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 = C*_{before} × *V*_{before}* = **C*_{after} × *V*_{after}

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:

*C*_{before} × *V*_{before } = *C*_{after} × *V*_{after}

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 (
*C*_{before}) - The target concentration (
*C*_{after}) to be achieved by dilution - The volume of the diluted solution to be produced (
*V*_{after})

The following decisions would need to be made:

- What volume of the starting solution to use (
*V*_{before})? 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:

*V*_{before }= (*C*_{after}×*V*_{after}) /*C*_{before} - What diluent to use (e.g. water or another solvent)?
- What volume of diluent to use (
*V*_{diluent})? The diluent is added to make up the difference between the starting volume and the target volume. It can simply be calculated as follows:

*V*_{diluent}=*V*_{after}–*V*_{before}

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