Using the following data, calculate the value of equilibrium constant for the following reaction at `298K`
`underset("Acetylene")(3HC-=CH)hArr underset("Benzene")(C_(6)H_(6)(g))`
Assuming ideal behaviour
`Delta_(f)G^(Theta) (HC-= CH) = 2.09 xx 10^(5) J mol^(-1)`
`Delta_(f)G^(Theta) (C_(6)H_(6)) = 1.24 xx 10^(5) J mol^(-1)`,
`R = 8.314 J K^(-1) mol^(-1)`
Can the reaction be recommended for the synthesis of benzene?

Explanation

`DeltaG^(Theta)` for the reaction:
`DeltaG^(Theta) = Delta_(f)G^(Theta) (C_(6)H_(6)) -3 [Delta_(f)G^(Theta) (HC -= CH)]`
`= 1.24 xx 10^(5) - 3 xx 2.09 xx 10^(5)`
`=- 5.03 xx 10^(5)`
Now, `DeltaG^(Theta) =- 2.303 RT log K`
or `log K =- (DeltaG)/(2.303RT)`
`=- (-5.03 xx 10^(5))/(2.303 xx 8.314 xx 298) = 88.155`
`:. K = Antilog (88.155) = 1.43 xx 10^(88)`
Since value of `DeltaG` is negative, the reaction is feasible and may be recommended for making benzene.