SO_3 gas can be prepared by a controlled oxidation of SO_2(g) according to the f

Question

SO_3 gas can be prepared by a controlled oxidation of SO_2(g) according to the following balanced reaction: At what temperatures is the reaction spontaneous under standard conditions of pressure? At what temperatures is the reaction non-spontaneous under standard conditions of pressure? Estimate Delta G degree for the reaction at 298 K und 573 K under standard conditions of pressure. Calculate the equilibrium constant K_p for the reaction at 298 K and 573 K based on the thermodynamic data above. In a reaction vessel. 3.0 atm of SO_2 is combined with 2.0 atm of O_2(g), and 0.5 atm of SO_3(g). Estimate Delta G under these conditions of pressure at 298 K and 573 K. Is the reaction capable of more, or less work under these non-standard conditions compared to standard conditions of pressure?

Explanation / Answer

1) we know that

for a reaction to be spontaneous

dGo < 0

so

dGo = dHo - TdSo < 0

given

dHo = -198 x 1000

dSo = -187

so

-198 x 1000 - ( T x -187) < 0

-198 x 1000 + 187T < 0

187T < 198 x 1000

T < 1058.82

so

for temperatures below 1058.82 , the reaction is spontaneous

and

for temperatures above 1058.82 , the reaction is non spontaneous

b)

At 298 K

dGo = dHo - TdSo

dGo = ( -198 x1000 ) - ( 298 x -187)

dGo = -142.274 kJ / mol

At 573 K

dGo = ( -198 x 1000) - ( 575 x -187)

dGo = -90.475 kJ/mol

c) now

we know that

dGo = - RT ln Kp

so

AT 298 K

-142.274 x 1000 = -8.314 x 298 x ln Kp

Kp = 2.66 x 10^57

AT 573 K

-90.475 x 1000 = -8.314 x 575 x ln Kp

Kp = 9.81 x 10^18

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