13.7Solution Dilution

The idea

• Use the dilution equation.
• Avoid adding the volumes incorrectly when the problem gives volumes of solution.

Dilution adds solvent, not solute. The moles you started with are the moles you end with: M₁V₁ = M₂V₂. Volumes can be in mL if both are, because the unit cancels, but do not mix mL and L. Solve for whichever variable is unknown. If you pour 10 mL of stock into a flask and fill to 100 mL, V₂ is 100 mL, not 110 mL and not 90 mL.

The equation does not apply when a reaction consumes solute, and it does not apply to mass percent unless you recompute masses. It is only conservation of moles under addition of solvent. A useful check: the diluted solution is always less concentrated, and the volume is always larger. If your algebra gives the opposite, the labels 1 and 2 were swapped.

Worked path

What volume of 12.0 M stock HCl is needed to prepare 500. mL of 0.100 M HCl?

1. Observe

   M₁ = 12.0, M₂ = 0.100, V₂ = 500 mL.

Check yourself