AP Chemistry Dilution Calculations
M1V1 = M2V2, why it works, and two full worked examples.
Diluting a solution, adding solvent to lower its concentration, is one of the most common calculations in the lab and on the exam. The formula is short, but knowing which number goes where, and why the formula works at all, is what actually gets tested.
The Formula
M1V1 = M2V2. M1 and V1 describe the concentrated starting solution; M2 and V2 describe the diluted final solution. Give any three values and you can solve for the fourth.
Why It Works
Diluting a solution means adding solvent, nothing else. The moles of solute don't change, only the total volume (and therefore the concentration) do. Since molarity × volume = moles of solute (M × V = mol), and that mole count is fixed before and after dilution, M1V1 has to equal M2V2, they're both just expressing the same unchanged number of moles.
Worked Example 1: Finding the Final Volume
You have 250. mL of 6.00 M HCl. What total volume do you need to dilute it to, to get a 1.50 M solution?
M1V1 = M2V2 → (6.00 M)(250. mL) = (1.50 M)(V2)
V2 = 1500 / 1.50 = 1000. mL (1.00 L)
In practice: measure out the original 250. mL, then add solvent until the total volume reaches 1.00 L.
Worked Example 2: Finding How Much Stock to Measure Out
You need to prepare 500. mL of 0.100 M solution from a 12.0 M stock solution. How much of the stock do you need?
M1V1 = M2V2 → (12.0 M)(V1) = (0.100 M)(500. mL)
V1 = 50.0 / 12.0 = 4.17 mL
In practice: measure out 4.17 mL of the 12.0 M stock, then add solvent until the total volume reaches 500. mL, not 4.17 mL plus 500 mL of solvent added on top.
Common Mistakes
- Swapping V1 and V2. V1 is always the smaller starting volume; V2 is always the larger final volume after dilution.
- Adding the final volume of solvent instead of diluting to a final total volume. "Dilute to 500 mL" means the finished solution totals 500 mL, not that you add 500 mL of solvent on top of what you already have.
- Confusing dilution with a titration reaction. Dilution never involves a chemical reaction or a mole ratio between two different substances, it's the same solute, just less concentrated.
- Mismatched units between the two sides. Volume units don't have to be liters, but both V1 and V2 need to use the same unit as each other for the equation to work directly.
Related Resources
- Unit 3 Review: Properties of Substances and Mixtures
- Unit 4 Review: Chemical Reactions
- AP Chemistry Limiting Reactant & Percent Yield
- AP Chemistry Significant Figures Rules
- AP Chemistry Study Guide
Frequently Asked Questions
What is the dilution formula?
M1V1 = M2V2, where M1 and V1 are the concentration and volume of the starting (concentrated) solution, and M2 and V2 are the concentration and volume of the diluted solution. Any three of the four values lets you solve for the fourth.
Why does M1V1 = M2V2 work?
Because adding solvent to dilute a solution changes its volume and concentration, but not the actual moles of solute present, you're not adding or removing any solute, just spreading the same amount through more liquid. Since molarity times volume equals moles (M x V = mol), and moles of solute stay constant, M1V1 must equal M2V2.
Does it matter which volume is V1 and which is V2?
V1 is always the smaller volume, the amount of concentrated stock solution you start with or measure out. V2 is always the larger, final, total volume after dilution. Mixing them up is the most common source of a wrong answer.
Can you use M1V1 = M2V2 for a dilution done in multiple steps?
Not directly in one line, each dilution step needs its own M1V1 = M2V2 calculation, using the previous step's output concentration as the next step's M1. AP Chemistry problems are almost always single-step dilutions, though.
Is dilution the same calculation as a titration?
No, even though both use a similar-looking equation. A dilution changes one solution's concentration by adding solvent, with the amount of solute staying fixed. A titration reacts two different solutions together, and needs the actual mole ratio from a balanced equation, not just M1V1 = M2V2, unless that ratio happens to be 1:1.
This page is not affiliated with or endorsed by College Board. AP® is a trademark registered by the College Board.