Consider the following reversible reaction, `AgB g rarr ABg` . The activation energy of the backward reaction exceeds that of the forward reaction by 2` (in J mol^(1))`. If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of`triangle G^(theta) (in J mol^(−1))` for the reaction at 300 K is ____. (Given, ln(2) = `0.7, = 2500 J mol^(−1)` at 300 K and G is the Gibbs energy)

Explanation

`A_((g))+B_((g))iffAB_((g))`
`E_(ab)-E_(af)=2RT implies DeltaH=-2RT and (A_(f))/(A_(b))=4`
`K_(eq)=((K_(f))/(K_(b)))=(A_(f)e^(-E_(af)//RT))/(A_(b)e^(-E_(ab)//RT))=4(e^(2))`
`DeltaG^(@)=-RTln K=-2500xxln(4xxe^(2))=-8500 J//mol`
`therefore` Absolute value of `DeltaG^(@)=8500 J//mol`.