Phenol associates in benzene to a certain extent to form a dimer. A solution containing `20xx10^(-1)` kg phenol in 1 kg of benzene has its freezing pint depressed by 0.69 K. Calculate the fraction of phenol that has dimerised. `"K"_("f")" for benzene"=5.12" kg mol"^(-1)"k"`.

Answer

0.734

Explanation

`M_(2)"(observed)"=(1000K_(f)w_(2))/(w_(1)DeltaT_(f))=("1000 g kg"^(-1)xx"5.12 K kg mol"^(-1)xx2.0xx10^(-2)kg)/(1.0kg xx0.69K)="148.4 g mol"^(-1)`
`M_(2)"(calculated) for "C_(6)H_(5)OH="94 g mol"^(-1)" "therefore" "i=(M_(2)"(calculated)")/(M_(2)"(observed)")=(94)/(148.4)=0.633`
`{:(,2C_(6)H_(5)OHhArr(C_(6)H_(5)OH)_(2)),("Initial"," 1mol"),("After asso."," "1-alpha" "alpha//2" Total "=1-alpha//2):}`
`i=(1-alpha//2)/(1)" or "alpha=2(1-i)=2(1-0.633)=0.734.`