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Using the following data, calculate the ...

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?

Text Solution

Verified by Experts

`DeltaG^(@)` for the reaction :
`DeltaG^(@) = Delta_(f)G^(@)(C_(6)H_(6)) - 3[Delta_(f)G^(@)(HC equiv CH)]`
` = 1.24 xx 10^(5) - 3 xx 2.09 xx 10^(5)`
` = -5.03 xx 10^(5)`
Now, `DeltaG^(@) = -2.303 RT "log K`
or `log "K = -(DeltaG)/(2.303 RT) = 88.155`
` = -(-5.03 xx 10^(5))/(2.303 xx 8.314 xx 298) = 88.155`
`therefore` 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.
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