Question

Given the thermodynamic data in the table below, calculate the equilibrium constant for the reaction:

2SO2(g)+O2--> 2SO3

Substance (DeltaH^o) (Delat S^o)
SO2 -297 249
O2 0 205
SO3 -395 256

Answer (it was given) 2.32x10^24

Even though the answer is given (2.32x10^24) I just can't get there. I calculated:
(Delta H^o)= ((2moles)(-395))-((2moles)(-297)+(1mole)(0))=-196
(Delta S^o)= ((2moles)(256))-((2moles)(249)+(1mole)(205)=-191

From here I thought: If I need to find the equilibrium constant K, I can use the formula (Delta G^0)= -RT ln K and thus K= e^(-(DeltaG^o)/RT)
To get there I figure I would need to find (Delta G^o)...which is possible because I do have (Delta H^o) and (Delta S^o) and I can use the formula
(Delta G^o)= (Delta H^o) - T(Delta S^o) ...I assumed that the temperature is 298K and that didn't work and then I calculated T (T= ((Delta H^o)/(Delta S^o))...I get 1026K and then I put that into (Delta G^o)= (Delta H^o) - T(Delta S^o)...and then solved all the rest but that doesn't work out either. Could you tell me were I am wrong or write down how you would solve the problem?
Thank You!!

Answer 1

Then it would be like this -196-{(1.91×10^-1)(298)=5.6918×10^1 }
-196+5.6918×10^1=-139.082
Calculation of K
-139.082/(8.314×10^-3)×(298)
-139.082/2.477572=-56.13641097
E^56.13641097=2.39×10^24