Dilution (M₁V₁ = M₂V₂)
M₁V₁ = M₂V₂ works because dilution adds solvent without changing the moles of solute: molarity times volume equals moles, so the product is the same before and after. Any volume or concentration units are fine as long as they match across both sides (both liters or both milliliters, not one of each).
Solve for the missing variable in each problem below; answers are accepted within ±1%.
Common Questions
What is the dilution equation?
M1V1 = M2V2, where M1 and V1 are the initial molarity and volume, and M2 and V2 are the final molarity and volume. It works because the moles of solute remain constant during dilution.
How do you use M1V1 = M2V2?
Identify the three known values and solve for the fourth. Make sure volumes are in the same units. The concentrated solution (higher M) always has the smaller volume, and the dilute solution (lower M) has the larger volume.
Why does M1V1 = M2V2 work?
Dilution only adds solvent, not solute. The moles of solute before dilution (M1 x V1) equal the moles after dilution (M2 x V2). Since molarity = moles/volume, the equation balances.
What is the difference between dilution and concentration?
Dilution adds solvent to decrease concentration. Concentrating removes solvent (by evaporation, for example) to increase concentration. Both can be described by M1V1 = M2V2.