Molarity Calculator
Molarity (M) is the concentration of a solution expressed as moles of solute per liter of solution. Calculate it from mass, molar mass, and volume — or convert between molarity and mass concentration.
Calculate Molarity
Mass concentration: 5.844 g/L
Volume: 1000 mL (1.000 L)
Formulas
n = m / M_w (moles from mass and molar mass) C = n / V (molarity from moles and volume in liters) C = m / (M_w × V) (molarity from mass, molar mass, volume)
Formula variables
- n — amount of substance in moles (mol).
- m — mass of the solute in grams (g).
- M_w — molar mass of the solute in grams per mole (g/mol).
- V — volume of the solution in liters (L). Note: molarity is per liter of solution, not solvent.
- C — molarity in moles per liter (mol/L = M).
Worked Examples
Example 1: Molarity of a simple salt solution
Dissolve 5.844 g of NaCl (M_w = 58.44 g/mol) in enough water to make 1.000 L of solution.
- Moles of NaCl: n = 5.844 ÷ 58.44 = 0.1000 mol.
- Volume: V = 1.000 L.
- Molarity: C = 0.1000 ÷ 1.000 = 0.1000 M.
Example 2: Molarity of glucose in 500 mL
Dissolve 18.016 g of glucose (M_w = 180.16 g/mol) in enough water to make 500 mL of solution.
- Moles of glucose: n = 18.016 ÷ 180.16 = 0.1000 mol.
- Volume: V = 0.500 L.
- Molarity: C = 0.1000 ÷ 0.500 = 0.2000 M.
Example 3: Mass needed for a target molarity
How much NaOH (M_w = 40.00 g/mol) is needed to prepare 250 mL of 0.500 M solution?
- Required moles: n = 0.500 × 0.250 = 0.125 mol.
- Required mass: m = 0.125 × 40.00 = 5.000 g.
- Result: Weigh 5.000 g of NaOH and dilute to 250 mL.
Example 4: Converting M to % w/v
A 0.150 M NaCl solution. What is the % w/v concentration?
- Mass concentration: 0.150 mol/L × 58.44 g/mol = 8.766 g/L.
- % w/v = (8.766 g / 1000 mL) × 100 = 0.8766 % w/v.
- Result: 0.150 M NaCl = 0.877 % w/v.
Common Concentration Units
| Unit | Symbol | Definition | Common use |
|---|---|---|---|
| Molarity | M (mol/L) | Moles of solute per liter of solution | General chemistry |
| Molality | m (mol/kg) | Moles of solute per kilogram of solvent | Colligative properties, temperature-independent |
| Normality | N (eq/L) | Equivalents of solute per liter of solution | Acid-base, redox titrations |
| Mass concentration | g/L, mg/mL | Mass of solute per volume of solution | Biological, pharmaceutical |
| Percent w/v | % w/v | Grams of solute per 100 mL of solution | Medical IV solutions |
| Percent w/w | % w/w | Grams of solute per 100 g of solution | Commercial acids and bases |
| Parts per million | ppm | mg/L (for dilute aqueous solutions) | Environmental, trace analysis |
Molar Masses of Common Compounds
| Compound | Formula | Molar mass (g/mol) |
|---|---|---|
| Water | H₂O | 18.015 |
| Sodium chloride | NaCl | 58.44 |
| Glucose | C₆H₁₂O₆ | 180.156 |
| Sucrose | C₁₂H₂₂O₁₁ | 342.30 |
| Hydrochloric acid | HCl | 36.461 |
| Sulfuric acid | H₂SO₄ | 98.079 |
| Nitric acid | HNO₃ | 63.012 |
| Sodium hydroxide | NaOH | 40.00 |
| Potassium hydroxide | KOH | 56.11 |
| Ammonia | NH₃ | 17.031 |
| Potassium chloride | KCl | 74.55 |
| Calcium carbonate | CaCO₃ | 100.09 |
| Sodium carbonate | Na₂CO₃ | 105.99 |
| Sodium bicarbonate | NaHCO₃ | 84.007 |
| Acetic acid | CH₃COOH | 60.052 |
| Ethanol | C₂H₅OH | 46.069 |
These values use the standard atomic weights from the 2021 IUPAC recommendations. Molar masses of specific compounds may vary slightly depending on the source of the atomic weights used.
Practical Notes
- Molarity uses liters of solution, not solvent. This is a common source of error. Add solute to a volumetric flask and dilute to the mark — do not add 1 L of solvent to the solute.
- Volumes are temperature-dependent. A solution made at 20 °C will have a slightly different volume at 30 °C, so molarity changes with temperature. Molality (mol/kg solvent) does not have this issue.
- Density matters for concentrated solutions. To convert between % w/w and molarity, you need the solution density (g/mL). The molarity calculator assumes the input is per liter of solution.
- For dilute aqueous solutions, 1 ppm ≈ 1 mg/L is a reasonable approximation. In other solvents or concentrated solutions, this does not hold.
- Always label with the correct unit. "M" means molarity (mol/L), "m" means molality (mol/kg), and "N" means normality (eq/L). These are different quantities.
Related Converters
Frequently Asked Questions
What is molarity?
Molarity (M) is the number of moles of solute per liter of solution. It is the most common concentration unit in general chemistry.
How do you calculate molarity?
Divide the moles of solute by the volume of solution in liters: C = n / V. Alternatively, C = m / (M_w × V) where m is mass in grams and M_w is molar mass in g/mol.
What is the difference between molarity and molality?
Molarity is moles per liter of solution; molality is moles per kilogram of solvent. Molality is temperature-independent (mass does not change with temperature), while molarity changes slightly with temperature because the solution's volume changes.
How do you prepare a 1 M solution of NaCl?
Weigh 58.44 g of NaCl, transfer to a 1 L volumetric flask, add distilled water to dissolve, then top up to the 1 L mark. The result is 1 mol/L = 1 M.
How do you convert molarity to percent?
First convert M to g/L by multiplying by molar mass. Then divide by 10 to get % w/v. For example, 0.150 M NaCl = 0.150 × 58.44 = 8.766 g/L = 0.8766 % w/v.