fH⁰_Reactant  

ΔH⁰_rxn = [ 2 x - 395.7 KJ/mol ] - [ 2 x - 296.8 KJ/mol]

ΔH⁰_rxn = - 791.4 KJ/mol + 593.6 KJ/mol

ΔH⁰_rxn = - 197.8 KJ/mol

Now, at T₁ = 800 K , P₁ = 13.95 atm and

at T₂ = 1000 K , P₂ = ?

From van der waal's equation, we have

logP₂/P₁ = ΔH⁰_rxn / 2.303R . [T₂-T₁/T₁T₂]

log P₂ - log 13.95 = -197.8 KJ mol^-1 / (2.303 x 8.314 x 10^-3 KJ K^-1mol^-1) .[1000-800/(1000)(800)]K

log P₂ = 1.1446 - 10,330.52 .[0.00025]

log P₂ = 1.1446 - 2.5826

P₂ = 10^-1.43803

P₂ = 0.0365 atm