Two ways to express concentration
The concentration of a solution is the amount of dissolved solute per unit volume of solution. It is measured in two units:
- Concentration in g dm−3 = mass of solute (g) ÷ volume of solution (dm3)
- Molarity (mol dm−3) = number of moles of solute ÷ volume of solution (dm3)
Key idea / 要点
Molarity (mol dm−3) = concentration (g dm−3) ÷ molar mass (g mol−1)
Also: number of moles = mass ÷ molar mass; and 1 dm3 = 1000 cm3.
Remember that 1 dm3 = 1000 cm3, so a volume given in cm3 must be divided by 1000.
Dilution
Adding water lowers the concentration but keeps the number of moles the same, so:
Key idea / 要点
M1V1 = M2V2
where M is molarity and V is volume, before (1) and after (2) dilution.
These relationships link mass, moles, volume and concentration, so a value given in one form can always be converted to another. A common exam task is to work backwards — for example, calculating the mass of solute that must be weighed out to make a solution of a stated molarity and volume. Careful conversion of the volume between cm3 and dm3 is the step where most marks are lost.
Worked example
Calculate the molarity of a solution containing 20 g of sodium hydroxide (NaOH, M = 40 g mol−1) in 500 cm3 of solution.
Moles = 20 ÷ 40 = 0.5 mol. Volume = 500 ÷ 1000 = 0.5 dm3.
Molarity = 0.5 ÷ 0.5 = 1.0 mol dm−3
Remember
- Always convert cm3 to dm3 by dividing by 1000.
- Molar mass = sum of relative atomic masses.
- On dilution, moles stay constant: M1V1 = M2V2.