# How is osmolarity related to molarity?

Aug 3, 2014

Osmolarity equals molarity times the van't Hoff $i$ factor.

#### Explanation:

Osmolarity is the number of osmoles of solute per litre of solution .

An osmole is 1 mol of particles that contribute to the osmotic pressure of a solution.

The term comes from the formula for calculating osmotic pressure:

Π = MRT, where $M$ is the molarity and $T$ is the Kelvin temperature.

Osmotic pressure is a colligative property. It depends on the number of particles.

If the solute is a nonelectrolyte like glucose, 1 mol of solute forms 1 mol of solute particles.

If the solute is an electrolyte, it will dissociate into ions.

"NaCl(s)" → "Na"^+("aq") + "Cl"^(-)("aq")

Thus, 1 mol of $\text{NaCl}$ forms 2 mol of solute particles. It contains 2 Osmol of particles.

The osmotic pressure of a 1 mol/L $\text{NaCl}$ solution will be twice that of a 1 mol/L solution of glucose.

The osmotic pressure formula becomes

Π = iMRT, where $i$ is the van't Hoff factor.

The van't Hoff factor is the number of moles of particles formed from 1 mol of solute.

Thus, a solution of 1 mol/L $\text{NaCl}$ has an osmolarity of 2 Osmol/L,

and a solution of 1 mol/L ${\text{CaCl}}_{2}$ has an osmolarity of 3 Osmol/L (1 mol ${\text{Ca}}^{2 +}$ and 2 mol ${\text{Cl}}^{-}$.

We can rewrite the formula for osmotic pressure as

Π = OsM×RT

If we compare the two formulas, we see that

OsM = i×M

That is, the osmolarity is the molarity times the van't Hoff factor.

The video below explains the difference between molarity and osmolarity.