A `0.025` m solutio of mono basic acid had a freezing point of `0.06^(@)C`. Calculate `K_(s)` for the acid `K_(f)` for `H_(2)O=1.86^(@) "molality"^(-1)`.

Explanation

For mono basic acid HA
`HA hArr H^(+)A^(-)`
`{:(1,0,0),((1-alpha),alpha,alpha):}` " " i= (1+alpha)`
From Ostwald Dilution Law,`K_(a)=(Calpha^(2))/((1-alpha))`
`DeltaT_(f)=K_(f)xx(i)`
`rArr 0.06=1.876xx0.025xx(1+alpha)`
`:.(1+alpha)=(0.06)/(0.0465)`
`:. alpha=0.029, C=0.025M`
`K_(s)=(alpha^(2))/((1-alpha))`
From equation (i) `K_(a)=(0.025xx(0.029)^(2))/((1-0.029))`
`=2.96xx10^(-3)`