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The molar volume of liquid benzene (dens...

The molar volume of liquid benzene (density `=0.877 g ml^(-1)`) increases by a factor of `2750` as if vaporises at `20^(@)C` while in equilibrium with liquid benzene. At `27^(@)C` when a non-volatile solute (that does not dissociate) is dissolved in `54.6cm^(3)` of benzene vapour pressure of this solution, is found to be `74.76 mm Hg`.
Calculate the freezing point of the solution. Given: Enthalpy of vaporization of benzene `(l)=394.57J` Molal depression constant for benzene `=5.0K` kg. Mol^(-1)`. Freezing point of benzene `=278.5K`.

Text Solution

Verified by Experts

As `(P^(@)-P_(s))/(P_(s))=(n_(1))/(n_(2))=(w_(1)xxm_(2))/(m_(1)xxw_(2))`
`rArr (P^(0)-P_(s))/(P_(s))=((1000xxw_(1))/(m_(1)xxw_(2)))xx(m_(2))/(1000)=mxx(m_(2))/(1000)`
`{:(m="molality"),(m_(2)="molecular wt of solvent"):}`
`:.(100-98.88)/(98.88)=mxx(78)/(1000)`
`:.m=(1.12xx1000)/(78xx98.88)=0.1452`
Also, `DeltaT_(f)=K_(t)xx` molality
`:.0.73=K_(f)xx0.1452`
`K_(i)= 6.028 K` molality
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