The `K_(sp) (25^(@)C)` of sparingly soluble salt `XY_(2)(s)` is `3.56 xx 10^(-5) ("mol" L^(-1))^(3)` and at `30^(@)C`, the vapour pressure of its saturated solution in water is `31.78 mm `of `Hg`.
Given: Vapour pressure of pure water=31.82 mm of Hg

Explanation

Let the solubility `XY_(2)(s)` at `30^(@)C` be `s mol L^(-1)`.
`XY_(2) (s) hArr X^(2+) (aq) + 2 Y^(ɵ)(aq) `
` (P^(@)-P_(S))/P_(S)=n/N (i=3, if 100% "ionization")`
`(31.82-31.78)/31.78=3chi_(2),chi_(2)= 0.0004 ,n_(2)/n_(1)=0.004`
`n_(2)=55.6 xx 0.004 =0.0233`
`S=0.2333 "mol" L^(-1)`
`K_(sp)("at" 30^(@)C)=(0.0233)(2xx0.0233)2`
`=5.05 xx 10^(-5) ("mol" L^(-1)3`
`K_(sp)("at" 25^(@)C)=3.56 xx 10^(-5) ("mol" L^(-1)^(3))`
Now, `log(K_(sp)(at `30^(@)C))/(K_(sp)(at 30^(@)C))=(DeltaH)/(2.303R)((T_(2)-T_(1))/(T_(1)T_(2)))`
`(log)((5.05 xx 10^(-5))/(3.56 xx 10^(-5)))=(DeltaH)/(2.303 xx 8.314)=(5/(303 xx 298))`
`DeltaH=52.5 kJ mol^(-1)`