Acetic acid associates in benzene to form a dimer. `1.65 g` of acetic acid when dissolved in `100 g` of benzene raised the boiling point by `0.36^(@)C`. Calculate the Van't Hoff factor and degree of association of acetic acid.
(`K_(b)` for benzene=`2.57^(@)C`)

Explanation

Normal molar mass of acetic acid =60
Obseved molar mass of acetic acid
`M=(K_(b)xxW_("solvent")xx1000)/(W_("solvent")xxDeltaT)`
`=(2.57xx1.65xx1000)/(100xx0.36)=118`
Van.t Hoff Factor `=("Normal molar mass")/("Observed molar mass") =(60 "g mol"^(-1))/(118"gmol"^(-1))=0.508`
`=0.508=(1-alpha//2)`
`alpha//2=-1-0.508 :. alpha =2xx0.429=0.984`
Thus acetica acid is `98.4%` associated in benzene.