Dilution Calculations From Stock Solutions

If you're working in a chemistry lab, it's essential to know how to calculate a dilution.

Review of Dilution, Concentration, and Stock Solutions

A dilution is a solution made by adding more solvent to a more concentrated solution (stock solution), which reduces the concentration of the solute. An example of a dilute solution is tap water, which is mostly water (solvent), with a small amount of dissolved minerals and gasses (solutes).

An example of a concentrated solution is 98 percent sulfuric acid (~18 M). The primary reason you start with a concentrated solution and then dilute it to make a dilution is that it's very difficult—and sometimes impossible—to accurately measure solute to prepare a dilute solution, so there would be a large degree of error in the concentration value.

Read More

Calculating Concentrations with Units and Dilutions

By Anne Marie Helmenstine, Ph.D.

Use the law of conservation of mass to perform the calculation for the dilution:

M_dilutionV_dilution = M_stockV_stock

Dilution Example

As an example, say you need to prepare 50 milliliters of a 1.0 M solution from a 2.0 M stock solution. Your first step is to calculate the volume of stock solution that is required.

M_dilutionV_dilution = M_stockV_stock
(1.0 M)(50 ml) = (2.0 M)(x ml)
x = [(1.0 M)(50 ml)]/2.0 M
x = 25 ml of stock solution

To make your solution, pour 25 ml of stock solution into a 50 ml volumetric flask. Dilute it with solvent to the 50 ml line.

Avoid This Common Dilution Mistake

It's a common mistake to add too much solvent when making the dilution. Make sure you pour the concentrated solution into the flask and then dilute it to the volume mark. Do not, for example, mix 250 ml of concentrated solution with 1 liter of solvent to make a 1-liter solution.