How to Dilute a Solution Using C1V1 = C2V2

Diluting a solution means adding solvent, usually water, to lower its concentration. The amount of dissolved substance stays the same, which gives a very handy formula.

The formula

• C1: concentration of the stock (starting) solution
• V1: volume of stock you'll use
• C2: the concentration you want
• V2: the final total volume

Any units work, as long as both concentrations use the same unit and both volumes use the same unit.

Example

You have a 2 M salt solution and need 500 ml at 0.25 M.

Measure 62.5 ml of stock and top it up with water to a total of 500 ml. Top up to the final volume rather than adding a calculated 437.5 ml of water, because the volumes of mixed liquids don't always add exactly.

Dilution factor

In the example, 500 ÷ 62.5 = 8, so it's a 1:8 dilution: 1 part stock in 8 parts total. Be careful, because some people write "1:8" to mean 1 part stock plus 8 parts water (9 in total). Say which you mean.

Serial dilutions

For very large dilutions, dilute in steps. Three 1:10 dilutions in a row give 1:1,000 overall, and each step uses volumes big enough to measure accurately.

Percent solutions

The formula works for percentages too. To make 1 liter of a 3% solution from 30% stock: V1 = 3 × 1,000 ÷ 30 = 100 ml of stock, topped up to 1 liter.

Safety

When diluting concentrated acids, always add acid to water, slowly, never water to acid, and wear eye protection. Follow your lab's or the manufacturer's safety instructions.