Question

What mass, in grams, of NaCl needs to be added to 1.6 kg of water in order to create a solution with a freezing point of -5.6 °C? The freezing point depression constant of water is 1.86 ºC/m.

Answer 1

Answer:

Mass of NaCl required = 141 g

Explanation:

Given:

• Mass of water = 1.6 kg = 1600 g
• Freezing point of solution = -5.6 °C
• Freezing point depression constant = 1.86 °C/m

To Find:

• Mass of NaCl to be added

Solution:

First finding the depression in freezing point of the solution,

$\sf \Delta\:T_f=Freezing\:point\:of\:pure\:solvent-Freezing\:point\:of\:solution$

Therefore,

$\sf \Delta\:T_f=0^oC+5.6^oC$

$\sf \Delta\:T_f=5.6^oC$

The molar mass of NaCl = 23 + 35.5 = 58.5 g

Van't hoff factor for NaCl = 2

We know that,

$\boxed{\sf M_2=\dfrac{i\times K_f\times w_2\times 1000}{\Delta\:T_f\times w_1}}$

where M₂ = molar mass of the solute

$\sf K_f$ = Cryoscopic constant/Freezing point depression constant

w₂ = weight of solute

w₁ = weight of solvent

$\sf \Delta\:T_f$ = Depression in freezing point

i = van't hoff factor

Substitute the data,

$\sf 58.5=\dfrac{2\times 1.86\times w_2\times 1000}{5.6\times 1600}$

$\sf 58.5=\dfrac{3720\times w_2}{8960}$

$\sf 58.5=0.415\:w_2$

$\sf w_2=\dfrac{58.5}{0.415}$

$\sf w_2=140.96 \approx 141\:g$

Hence 141 g of NaCl must be added to the solvent.