`75.2 g` of `C_(6)H_(5)OH` (phenol) is dissolved in a solvent of `K_(f) = 14`. If the depression in freezing point is `7K`, then find the percentage of phenol that dimerises.

Explanation

Calculation of molality of the solution.
1 molar solution means that 1 gram mole of KCI is dissolved in one litre of the solution.
Mass of 1L of solution =`Vxxd=(1000 mL)xx(1.04 g mL^(-1))=1040 g`
Mass of KCI (one mole)= 39+35.5= 74.5 g ,
Mass of solvent (water)= 1040074.5=965.5 g=0.9655 kg
`"Molality of solution (m)"=("No. of moles of solute")/("Mass of solvent in kg")=((1mol))/((0.9655 kg))=1.0357 molkg^(-1)`
=1.0357 m.
Calculatioin ofelevation in bolining point `(DeltaT_(b)`
KCI dissociates in aqueous solution as:
`KCI(s)overset((aq))toK^(+)(aq)+CI^(-)(aq)`
`"Van't Hoff factor (i)"=(" No. of particles after dissociation")/(" No. of particles originally present")=2/1=2`
`K_(b)=0.52 "K kf mol"^(-1), m=1.0357 "mol kg"^(-1)`, i=2
`DeltaT_(b)=ixxK_(b)xxm=(2)xx(0.52 K mol kg"^(-1))`=1.078K.
Calculation of boiling point of solution.
Boiling point of solution `(T_(b)=T_(b)^(@)+DeltaT_(b)=373K+1.078 K 374.078 K`