Molarity and Dilution Formulas
Molarity formula M = n/V (moles per liter) and dilution equation M1V1 = M2V2.
Covers solution concentration, dilution factors, and worked examples with units.
Molarity Formula
where n = mass / molar mass
Molarity (M) is the most common way to express the concentration of a solution. It tells you how many moles of solute are dissolved in one liter of solution.
Dilution Equation
When you dilute a solution (add more solvent), the amount of solute stays the same. This equation lets you find the new concentration or the volume needed.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| M | Molarity (concentration) | mol/L (M) |
| n | Number of moles of solute | mol |
| V | Volume of solution | Liters (L) |
| M₁ | Initial (concentrated) molarity | mol/L |
| V₁ | Initial volume | L or mL |
| M₂ | Final (diluted) molarity | mol/L |
| V₂ | Final volume | L or mL |
Example 1 — Calculating Molarity
You dissolve 58.44 g of NaCl (molar mass = 58.44 g/mol) in water to make 2 L of solution. What is the molarity?
n = mass / molar mass = 58.44 / 58.44 = 1 mol
M = n / V = 1 / 2
M = 0.5 mol/L (0.5 M NaCl solution)
Example 2 — Dilution
You have 100 mL of 6 M HCl. How much water must you add to make a 1 M solution?
M₁V₁ = M₂V₂
6 × 100 = 1 × V₂
V₂ = 600 mL (total final volume)
Add 500 mL of water (600 − 100 = 500 mL)
Example 3 — Finding Moles Needed
How many grams of KOH (molar mass 56.11 g/mol) are needed to make 500 mL of 0.25 M solution?
n = M × V = 0.25 × 0.5 L = 0.125 mol
mass = n × molar mass = 0.125 × 56.11
mass = 7.01 g of KOH
Key Notes
- Formula: M = n / V (mol/L): Molarity (M) equals moles of solute divided by liters of solution. Note: liters of solution, not liters of solvent — the solute occupies volume too. Prepare a 1 M solution by dissolving 1 mol in enough solvent to reach exactly 1 L total volume.
- Moles from mass: n = mass (g) / molar mass (g/mol): The two-step chain is always: grams → moles → molarity. Find molar mass from the periodic table by summing atomic masses. For NaCl: 22.99 + 35.45 = 58.44 g/mol; dissolve 58.44 g in water to 1 L → 1 M NaCl.
- Molarity changes with temperature: Because it is defined per liter of solution, and solution volume expands when heated, molarity decreases slightly at higher temperatures. Molality (mol/kg solvent) is temperature-independent — preferred for precision work and colligative property calculations.
- Dilution shortcut: C₁V₁ = C₂V₂: Moles of solute are conserved on dilution. To make 500 mL of 0.1 M HCl from 12 M stock: V₁ = C₂V₂/C₁ = (0.1 × 0.5)/12 ≈ 4.2 mL of stock, diluted to 500 mL total.
- Applications: Molarity is the standard concentration unit in chemistry laboratories: preparing buffer solutions, making titrant standards, pharmaceutical dosing calculations, industrial chemical processes, clinical lab assay standards, and environmental pollutant concentration reporting.