How do you calculate freezing point depression?

1 Answer
Ernest Z. · dwayne
Dec 31, 2013

You use the formula for freezing point depression.

Explanation:

EXAMPLE

What is the freezing point depression caused by adding 31.65 g of sodium chloride to 220.0 g of water. Kf for water is 1.86 °C⋅kg⋅mol-1.

Solution

The formula for freezing point depression expression is

∣∣ ∣∣¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯aaΔTf=iKfmaa∣∣−−−−−−−−−−−−−−−

where

ΔTf is the freezing point depression,

i is the van’t Hoff factor,

Kf is the molal freezing point depression constant for the solvent, and

m is the molality of the solution.

Step 1: Calculate the molality of the NaCl

moles of NaCl=31.65g NaCl×1mol NaCl58.44g NaCl=0.5416 mol NaCl

mass of water=220.0g H2O×1kg H2O1000g H2O=0.220 kg H2O

m=moles of NaClkilograms of water=0.5416 mol0.220 kg=2.46 mol/kg

Step 2: Determine the van't Hoff factor

The van't Hoff factor, i, is the number of moles of particles obtained when 1 mol of a solute dissolves.

Nonelectrolytes such as sugar do not dissociate in water. One mole of solid sugar gives one mole of dissolved sugar molecules.

For nonelectrolytes, i=1.

Electrolytes such as NaCl completely dissociate into ions.

NaCl→Na++Cl-

One mole of solid NaCl gives two moles of dissolved particles: 1 mol of Na+ ions and 1 mol of Cl- ions. Thus, for NaCl,i=2.

Step 3: Calculate ΔTf

ΔTf=iKfm=2×1.86 °C⋅kg⋅mol-1×2.46mol⋅kg-1=9.16 °C

The freezing point depression is 9.16 °C.

Here's a video on how to calculate freezing point depression.

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