`K_(a)` for acetic acid at `27^(@)C` is `2.0 xx 10^(-5)` and at `77^(@)C, K_(a) is 2.5 xx 10^(-5)`. What are `DeltaH^(Theta)` and `DeltaS^(Theta)` for the ionisation of acetic acid?

Explanation

Using: In `((K_(eq))_(2))/((K_(eq))_(1)) = (Delta_(r)H^(Theta))/(R ) ((1)/(T_(1))-(1)/(T_(2)))`
`rArr In ((2.5 xx 10^(-5))/(2.0 xx 10^(-5))) =(Delta_(r)H^(Theta))/(8.314) xx ((1)/(300)-(1)/(350))`
`rArr Delta_(r)H^(Theta) = 3.89 k J mol^(-1)`
Also, `Delta_(r)G^(Theta) =- RT In K_(eq)`
`rArr Delta_(r)G^(Theta) =- 8.314 xx 298 xx In (2.0 xx 10^(-5))`
`= 26.81 kJ mol^(-1)` [Taking `(K_(Eq))_(25^(@)C) ~~(K_(eq))_(27^(@)C)]`
Using `Delta_(r)G^(Theta) = Delta_(r)H^(Theta) - T Delta_(r)H^(Theta)`
`rArr 26.81 = 3.89 -(298 xx 10^(-3)) xx Delta_(r)S^(Theta)`
`rArr Delta_(r)S^(Theta) = 76.9 J mol^(-1)JK^(-1)`