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Quantitative Methods: Part 2. Diluting Solutions

Author(s): David R. Caprette, PhD

Example: Dilute a Stock Solution

To create a stock solution, first define clearly what you want to do. For example, suppose you have 500 ml of a stock solution of sucrose at 325 mM concentration. Then suppose you need to dilute it to 200 mM. First, make sure all the units agree. On other words, the units used for concentration must be the same on both sides of the equation, as must be the units used for volume.

Now you can set up the problem. The total amount of solute is given by the concentration of the solute times the volume of the solution, or C1V1. You have 0.5 liter times 0.325 moles/liter, which is 0.1625 moles. To dilute the solution means to increase its volume, obviously, by adding more solvent but no more solute. You know the final desired concentration, namely 200 mM, but you don't know the final volume yet. We'll call it V2. You know that V2 times the final concentration, 0.2 moles/liter, has to be 0.1626 moles. The final volume, then, is given by the equation

V2 = (0.5)(0.325)/0.2

The equation yields 0.8125 L, which is 812.5 ml. You already have 500 ml, so you must add 312 ml to that solution, or simply bring the final volume to 812 ml in a graduated cylinder.