Question

The following data for a chemical reaction with the general equation of X2(g) + Y2(g).-->2 XY(g) shows the equilibrium constant for this reaction measured at several different temperatures.
Use the data to determine Delta H rxn and Delta S rxn for the reaction.
Temperature | Kp
200 K | 1.1x10-7
250 K | 5.4x10-5
300 K | 1.6x10-2
Is the reaction spontaneous? If not, at what temperature will the reaction become spontaneous?

Answer 1

Since Kp is less than 1 for the temperature 200K-300K, the Delta G is positive in this case, which means the reaction is not spontaneous.

Using the first two values 200K and 250K

Using the arrhenius equation

For 200K

Delta G = Delta H - T*Delta S

26.64 = 51.5 - 200* Delta S(rxn)

Delta S(rxn) = (51.5 - 26.64)/(200) = 0.1243 kJ/mol or 124.3 J/mol

The reaction will become spontaneous when Delta G becomes negative which implies

51.5 - T*0.1243 < 0

T > 51.5/0.1243 or T > 414.3 K

Hence the temperature must be greater than 141C or 414K in order to make the reaction spontaneous

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