Concentration Formulas (Molarity and Molality)

Learn concentration formulas including molarity (M = mol/L) and molality (m = mol/kg) with worked examples.

The Formulas

Molarity (M) = moles of solute / liters of solution

Molality (m) = moles of solute / kilograms of solvent

Concentration describes how much solute is dissolved in a given amount of solution or solvent. Molarity and molality are the two most common ways to express concentration in chemistry. Understanding the difference is essential for lab work, stoichiometry, and colligative property calculations.

Variables

Symbol	Meaning
M	Molarity (measured in mol/L or "molar")
m	Molality (measured in mol/kg or "molal")
mol	Moles of solute (the substance being dissolved)
L	Liters of total solution (solute + solvent combined)
kg	Kilograms of solvent only (not the total solution)

Example 1 — Molarity

You dissolve 5.85 g of NaCl (molar mass = 58.5 g/mol) in enough water to make 500 mL of solution. What is the molarity?

Calculate moles: 5.85 g / 58.5 g/mol = 0.1 mol

Convert volume: 500 mL = 0.5 L

M = 0.1 mol / 0.5 L

M = 0.2 mol/L (0.2 M)

Example 2 — Molality

You dissolve 18 g of glucose (C₆H₁₂O₆, molar mass = 180 g/mol) in 250 g of water. What is the molality?

Calculate moles: 18 g / 180 g/mol = 0.1 mol

Convert solvent mass: 250 g = 0.25 kg

m = 0.1 mol / 0.25 kg

m = 0.4 mol/kg (0.4 m)

Example 3 — Dilution

You need 200 mL of 0.5 M HCl from a 2 M stock solution. How much stock do you need?

Use the dilution formula: M₁V₁ = M₂V₂

2 × V₁ = 0.5 × 200

V₁ = 100 / 2

V₁ = 50 mL of stock solution (then add water to reach 200 mL total)

When to Use Each

Choose between molarity and molality based on the situation.

Molarity — Most common in lab work. Used for stoichiometric calculations, titrations, and preparing solutions. Changes with temperature (because volume changes with temperature).
Molality — Used for colligative properties: boiling point elevation, freezing point depression, osmotic pressure. Does NOT change with temperature (because mass does not change with temperature).
Dilution formula (M1V1 = M2V2) — Used when diluting a concentrated solution to a lower concentration.

Other Concentration Units

Additional ways to express concentration include:

Mass percent: (mass of solute / mass of solution) × 100%
Parts per million (ppm): mg of solute per kg of solution
Mole fraction: moles of component / total moles of all components