Preparing solutions via accurate dilution

Solutions of accurately known concentration are often prepared both from stock solutions (see preparing solutions of accurately known concentration from solids) or from neat liquid reagents. In both cases the same principles apply.

Calculations for the quantities required are generally achieved using:

 c1 v1 = c2 v2

Where c1 is the concentration of the stock solution and c2 the desired concentration of the diluted solution. For the volumes, v2 needs to the size of a volumetric flask which is sufficient for the amount of solution required. For instance, if you require 15 mL of solution, the next size of volumetric flask is 25 mL, so you should prepare 25 mL of solution. The remaining value, v1, will be determined as the amount of the stock solution to be taken. This needs to be an amount that can be accurately measured. If it is a very small volume which could not be measured, then you should consider making a more concentrated solution and diluting that solution down to produce a solution at the desired concentration.

For example, if you had a 0.1M stock solution, and you wanted to make a 0.02M stock solution, in a 10 mL volumetric flask, you would require 2 mL of concentrated solution to add to the flask.

Once you have calculated the required volumes and selected an appropriate volumetric flask and ideally fill the flask roughly half full with solvent (providing the volume of concentrated solution required is less than 50% of the flask volume, otherwise adjust the solvent volume appropriately). 

Then using a graduated pipette, draw up the volume of concentrated solution required, and transfer it into the volumetric flask.

The volumetric flask can then be brought to the mark with solvent.

As with solids, this procedure may need to be modified when handing solutions which generate exotherms or endotherms on mixing. Most commonly this will be where concentrated acids are diluted, especially where large volumes are diluted by low ratios of solvent. It may be necessary to perform an initial dilution in a conical flask (possibly in an ice-bath) and transfer with washings into the volumetric flask after the heat has dissipated.