Among the following 0.10 m aqueous solutions, which one will exhibit the largest freezing point depression?

Options

A. `KCl`
B. `C_(6)H_(12)O_(6)`
C. `Al(2)(SO_(4))_(3)`
D. `K_(2)SO_(4)`

Answer

C

Explanation

`Delta T_(f)` (freezing point depression) is a colligative property and depends upon the van't Hoff factor (i), i.e. number of ions given by the electrolyte in aqueous solution.
`Delta T_(f)=I xx K_(f)xx m`
where, `K_(f)` = molal freezing point depression constant
`therefore K_(f)` and m are constant,
`therefore " " Delta T_(f) prop i`
van't Hoff factor for ionic solution.
(a) `KCl(aq)hArr K^(+)(aq)+Cl^(-)(aq)`, (Total ions = 2 thus, i = 2)
(b) `C_(6)H_(12)O_(6)hArr` no ions [i = 0] because glucose does not given ions.
(c ) `Al_(2)(SO_(4))_(3)(aq)hArr 2Al^(3+)+3SO_(4)^(2-)` [Total ions = 5, thus, i = 5]
(d) `K_(2)SO_(4)(aq) hArr 2K^(+)+SO_(4)^(2-)` [Total ions = 3, thus, i = 3]
Hence, `Al_(2)(SO_(4))_(3)` will exhibit largest freezing point depression due to the highest value of i.