Molarity Calculator
How Molarity Works
Molarity is the most widely used unit of concentration in chemistry, defined as the number of moles of solute dissolved per liter of solution. According to IUPAC (International Union of Pure and Applied Chemistry), the proper SI symbol for molarity is "mol/L" or "mol dm^-3," though the notation "M" remains standard in educational and laboratory contexts worldwide.
Molarity is fundamental to virtually every quantitative chemistry operation: preparing solutions, performing titrations, calculating reaction stoichiometry, and determining reaction rates. A 1 M solution of any substance contains exactly one mole of solute dissolved in enough solvent to make one liter of total solution. This calculator computes molarity from moles of solute and solution volume, and also shows the equivalent millimolar concentration. Pair it with our molecular weight calculator to convert between grams and moles.
One important distinction: molarity is temperature-dependent because liquid volume expands with heat. At 25C, water occupies about 1.003 mL/g, but at 80C it expands to approximately 1.029 mL/g. For precision work requiring temperature independence, chemists use molality (moles per kilogram of solvent) instead. Our dilution calculator helps with the common task of diluting concentrated solutions to target molarities.
The Molarity Formula
The molarity formula relates the amount of solute to the total volume of solution:
M = n / V
- M — molarity in mol/L (moles per liter)
- n — moles of solute (calculated as mass / molar mass)
- V — volume of solution in liters (not solvent alone, but total solution)
Worked example: Prepare a 0.5 M NaCl solution. NaCl molar mass = 58.44 g/mol. Moles needed for 1 L: 0.5 mol. Mass = 0.5 x 58.44 = 29.22 g. Dissolve 29.22 g NaCl in water and add water to make exactly 1 L total volume. Note: add solute first, then bring to volume with solvent.
Key Terms You Should Know
- Molarity (M) — moles of solute per liter of solution. Temperature-dependent due to volume changes.
- Molality (m) — moles of solute per kilogram of solvent. Temperature-independent. Preferred for colligative property calculations.
- Mole (mol) — the SI unit for amount of substance. One mole = 6.022 x 10^23 particles (Avogadro's number). Use our mole calculator for conversions.
- Molar Mass — the mass of one mole of a substance in g/mol. Equal to the molecular weight. Use our molecular weight calculator to find it.
- Normality (N) — moles of reactive equivalents per liter. For acids, N = M x number of H+ ions. 1 M H2SO4 = 2 N.
Common Laboratory Solution Concentrations
The following table lists the approximate molarities of common concentrated laboratory reagents as supplied commercially. These values are based on standard reference data from Sigma-Aldrich and the CRC Handbook of Chemistry and Physics.
| Reagent | Concentration | Approx Molarity |
|---|---|---|
| Hydrochloric Acid (HCl) | 37% | 12.1 M |
| Sulfuric Acid (H2SO4) | 98% | 18.0 M |
| Nitric Acid (HNO3) | 70% | 15.9 M |
| Acetic Acid (CH3COOH) | 99.7% | 17.4 M |
| Ammonia (NH3) | 28% | 14.8 M |
| Sodium Hydroxide (NaOH) | 50% | 19.1 M |
Practical Examples
Example 1 — Lab preparation: Prepare 500 mL of 0.1 M glucose (C6H12O6, MW = 180.16 g/mol). Moles needed = 0.1 x 0.5 = 0.05 mol. Mass = 0.05 x 180.16 = 9.01 g. Weigh 9.01 g glucose, dissolve in about 400 mL water, then add water to reach exactly 500 mL in a volumetric flask.
Example 2 — Dilution from stock: Dilute 12.1 M concentrated HCl to 1 M. Using C1V1 = C2V2: 12.1 x V1 = 1.0 x 1000 mL. V1 = 82.6 mL. Add 82.6 mL of concentrated HCl to about 800 mL water (always add acid to water), then bring to 1000 mL. Use our dilution calculator for this calculation.
