The formula
- Molarity
M = mol solute / L solution- Moles from molarity and volume
n = M × V- Starting from a mass
M = (m / M_molar) / V- Dilution, where molarity most often appears next
C₁V₁ = C₂V₂
What the symbols mean
| Symbol | Meaning | Unit |
|---|---|---|
M | Molarity, the molar concentration of the solution | M (1 M = 1 mol/L) |
n | Moles of solute | mol |
V | Total volume of the solution | L |
m | Mass of solute weighed out | g |
M_molar | Molar mass of the solute | g/mol |
C₁, C₂, V₁, V₂ | Concentrations and volumes before and after a dilution | M and L |
When it applies
- The volume in the denominator is the final solution volume. Dissolving solute in 500 mL of water gives slightly more than 500 mL of solution, so volumetric flasks are filled to a mark.
- Volume goes in liters, so convert milliliters first. This is the single most common place a molarity answer lands out by a factor of a thousand.
- Molarity changes with temperature because the solution expands, which is why molality is preferred for work over a wide temperature range.
- For an ionic compound, the ion concentrations follow the formula: 0.10 M CaCl₂ is 0.10 M in Ca²⁺ and 0.20 M in Cl⁻.
Worked example
Problem. What is the molarity of a solution made by dissolving 25.0 g of sodium chloride and diluting to a total volume of 500.0 mL?
- Find the molar mass of NaCl: 22.990 + 35.45 = 58.44 g/mol.
- Convert the mass to moles: n = 25.0 / 58.44 = 0.42779 mol.
- Convert the volume to liters: 500.0 mL = 0.5000 L.
- Divide: M = 0.42779 mol / 0.5000 L = 0.85558 M, which is 0.856 M to three significant figures.
- Read the ions off the formula: the solution is 0.856 M in Na⁺ and 0.856 M in Cl⁻, since NaCl gives one of each.
Answer. 0.856 M sodium chloride, which is 0.856 M in each of its two ions.
Common mistakes
- Leaving the volume in milliliters, which makes the molarity a thousand times too large.
- Dividing mass by volume without converting to moles first. Grams per liter is a real unit, but it is not molarity.
- Using the volume of solvent added instead of the final solution volume.
- Forgetting that a dissolved salt contributes more than one ion. A 0.10 M solution of aluminum chloride is 0.30 M in chloride.
Related formulas
- Titration:
n(titrant) = M(titrant) × V(titrant) - Molar mass:
M = Σ (atoms of each element × atomic mass) - Dilution formula:
C₁V₁ = C₂V₂, often written M₁V₁ = M₂V₂