Dilution is the process of reducing the concentration of a defined substance (solute) in a solution. The term concentration denotes how much (i.e. what mass, in terms of number of molecules or weight) of the solute is present in a given volume of solution. More precisely, the relationship between concentration (C), mass (M) and volume (V) is as follows:

C = M / V

From the equation, it is clear that concentration may be reduced by:

• reducing solute mass (by removing some of the solute molecules from the solution), or
• increasing the volume of the solution (by adding a diluent).

In practice, the latter is easier to do than the former. Thus, dilutions are nearly always performed by adding a diluent, increasing the volume.

It should be noted that the mass of the solute present (M) remains the same before and after dilution. For this reason, one could rearrange the equation above and derive a relationship between solute concentration (C) and solution volume (V) before and after dilution:

M = C × V

Because M remains the same before and after dilution, the following relationship holds:

M = Cbefore × Vbefore = Cafter × Vafter

When diluting a solution, one does not need to know the exact value of M, so that variable may be disregarded, and the following equation is sufficient for the purpose of decision-making:

Cbefore × Vbefore = Cafter × Vafter

In a typical dilution problem, the following variables (those that appear in green in the equation above) would be known:

• The concentration of the starting solution (Cbefore)
• The target concentration (Cafter) to be achieved by dilution
• The volume of the diluted solution to be produced (Vafter)

The following decisions would need to be made:

• What volume of the starting solution to use (Vbefore)? Note that this different from the volume of starting solution available to use, as one usually only needs to use a fraction of what is available. The volume to use can simply be calculated as follows:
Vbefore = (Cafter × Vafter) / Cbefore
• What diluent to use (e.g. water or another solvent)?
• What volume of diluent to use (Vdiluent)? The diluent is added to make up the difference between the starting volume and the target volume. It can simply be calculated as follows:
Vdiluent = VafterVbefore

A reminder that in performing the calculations above, units should be harmonised.