Find `K_(s)` the inoziation constant of tartaric acid if a `0.100` aqueous solution of tartaric acid freezes at `0.0205^(@)C`. Assume that only the first ionization is of importance and that `0.1 m=0.1 1M K_(f)=1.86 kg "mol"^(-1)`.

Explanation

Assuming that the tartaric acid be monobasic as AH. It ionizes as
`{:(, AH hArr, A+, H^(+)),("Initially conc", C,0,0),("Con.After dissociation",C(1-alpha),Calpha,Calpha):}`
Here `i=(C(1-alpha)+C alpha+C alpha)/(C)` where `alpha` = degree of dissociation
`=(C(1+alpha))/(C)=1+alpha`
Molal cponcentration `=0.1`
`DeltaT_(1)=K_(t)xxC_(m)xxi`
`0.205]=1.86xx0.1xx(1+alpha), :. alpha=0.1`
`K_(s)=([A^(-2)][H^(+)])/([AH])=(Calpha xx Calpha)/(C(1-alpha))=(alpha^(3)C)/(1-alpha)`
`K_(s)=((0.1)^(2)xx0.1)/(1-0.1)=1.11xx10^(-3)`
`:.K_(s)=1.11xx10^(-3)`