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K(a) for acetic acid at 27^(@)C is 2.0 x...

`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?

Text Solution

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Using : `ln((K_(eq))_(2))/((K_(eq))_(1))=(Delta_(r )H^(Θ))/(R )((1)/(T_(1))-(1)/(T_(2)))`
`rArr ln((2.5xx10^(-5))/(2.0xx10^(-5)))=(Delta_(r )H^(Θ))/(8.314)xx((1)/(300)-(1)/(350))`
`rArr Delta_(r ) H^(Θ)=3.89 kJ mol^(-1)`
Also, `Delta_(r ) G^(Θ)=-RT ln K_(eq)`
`rArr Delta_(r ) G^(Θ)=-8.314xx298xx ln(2.0xx10^(-5))=26.81 "kJ mol"^(-1) " " ["Taking" (K_(eq))_(25^(@)C)~~(K_(eq))_(27^(@)C)]`
Using : `Delta_(r )G^(Θ)=Delta_(r )H^(Θ)-T Delta_(r )S^(Θ)`
`rArr 26.81=3.89-(298xx10^(-3))xxdelta_(r )S^(Θ) " " rArr " " Delta_(r ) S^(Θ) = 76.9 "J mole"^(-1)K^(-1)`
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