(a) Calculate the `Delta T_f` (depression in freezing point) of `0.4 m` solution of `CH_3 COOH` in benzene solution. `K_f = x K kg mol^-1`.
(b) Calculate the `Delta T_f` of `0.2 m` solution of an acid `(RCOOH)` is `conc. H_2 SO_4`, in which `(Rc -= O^(oplus))` acylium ion is formed. `K_f = x K kg mol^-1`.
( c) Calculate the `Delta T_f` of `0.3 m` solution of an acid `(RCOOH)` in `conc. H_2 SO_4` in which a protonated acid `(R-underset(.^o+OH)underset(||)(C)-OH)` (I) is formed.
`K_f = x K kg mol^-1`.

Explanation

(a) `CH_3 COOH` in aprotic or non-polar solvent which exists as a dimer.
`2(CH_3 COOH) rarr (CH_3 COOH)_2`.
If `100 %` dimerisation takes place, the van't Hoff factor `i= (1)/(2)`
`Delta T_f = i K_f xx m = (1)/(2) xx x xx 0.4 = 0.2 x K`
(b) If forms acylium ion. The net equation with `i` is :

`Delta T_f = i K_f m = 4 xx x xx 0.2 = 0.8 x K`.
( c) If forms protanated acid `(I)`. The net equation and `i` is :

`Delta T_f = i K_f m = 2 xx x xx 0.3 = 0.6 x K`.