Example 3 — Titration calculation: 25.0 mL of 0.1 M NaOH neutralizes an unknown HCl solution. Moles NaOH = 0.025 x 0.1 = 0.0025 mol. Since NaOH + HCl is 1:1, moles HCl = 0.0025 mol. If 20.0 mL of HCl was used, its molarity = 0.0025 / 0.020 = 0.125 M. Use our pH calculator to determine the pH at various points during titration.
Tips for Working with Molarity
- Always measure total solution volume: Molarity is based on the final volume of solution, not the volume of solvent added. Use volumetric flasks for accurate preparation.
- Convert mL to L before calculating: A common error is using milliliters directly in the formula. Divide mL by 1000 to get liters, or multiply the result by 1000 to convert to millimolar (mM).
- Add acid to water, never reverse: When preparing acidic solutions from concentrated stock, always add the acid to water to prevent dangerous exothermic splashing.
- Record temperature for precision: Solution volume changes with temperature. For analytical work, note the temperature and use appropriate correction factors.
- Use serial dilutions for low concentrations: Preparing a 0.001 M solution directly from solid is impractical due to tiny masses. Instead, prepare 0.1 M first, then dilute 1:100.
Frequently Asked Questions
What is the difference between molarity and molality?
Molarity (M) measures moles of solute per liter of total solution, while molality (m) measures moles of solute per kilogram of solvent. The key practical difference is temperature dependence: molarity changes with temperature because liquid volume expands when heated (water is about 1.003 mL/g at 25C but 1.029 mL/g at 80C). Molality uses mass, which does not change with temperature, making it preferred for calculating colligative properties like boiling point elevation, freezing point depression, and osmotic pressure. For most routine lab work at room temperature, molarity is sufficient and more convenient.
How do I convert molarity to grams per liter?
Multiply the molarity by the molar mass (molecular weight) of the solute. The formula is: g/L = M x MW. For example, 0.5 M NaCl: g/L = 0.5 mol/L x 58.44 g/mol = 29.22 g/L. This means you need 29.22 grams of NaCl per liter of solution to make a 0.5 M concentration. To convert in the other direction (g/L to M), divide grams per liter by the molar mass. Use our molecular weight calculator if you do not know the molar mass of your compound.
What does a 1M solution mean?
A 1M (one molar) solution contains exactly 1 mole of solute dissolved in enough solvent to make 1 liter of total solution. The mass of solute needed depends on its molar mass: 1 M NaCl requires 58.44 g per liter, while 1 M glucose requires 180.16 g per liter. Note that 1 M refers to the final solution volume, not the volume of solvent. In practice, you dissolve the solute in less than 1 liter of solvent, then add solvent to bring the total to exactly 1 liter in a volumetric flask. Stock solutions in labs are commonly prepared at 1 M or 10 M concentrations for dilution.
Can molarity be greater than 1?
Yes, concentrated solutions frequently have molarities well above 1 M. Concentrated hydrochloric acid from the supplier is approximately 12.1 M, concentrated sulfuric acid is about 18 M, and glacial acetic acid is 17.4 M. The theoretical maximum molarity depends on the density and molecular weight of the pure substance. For solids dissolved in water, the practical limit depends on solubility: NaCl saturates at about 6.1 M at 25C, while sucrose can reach about 5.8 M. Gases dissolved in liquids typically have low molarities due to limited solubility.
How do I dilute a concentrated solution to a target molarity?
Use the dilution equation: C1 x V1 = C2 x V2, where C1 and V1 are the initial concentration and volume, and C2 and V2 are the target concentration and volume. For example, to make 500 mL of 0.1 M HCl from 12.1 M stock: 12.1 x V1 = 0.1 x 500. V1 = 4.13 mL. Measure 4.13 mL of concentrated HCl, add it to about 400 mL of water (always add acid to water), then bring to exactly 500 mL with water. Use our dilution calculator for this common laboratory calculation.