Question

The freezing point of a diluted milk sample is found to be 0.2c, while it should have been 0.5c for pure milk. How much water has been added to pure milk to make the diluted sample

Answer 1

freezing point is directly proportional to molality of solution.as formula of freezing point is $\Delta T_f=K_fm$

here m denotes molality.

and we know, molality = number of mole of solute /mass of solvent in kg.

means, molality is inversely proportional to mass of solvent.

i.e., $\frac{\Delta T_f}{\Delta T^{\circ}_f}=\frac{m'}{m}$

if initial mass of solvent (water) = M kg

Let x g amount of water is added to solution of milk,

then, mass of solvent = (M + x) , where M is Initial mass of solvent

now, $\frac{\Delta T_f}{\Delta T^{\circ}_f}=\frac{(M+x)}{M}$

or, 0.5/0.2 = (M + x)/M

or, 0.5M = 0.2(M + x)

or, 5M= 2M + 2x

or, x = 1.5M kg

hence, M kg of pure milk 1.5M kg water should be added to dilute sample.

or, you can say that, 3 cup of water is added to 2 cup of pure milk