Dilution Calculation

Diluting a solution does not change the amount of solute, so c₁V₁ = c₂V₂. This finds the final volume needed and how much solvent to add.

Explanation

When you dilute a solution, the amount of solute does not change. Only the solvent increases. That single fact gives the dilution equation.

c_1 V_1 = c_2 V_2

Both sides are the amount of solute in moles. The equation says nothing more than that this amount is the same before and after.

Example

Dilute 100 mL of a 2 mol/L solution down to 0.5 mol/L.

V_2 = \dfrac{c_1 V_1}{c_2} = \dfrac{2 \times 100}{0.5} = 400\ \text{mL}

The final volume must be 400 mL, so you add $400 - 100 = 300$ mL of water.

The concentration fell to a quarter and the volume rose fourfold. Concentration and volume are inversely proportional.

Safety in the laboratory

Always add acid to water, never water to acid.

Concentrated sulfuric acid releases a great deal of heat when it meets water. Pour water onto the acid and the droplet flashes to steam, spitting concentrated acid out of the vessel. "Do as you oughta, add acid to water."

Where it is used

Preparing reagents by diluting a concentrated stock solution
Disinfectants and garden chemicals sold as concentrates
The same equation works for mass percent, as long as both sides use the same units