Dilution and the relationship C1.V1 = C2.V2

What does it mean to dilute a solution?

Diluting a solution involves adding solvent (usually water) to a solution that has already been prepared, known as the stock solution, to produce a new, less concentrated solution, known as the diluted solution. The amount of solute remains unchanged during dilution: we are simply spreading this same amount over a larger volume.

The fundamental relationship

As the amount of solute is conserved, we have n(stock) = n(dilute), which gives, where C1 and V1 denote the concentration and volume of the stock solution taken, and C2 and V2 those of the resulting dilute solution:

C1 x V1 = C2 x V2

Practical example

V1 = 10 mL (0.010 L) is taken from a stock solution of concentration C1 = 1.0 mol/L. We wish to obtain a daughter solution of concentration C2 = 0.10 mol/L. What final volume V2 must be achieved?

V2 = (C1 x V1) / C2 = (1,0 x 0,010) / 0,10 = 0,10 L (i.e. 100 mL)

The dilution factor

The dilution factor is denoted by F and defined as the ratio F = C1/C2 = V2/V1. In the example above, F = 1.0/0.10 = 10: we say that the solution has been diluted 10 times. We must therefore take 10 mL of the stock solution and make it up to 100 mL with water.

Common mistake

Do not confuse dilution with dissolution: dilution involves adding solvent to an existing solution (without adding any new solid solute); dissolution involves bringing a solute (often solid) into solution. Another common mistake is to forget that the concentration decreases as the volume increases, but that the amount of solute remains exactly the same.