One step in the commercial synthesis of sulfuric acid is the catalytic oxidation

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.

Explanation / Answer

Ptotal ( att 800K) = pSO3 + pSO2 + pO2 = 13 + 0.63+ 0.32 = 13.95 atm

The pressure at 1000K will be

PV = nRT

T = 1000 K

V = 15 L

R = 0.0821 L atm / mol K

assuming moles constant

P1 / T1 = P2 / T2

13.95 / 800 = P2 / 1000

P2 = 17.44 atm

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