Answer:
a) ΔHºrxn = 116.3 kJ, ΔGºrxn = 82.8 kJ,  ΔSºrxn =  0.113 kJ/K
b) At 753.55 ºC or higher
c )ΔG =  1.8 x 10⁴ J
     K = 8.2 x 10⁻²
Explanation:
 a)                                 C6H5−CH2CH3  ⇒  C6H5−CH=CH2  + H₂
ΔHf kJ/mol                    -12.5                           103.8                      0
ΔGºf kJ/K                        119.7                         202.5                      0
Sº J/mol                          255                          238                      130.6*
Note: This value was not given in our question, but is necessary and can be found in standard handbooks.
Using Hess law to calculate  ΔHºrxn we have
ΔHºrxn  = ΔHfº C6H5−CH=CH2 +  ΔHfº H₂ - ΔHºfC6H5−CH2CH3
ΔHºrxn =     103.8 kJ + 0 kJ  - (-12.5 kJ)
ΔHºrxn = 116.3 kJ
Similarly,
ΔGrxn = ΔGºf C6H5−CH=CH2 +  ΔGºfH₂ - ΔGºfC6H5CH2CH3
ΔGºrxn=   202.5 kJ + 0 kJ - 119.7 kJ  = 82.8 kJ
ΔSºrxn = 238 J/mol + 130.6 J/mol -255 J/K = 113.6 J/K = 0.113 kJ/K
b) The temperature at which the reaction is spontaneous or feasible occurs when ΔG becomes negative and using
ΔGrxn =  ΔHrxn -TΔS 
we see that will happen when the term  TΔS  becomes greater than ΔHrxn since ΔS  is positive  , and so to sollve for T we will make ΔGrxn equal to zero and solve for T. Notice here we will make the assumption that  ΔºHrxn and ΔSºrxn remain constant at the higher temperature  and will equal the values previously calculated for them. Although this assumption is not entirely correct, it can be used.
0 = 116 kJ -T (0.113 kJ/K)
T = 1026.5 K  =  (1026.55 - 273 ) ºC = 753.55 ºC 
c) Again we will use 
                        ΔGrxn =  ΔHrxn -TΔS 
to calculate ΔGrxn   with the assumption that ΔHº and ΔSºremain constant.
ΔG =  116.3 kJ - (600+273 K) x 0.113 kJ/K =  116.3 kJ - 873 K x 0.113 kJ/K
ΔG =  116.3 kJ - 98.6 kJ =  17.65 kJ = 1.8 x 10⁴ J ( Note the kJ are converted to J to necessary for the next part of the problem )
Now for solving for K, the equation to use is
ΔG = -RTlnK and solve for K
- ΔG / RT = lnK  ∴ K = exp (- ΔG / RT)
K = exp ( - 1.8 x 10⁴ J /( 8.314 J/K  x 873 K)) = 8.2 x 10⁻²