The freezing point of benzene decreases by `0. 45 ^(@)C` on adding `0.2 g` of acetic acid to 20 g of acetic acid to 20 g of benzene. If acetic acid associates to form a dimer in benzene, then what is the percentage association of acetic acid in benzene ?
(`K _(f)` for benzene `= 5. 12 K kg mol ^(-1))`

Options

A. `80. 4 %`
B. `74.6 %`
C. `94.6 %`
D. `64.6 %`

Answer

C

Explanation

`underset( 1 - alpha ) ( 2 CH _(3) COOH ) hArr underset( ( alpha )/(2) ) ( ( CH _(3) COOH ) _(2))`
`i = 1 - (alpha )/(2)`
`Delta T _(f) - i xx K _(f) xx m`
` 0. 45 = i xx 5. 12 xx ( 0. 2 xx 1000)/( 60 xx 20)`
`i = 0. 527 = 1 - (alpha )/(2)`
`implies alpha = 0. 9 46 or 94. 6 %`