Diluting solutions to the right molarity

There’s one more way to prepare solutions — the dilution of a more concentrated solution to a less-concentrated one. For example, you can buy hydrochloric acid from the manufacturer as a concentrated solution of 12.0 M. Suppose that you want to prepare 500 milliliters of 2.0 M HCl. You can dilute some of the 12.0 M to 2.0 M, but how much of the 12.0 M HCl do you need? You can easily figure the volume (V) you need by using the following formula:

V_old × M_old = V_new × M_new

In the preceding equation, V_old is the old volume, or the volume of the original solution, M_old is the molarity of the original solution, V_new is the volume of the new solution, and M_new is the molarity of the new solution. After substituting the values,

you have the following:

V_old × 12.0 M = 500.0 milliliters × 2.0 M

V_old = (500.0 milliliters × 2.0 M)/12.0 M = 83.3 milliliters

You then take 83.3 milliliters of the 12.0 M HCl solution and dilute it to exactly 500.0 milliliters.

If you’re actually doing a dilution of concentrated acids, be sure to add the acid to the water instead of the other way around! If the water is added to the concentrated acid, then so much heat will be generated that the solution will quite likely splatter all over you. So to be safe, you should take about 400 milliliters of water, slowly add the 83.3 milliliters of the concentrated HCl as you stir, and then dilute to the final 500 milliliters with water.