Conversions Between Concentration Units
An Example using Hydrochloric Acid
A common laboratory reagent is 37% HCl. A solution that is 37% HCl is 37% dissolved
hydrogen chloride and 62% water. This handout will show you how to convert between
weight percent and molarity (M), molality (m), mole percent and ppm. The only
additional information you need is the density of the 37% HCl, which is 1.19 g/cm3
Let’s do the easy ones first.
Weight percent to mole percent. Just divide the solute by its molar mass and the
solvent by its molar mass and then take the ratio.
37
 1.01 moles HCl
36.5
63
1.01
= 3.5 moles H2O
= 0.224 mole fraction of HCl
18
4 .5
Weight percent to ppm. Just divide the weight of the solute by the total weight of the
solution and multiply by 106
37
x 106 = 3.7 x 105 ppm That’s a lot of parts! Usually ppm is only used for much
100
smaller concentrations.
Weight percent to molarity. Now you need the density. We know there are 37 grams
of HCl in 100 grams of solution, but what is that volume? The volume is
100 grams 100
=
= 84.03 mL = 0.084 L
1.19
density
Moles of HCl =
37
= 1.01 moles HCl
36.5
Molarity = M =
1.01molesHCl
= 12.02 M
0.084 L
Molarity to Molality.
Molality is moles solute per kilogram solvent. We have 12.02 M solution. We know 1
Liter of solution contains 12.02 moles HCl and we know that one liter weighs 1000 mL x
1.19 grams
= 1190 grams. Of that 1190 grams of solution,
ml
36.5 grams
12.02 x
= 438.75 grams are HCl. The solvent, water, is 1190 – 438.75 =
moleHCl
751.25 grams.
12.02molesHCl
1000 grams
So the molality is
x
= 16 m or 16 molal.
751.25 gramssolvent
kg
The molality may be calculated directly from the weight percent or mole percent as long
as you have the density. Try it. You should get the same answer.
Then practice by making up some concentrations and converting them on your own. If
you make up a density of between 1 – 2 grams/cm3 you won’t be too far from reality.