Electrolytes: van't Hoff Factor

Colligative properties of a solution depend on the actual number of dissolved solute particles.

For a non-electrolyte, each solute molecule that dissolves yields one dissolved solute molecule.

However, ionic electrolytes, such as sodium chloride, dissociate into ions when dissolved, while ammonia gas, a covalent electrolyte, reacts with water to release ammonium and hydroxide ions in solution.

So for electrolytes, each solute molecule that dissolves yields more than one dissolved solute particle.

Thus, a 1 M solution of a non-electrolyte such as dextrose, will have 1 mole of dextrose molecules in a 1-liter solution, whereas a 1 M solution of an electrolyte such as potassium chloride will dissociate into nearly 1 mole of potassium ions and 1 mole of chloride ions-- a total of 2 moles of ions in a 1-liter solution.

With double the number of solute particles, the osmotic pressure of a 1 M potassium chloride solution will be twice that of a 1 M dextrose solution.

The ratio between the moles of particles that a dissolving solute forms in solution and the moles of solute added to make a solution, is called the van’t Hoff factor represented by i.

It is calculated by dividing the measured value of a colligative property by the value calculated from a formula.

Consider the freezing point depression of a potassium chloride solution. Freezing-point depression, ΔT_f, is calculated by multiplying the van’t Hoff factor for potassium chloride with the molal freezing-point-depression constant and the molality of the solute.

If i is 2 and the freezing point depression constant for water is 1.86 °C/m, the freezing-point depression of a 0.100 m potassium chloride solution is calculated to be 0.372 °C.

However, the measured freezing point depression for a 0.100 m potassium chloride solution is 0.344 °C.

This difference exists because when an electrolyte dissociates into ions in solution, some of the cations and anions recombine. This phenomenon is called ion pairing.

Strong electrolytes with highly charged ions, such as iron(III) chloride and magnesium sulfate, can form strong electrostatic interactions and thus have a greater tendency to form ion pairs.

For weak electrolytes, such as ammonium hydroxide, the dissociation into ions is incomplete.

Thus, for both strong and weak electrolytes, the van’t Hoff factor is less than expected.