a. Calculate the depression in freezing point `(Delta T_(f))` of `0.1` m solution of ROH in cold conc. `H_(2)SO_(4)` . `K_(f) = x K kg mol^(-1)`
b. Calculate the `Delta T_(1)` of `0.2` m solution of `Ph_(3) C--OH` in cold conc. `H_(2)SO_(4)` . `K_(f) = x K kg mol^(-1)` .

Explanation

a. ROH reacts with cold cons. `H_(2)SO_(4)` as follows:
1. `ROH + H_(2)SO_(4) rarr RO^(o+)H_(2) + HSO_(4)^(-) rarr ROSO_(2)OH` + `cancel (H_(2)O)`
2. `{:(H_(2)SO_(4)+cancel(H_(2)O)toH_(3)O^(o+)+HSO_(4)^(-)),(ulbar(ROH+2H+2H_(2)SO_(4)toROSO_(2)OH+H_(3)O^(o+)+HSO_(4)^(-))):}
Number of moles of particles formed per mole of solute (i) (van't Hoff factor) = 3 (The reaction does not produce `R^(o+)`, because `R^(o+)` ion or even `R_(3)C^(o+)` ion is not stable enogh to persist.
`:. Delta T_(f) = i K_(f)xxM`
`= 3x xx 0.1 = 0.3x K`
b. `Ph_(3)C---OH` reacts with cold conc. `H_(2)SO_(4)` as follows:
1. `Ph_(3)COH + H_(2)SO_(4) rarr Ph_(3)C^(o+)` + `cancel (H_(2)O)` + `HSO_(4)^(-)`
2. `{:(H_(2)SO_(4)+cancel(H_(2)O)toH_(3)O^(o+)+HSO_(4)^(-)),(ulbar(Ph_(3)COH+2H+2H_(2)SO_(4)toPh_(3)C^(o+)+H_(3)O^(o+)+2HSO_(4)^(-))):}
Number of moles of particles formed per mole of solute (i) (Van't Hoff factor) = 4
(The reaction produces stable `Ph_(3)C^(o+)` ion due to resonance stabilisation, and `Ph_(3)C^(o+)` persists in the solution.)
`:. Delta T_(f) = i K_(f)xxM`
`= 4x xx 0.2 = 0.8x K`.