How do you calculate molality from molarity?

See explanation.

If all you are given is , then you also need to know the of the solution to calculate , 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 , so be careful.

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

##"? g soln" = 1.00 cancel("L") xx (1000 cancel("mL"))/(1 cancel("L")) xx ("1.12 g")/(1 cancel("mL")) = "1120 g solution"##

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

##"? g water" = "mass of the solution" - "mass of NaCl in the solution"##

##= "1120 g soln" - (3.00 cancel("mol NaCl") xx "58.4 g"/cancel("1 mol NaCl"))##

##= "1120 g soln" - "175 g NaCl" = "945 g water"##

## = "0.945 kg of water"##

Now, use the units of molality as an equation:

##"molality" ("mol solute"/"kg solvent") = ("no. moles NaCl")/("no. kg water")##

So,

##"molality" = ("3.00 mol NaCl")/("0.945 kg water") = "3.17 m NaCl"##