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?

Answer

`K = 1.43 xx 10^(88) ,` Yes

Explanation

`Delta_(r) G^(@) =Delta_(f)G^(@) (C_(6)H_(6)) - 3 Delta_(f)G^(@) (HC -= CH) = 1.24 xx 10^(5) - 3 ( 2.9 xx 10^(5)) J = - 5.03 xx 10^(5)J`
`Delta_(r)G^(@) = - 2.303 RT log K `. Calculate K
`Delta _(r)G^(@) ` is negative and K is very high . Hence, the process can occur easily.