AP® Chemistry · Unit 3 · Topic 3.7
Dilution and Stock Solutions
Dilution adds solvent without adding solute, so moles stay fixed while volume grows and concentration drops. That conservation of moles gives the formula M1V1 = M2V2.
When you add water to a solution, you are not touching the solute at all. The same number of moles of dissolved particles just spreads through a bigger volume. Since concentration is moles divided by volume, moles stay constant while volume climbs, so molarity falls. That single fact, moles of solute unchanged, is the whole idea behind dilution.
Write it out and the formula falls into place. Moles before equal moles after: M1 x V1 = M2 x V2, where M1 and V1 describe the concentrated stock before dilution and M2 and V2 describe the dilute solution after. Solve for whichever quantity is missing. This only works when the solute itself does not react or change identity, and when no solute is added or removed, only solvent.
This connects directly to how solutions get made in practice: a concentrated stock solution sits on a shelf, and a chemist dilutes it to whatever concentration an experiment needs, often checking the result with light absorbance later in this unit. It also sets up a trap: mixing two solutions of the same solute is not dilution with solvent, it is combining two sources of moles. The final concentration there is a mole-weighted average over the total volume, not a simple halfway point between the two starting concentrations.
Key terms
- Stock solution
- A solution of known, usually high, concentration kept on hand to be diluted as needed.
- Dilution
- Adding solvent to a solution to lower its concentration without changing the moles of solute.
- Molarity
- Concentration expressed as moles of solute divided by liters of solution.
- Mole-weighted average
- A combined concentration found by adding total moles from each source and dividing by total volume.
Watch it explained
- How it worksHow does the relationship M1V1 equals M2V2 fall straight out of conserving moles?
- Worked exampleFind the volume of 6.00 M HCl needed to make 250 mL of 0.500 M HCl.
- Common mistakeWhy isn't a solution twice as dilute when you add an equal volume of a weaker solution?
- Going furtherWhat happens to the particle picture of a solution as it is diluted three times over?
Check yourself
End of topic.