Acetoc acid `CH_(3)COOH` can form a dimer `(CH_(3)COOH)_(2)` in the gas phase. The dimer is held togther by two `H-`bonds with a total strength of `60.0 kJ per` mole of dimer

If at `25^(@)C`, the equilibrium constant for the dimerisation is `1.3 xx 10^(3)`, calculate `DeltaS^(Theta)` for the reaction
`2CH_(3)COOH (g) hArr (CH_(3)COOH)_(2)(g)`

Explanation

`DeltaG^(Theta) =- 2.303 RT log_(10)k`
`=- 2.303 xx 8.314 xx 298 log (1.3 xx10^(3))`
`=- 17767.688 J = - 17.767 kJ`
`DeltaG^(Theta) = DeltaH^(Theta) - T DeltaS^(Theta)`
`- 17.767 =- 60.0 - 298 xx DeltaS^(Theta)`
`DeltaS^(Theta) = (-60.0+17.767)/(298) =- 0.141 kJ`