When `20g` of naphtholic acid `(C_(11)H_(8)O_(2))` is dissolved in `50g` of benzene `(K_(f) = 1.72 K kg mol^(-1))` a freezing point depression of `2K` is observed. The van'f Hoff factor (i) is

Options

A. 0.5
B. 1
C. 2
D. 3

Answer

A

Explanation

`DeltaT_(f)=(ixxK_(f)xxW_(B))/(M_(B)xxW_(A)(kg))`
`DeltaT_(f)=2K,K_(f)=1.72" K kg mol"^(-1),W_(B)=20g`
`W_(A) = 50g = 0.05kg`,
`M_(B)=12xx11+8+32=172"g mol"^(-1)`
`i=(DeltaT_(f)xxM_(B)xxW_(A)(kg))/(K_(f)xxW_(B))`
`=(2xx172xx0.05)/(1.72xx20)=(2xx172xx5)/(172xx20)`.