Molarity Formula
The molarity formula M = moles/volume calculates the concentration of a solution.
Essential for chemistry lab work and solution preparation.
The Formula
M = n / V
Molarity measures how concentrated a solution is. It tells you how many moles of solute are dissolved in each liter of solution.
Variables
| Symbol | Meaning |
|---|---|
| M | Molarity (measured in moles per liter, mol/L or M) |
| n | Number of moles of solute (mol) |
| V | Volume of solution (measured in liters, L) |
Example 1
You dissolve 0.5 moles of NaCl in 2 liters of water. What is the molarity?
Identify the values: n = 0.5 mol, V = 2 L
Apply the formula: M = n / V = 0.5 / 2
M = 0.25 mol/L (or 0.25 M)
Example 2
You need 500 mL of a 0.1 M HCl solution. How many moles of HCl do you need?
Convert volume: V = 500 mL = 0.5 L
Rearrange: n = M × V = 0.1 × 0.5
n = 0.05 mol
When to Use It
Use the molarity formula when working with solutions in chemistry.
- Preparing solutions of a specific concentration
- Stoichiometry calculations involving solutions
- Titration calculations
- Determining how much solute to add to achieve a target concentration
Key Notes
- Molarity is moles per liter of solution — not per liter of solvent; when preparing a solution, add solute then bring the total volume to the target (do not just add a liter of water)
- Molality (mol/kg solvent) differs from molarity and is preferred for colligative properties (boiling point elevation, freezing point depression) because it does not change with temperature
- Dilution formula M₁V₁ = M₂V₂ applies because moles of solute are conserved — adding more solvent decreases concentration proportionally
- Common unit prefixes: mM (millimolar = 10⁻³ M), μM (micromolar = 10⁻⁶ M) — blood glucose of ~5 mM is the same as 0.005 mol/L
Key Notes
- Formula: M = moles solute / liters of solution: The unit mol/L is written as M (molarity). The standard conversion chain: grams → moles (÷ molar mass) → molarity (÷ volume in L). Molar mass comes from the periodic table by summing atomic masses of all atoms in the formula.
- Prepare a solution correctly: To make 500 mL of 0.25 M NaCl (molar mass 58.44 g/mol): moles needed = 0.25 × 0.5 = 0.125 mol; mass = 0.125 × 58.44 = 7.305 g. Dissolve in ~400 mL water, then add water to the 500 mL mark in a volumetric flask. Always add to water, not water to concentrate.
- Molarity vs molality: Molarity M (mol/L solution) changes with temperature because liquid volume expands. Molality m (mol/kg solvent) is independent of temperature. For dilute aqueous solutions at room temperature, M ≈ m, but at high concentrations or temperatures they diverge.
- Dilution: C₁V₁ = C₂V₂: Moles are conserved on dilution. To prepare 1 L of 0.1 M HCl from 12 M stock: V₁ = (0.1 × 1)/12 ≈ 8.33 mL of stock, diluted to 1.00 L total with water.
- Applications: Molarity calculations are the daily currency of chemistry labs: preparing buffer solutions and standards, calculating reagent amounts for reactions, pharmaceutical formulation (drug concentration in mg/mL converted to molarity), titration analysis, and environmental sample dilution for instrument analysis.