Molality is a measure of the concentration of a solute in a solution. It is used primarily when temperature is a concern. Molarity depends on the volume, but volume can change when temperature changes. Molality is based on the mass of solvent used to create the solution because mass does not change as the temperature changes.
This molality example problem shows the steps needed to calculate the molarity of a solution given the amount of solute and the mass of the solvent.
Problem
Calculate the molality of a solution prepared from 29.22 grams of NaCl in 2.00 kg of water.
Solution
Molarity is calculated using the formula:
where molesSOLUTE is the number of moles of solute, in this case NaCl
and KgSolvent is the mass in kilograms of the solvent.
First, calculate the number of moles of NaCl.
Using a periodic table, the atomic masses are:
Na = 22.99 g/mol
Cl = 35.45 g/mol
Add them together to get the molecular mass of NaCl
molecular mass NaCl = 22.99 g/mol + 35.45 g/mol
molecular mass NaCl = 58.44 g/mol
Convert grams to moles of the NaCl
moles NaCl = 0.50 moles
Plug in this and the mass of the water into the molarity formula
m = 0.25 moles/kg
or
m = 0.25 molal
Answer
The molality of the NaCl solution is 0.25 molal.
As you can see, calculations for molality are straightforward. Remember to find the number of moles of solute and the mass of the solvent and the rest is simple. If you do not know the mass of your solvent, you often know the volume. Use the density of the solvent to find the mass you need.