Colligative properties are those that depend on the number of solute particles.

Question

Colligative properties are those that depend on the number of solute particles. Because electrolytes dissociate into ions, the concentration of particles in the solution is greater than the formula-unit concentration of the solution. For example, if

1 mol of Na2SO4 totally dissociates, 3 mol of ions are produced (2 mol of Na+ ions and 1 mol of SO42 ions). Thus, a colligative property such as osmotic pressure will be three times greater for a 1 M Na2SO4 solution than for a 1 M nonelectrolyte solution.

However, complete dissociation of electrolytes does not always occur. The extent of dissociation is expressed by the van't Hoff factor, i:

i = moles of particles in solutionmoles of solute dissolved

The equations for colligative properties can be written to include i. For example,

Tf = Kfmi

Tb = Kbmi

Assuming complete dissociation of the solute, how many grams of KNO3 must be added to 275 mL of water to produce a solution that freezes at 14.5 C? The freezing point for pure water is 0.0 C and Kf is equal to 1.86 C/m.

Explanation / Answer

Tb   = 0 - (-14.5) = 14.5

i for KNO3 = 2

m = molality

water solvent mass = density x volume = 1 x 275 = 275 g = 0.275 kg

Tb = i x Kf x m

14.5 = 2 x 1.86 x m

m = 3.90 molal

molality = moles of solute / mass of solvent

3.90 = moles / 0.275

moles = 1.072

mass / molar mass = 1.072

mass / 101.1 = 1.072

mass = 108.4 g

mass of KNO3 = 108.4 g

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