Question

An aqueous solution of ethylene glycol
(C2H6O2) of mass 624 grams has molality of
4 mol/kg. If this solution is placed at –10°C
then 'w' kg of water freezes out from the
solution.
Given that value of Kf
(H2O) = 2 k–kg mol–1

Find value of 'w' ?

Answer 1

Given that,

Molatity = 4 mol/kg

The mass of ethylene glycol is 6.2 gram.

Suppose, The weight of aqueous solution is 55g.

We know that,

The molar mass of ethylene glycol is 62 g/mol.

We need to calculate the number of moles

Using formula of number of moles

$N=\dfrac{m}{M}$

Put the value into the formula

$N=\dfrac{6.2}{62}$

$N=0.1\ mol$

Now 1 m solution contains 1 mole of solute in 1 kg of solvent.

We need to calculate the weight of water present in 4 molal solution containing 0.1 mole of ethylene glycol

Using formula of mass

$mass=\dfrac{N}{m}$

Put the value into the formula

$mass=\dfrac{0.1}{4}\times1000$

$m=25\ g$

We need to calculate the amount of ice separated

Using formula for weight

$w=\text{mass of aqueous solution}-m$

Put the value into the formula

$w=55-25$

$w=30\ g$

Hence, The amount of ice separated is 30g.