# How can molarity and osmolarity be calculated from m/v?

May 19, 2014

Molarity is the number of moles of solute per litre of solution; osmolarity is the number of osmoles per litre of solution.

By "m/v", I assume that you mean "mass per unit volume".

Assume you have a solution that contains 40.0 g of NaCl in 1.00 L of solution.

MOLARITY

The molarity of a solution is the number of moles of solute per litre of solution.

$M = \frac{n}{V}$

You have to convert the mass of NaCl to moles of NaCl.

Moles of NaCl = 40.0 g NaCl × $\left(1 \text{ mol NaCl")/(58.44" g NaCl}\right)$ = 0.684 mol NaCl

$M = \frac{n}{V} = \left(0.684 \text{ mol")/(1.00" L}\right)$ = 0.684 mol/L

OSMOLARITY

An ionic compound such as NaCl separates into cations and anions on dissolving.

NaCl(s) →Na⁺(aq) + Cl⁻(aq)

Osmosis depends on the number of solute particles in a solution. Both the number of moles of Na+ and the number of moles of Cl- contribute to the osmotic pressure. Thus, 1 mol of NaCl gives 2 mol of osmotic particles.

Each mole of solute that contributes to the osmotic pressure of a solution is an osmole.

The osmolarity is the molarity of the compound times the number of particles produced by one mole of compound.

The osmolarity of the NaCl solution is

OsM =$\left(0.684 \text{ mol")/(1" L") × (2" Osmol")/(1" mol}\right)$ = 1.37 Osmol/L