Moles per unit volume
The last of the five ways, and the one chemistry uses most. It counts the solute in moles rather than grams, and it has a name of its own.
Concentration
amount of solute in moles ÷ volume of solution
C = n ÷ V
C = concentration, n = amount of solute (mol), V = volume of solution (dm3)
When the composition is expressed as the amount of solute, in moles, contained in a unit volume of solution, it is called the concentration. The international unit for measuring an amount of substance is the mole, which is why this is the form chemistry reaches for.
The unit, and the volumes behind it
In chemistry a concentration is most often expressed using the amount of solute, in moles, contained in a cubic decimetre of solution — so the unit is mol dm-3. Getting that right means being sure of these:
Relationships worth knowing by heart
1 dm3 = 1 l (litre)
1 dm3 = 1000 cm3
1 dm3 = 1000 ml
1 cm3 = 1 ml
Why moles and not grams
Two solutions of the same concentration in mol dm⁻³ hold the same number of solute particles in the same volume, whatever the solute is. Two solutions of the same g dm⁻³ do not — 5 g of a heavy molecule is far fewer particles than 5 g of a light one. Since reactions happen between particles, moles are what count.
A volume in cm³ must be converted
Concentration in mol dm⁻³ needs the volume in dm³. A volume given in cm³ has to be divided by 1000 first. Nearly every wrong answer in this skill comes from skipping that step.