`K_(a)` for `CH_(3)COOH` at `25^(@)C` is `1.754xx10^(5)`. At `50^(@)C, K_(a)` is `1.633xx10^(-5)` what are `Delta H^(@)` and `Delta S^(@)` for the ionisation of `CH_(3)COOH` ?

Explanation

`(DeltaG^(@))_(298)= -2.303RT log K= -2.303xx8.314xx298xxlog(1.754xx10^(-5))=27194 J`
`(DeltaG^(@))_(323)=2.303xx8.314xx323xxlog(1.633xx10^(-5))=29605J`
`DeltaG^(@)=DeltaH^(@)-TDeltaS^(@)`
`27194=DeltaH^(@)-298DeltaS^(@)`
`29605=DeltaH^(@)-323 Delta S^(@)`
`:. Delta H^(@) = -1.55kJ//mol`
`Delta S^(@)= -96.44 K//mol.K`