Molecules of benzoic acid `(C_(6)H_(5)COOH)` dimerise in benzene. ‘w’ g of the acid dissolved in 30g of benzene shows a depression in freezing point equal to 2K. If the percentage association of the acid to form dimer in the solution is 80, then w is : (Given that `K_(f)=5K Kg "mol"^(-1)` Molar mass of benzoic acid `=122 g "mol"^(-1)`)

Options

A. 1.8g
B. 2.4g
C. 1.0g
D. 1.5g

Answer

B

Explanation

`2C_(6)H_(5)CO OH hArr (C_(6)H_(5)CO OH_(2))`
If `alpha` is the degree of association .
Initial `" "1 " "0`
After `1 - alpha" " (alpha)/(2)`
` i= (1-alpha-(alpha)/(2))/(1) = 1- alpha`
`=1-(0.8)/(2) = 0.6`
`Delta T_(f) = (ixx K_(f) xx w_(B) xx 1000)/(M_(B) xx w_(A))`
` 2 = (0.6 xx 5 xx w_(B) xx 1000)/(122 xx30)`
` or W_(B) = (2xx 122 xx 30)/(0.6 xx 5 xx 1000) =2.44g`