How do you calculate molality from molarity?

1 Answer

See explanation.

Explanation:

If all you are given is Molarity, then you also need to know the density of the solution to calculate molality, m (mol/kg solvent).

The easiest way to understand the process is to assume you have 1L of solution which is 1000 mL. Think of the units of molarity and molality. So here is an example:

What is the molality of a 3.00 M solution of NaCl? The density of the solution is 1.12 g/mL.

We know that in 1.00 L of solution, there are 3.00 mol of NaCl, since that is the meaning of 3.00 M.

If we figure out how many kg of water there are in 1.00 L of this solution, we are almost done! Many students are confused between solution and solvent, so be careful.

First let's figure out the mass of the solution using dimensional analysis and density:

? g soln=1.00L×1000mL1L×1.12 g1mL=1120 g solution

Now we need to know the mass of just the water.

? g water=mass of the solutionmass of NaCl in the solution

=1120 g soln(3.00mol NaCl×58.4 g1 mol NaCl)

=1120 g soln175 g NaCl=945 g water

=0.945 kg of water

Now, use the units of molality as an equation:

molality(mol solutekg solvent)=no. moles NaClno. kg water

So,

molality=3.00 mol NaCl0.945 kg water=3.17 m NaCl