What is the molarity?
Enter any three of mass of solute, molar mass, volume of solution and molarity. The calculator finds the fourth, plus the moles and the mass concentration.
- Molarity (mol/L)
- 1
Dissolving 58.44 g of a solute with molar mass 58.44 g/mol to make 1 L of solution gives 1 mol/L.
- Molarity (mmol/L)
- 1,000
- Amount of solute (mol)
- 1
- Mass concentration
- 58.44 g/L
Molarity (mol/L): 1. Dissolving 58.44 g of a solute with molar mass 58.44 g/mol to make 1 L of solution gives 1 mol/L.
How to calculate
Computes the molar concentration (mol/L) of a solution from the mass of solute, its molar mass and the solution volume, or the mass, volume or molar mass from the other three.
Example with the default inputs (Mass of solute 58.44 g, Molar mass (g/mol) 58.44, Volume of solution 1 L): Dissolving 58.44 g of a solute with molar mass 58.44 g/mol to make 1 L of solution gives 1 mol/L.
Formula: c = n ÷ V and n = m ÷ M, so c = m ÷ (M × V), with c in mol/L, m in g, M in g/mol and V in L (IUPAC Gold Book).
- The volume is the final volume of the solution, measured after the solute dissolves.
- The molar mass is for the form you weigh, including any water of crystallization (for example CuSO₄·5H₂O, not CuSO₄).
- The molar mass is from 1 to 10,000,000 g/mol and the molarity is at most 100 mol/L (pure water is about 55.5 mol/L). A solved value outside that range has no answer.
- The solute is fully dissolved, and the concentration is of the formula unit as weighed (not of the separate ions).
Worked examples
Each example is checked against the calculator on every build.
- Mass of solute 58.44 g, Molar mass (g/mol) 58.44, Volume of solution 1 L gives Molarity (mol/L) 1, Amount of solute (mol) 1, Mass concentration 58.44 g/L.Source: hand calculation in content.mdx: M(NaCl) = 22.990 + 35.45 = 58.44 g/mol (CIAAW 2021 abridged atomic weights); n = 58.44 ÷ 58.44 = 1 mol; c = 1 mol ÷ 1 L = 1 M
- Molarity (mol/L) 0.1, Molar mass (g/mol) 180.156, Volume of solution 0.25 L gives Mass of solute 4.504 g, Amount of solute (mol) 0.025.Source: hand calculation in content.mdx: M(C₆H₁₂O₆) = 6 × 12.011 + 12 × 1.008 + 6 × 15.999 = 180.156 g/mol (CIAAW 2021); m = 0.1 × 0.25 × 180.156 = 4.5039 g
- Mass of solute 10.6 g, Molar mass (g/mol) 105.988, Volume of solution 0.5 L gives Molarity (mol/L) 0.200023.Source: hand calculation in content.mdx: M(Na₂CO₃) = 2 × 22.990 + 12.011 + 3 × 15.999 = 105.988 g/mol; c = 10.6 ÷ (105.988 × 0.5) = 0.20002 M
- Mass of solute 2 g, Molar mass (g/mol) 39.997, Molarity (mol/L) 0.5 gives Volume of solution 0.1 L.Source: hand calculation in content.mdx: V = 2 ÷ (39.997 × 0.5) = 0.10001 L = 100.01 mL
How it works
The amount of solute n (in moles) is its mass divided by its molar mass, and molarity is that amount divided by the volume of the solution:
- n = m ÷ M
- c = n ÷ V = m ÷ (M × V)
Here c is the molarity in mol/L, m is the mass of solute in grams, M is the molar mass in g/mol, and V is the volume of the solution in liters. Rearranged:
- m = c × M × V
- V = m ÷ (M × c)
- M = m ÷ (V × c)
Masses are converted to grams (1 mg = 0.001 g, 1 kg = 1,000 g) and volumes to liters (1 mL = 1 cm³ = 0.001 L, 1 m³ = 1,000 L) first. The calculator also shows:
- the molarity in mmol/L (mM): c × 1,000,
- the amount of solute in moles: m ÷ M,
- the mass concentration in g/L: m ÷ V.
Assumptions
- V is the final volume of the solution.
- The molar mass is for the form you weigh, including any water of crystallization.
- The molar mass is from 1 to 10,000,000 g/mol, and the molarity is above 0 and at most 100 mol/L. If a solved value falls outside that range, there is no answer.
Worked examples by hand
58.44 g of sodium chloride made up to 1 L. M(NaCl) = 22.990 + 35.45 = 58.44 g/mol. n = 58.44 ÷ 58.44 = 1 mol. c = 1 ÷ 1 = 1 mol/L. The mass concentration is 58.44 ÷ 1 = 58.44 g/L.
The mass of glucose for 250 mL of 0.1 M. M(C₆H₁₂O₆) = 6 × 12.011 + 12 × 1.008 + 6 × 15.999 = 180.156 g/mol. n = 0.1 × 0.25 = 0.025 mol. m = 0.025 × 180.156 = 4.5039 g.
10.6 g of sodium carbonate in 500 mL. M(Na₂CO₃) = 2 × 22.990 + 12.011 + 3 × 15.999 = 105.988 g/mol. c = 10.6 ÷ (105.988 × 0.5) = 10.6 ÷ 52.994 = 0.20002 mol/L.
How much 0.5 M sodium hydroxide 2 g makes. M(NaOH) = 22.990 + 15.999 + 1.008 = 39.997 g/mol. V = 2 ÷ (39.997 × 0.5) = 0.10001 L (100.01 mL).
Other questions people ask
What is molarity?
Molarity (molar concentration, symbol c or M) is the amount of solute in moles per liter of solution. A 1 M solution of sodium chloride has 1 mol (58.44 g) of NaCl in every liter of solution. IUPAC calls it amount concentration, with the SI unit mol/m³; chemists usually use mol/L.
How do I calculate molarity from grams?
Divide the mass in grams by the molar mass to get moles, then divide by the volume in liters: c = m ÷ (M × V). For 10.6 g of sodium carbonate (105.988 g/mol) in 500 mL: 10.6 ÷ (105.988 × 0.5) = 0.200 M.
How many grams do I need to make a solution?
Multiply the molarity, the volume in liters and the molar mass: m = c × V × M. For 250 mL of 0.1 M glucose (180.156 g/mol): 0.1 × 0.25 × 180.156 = 4.504 g.
How do I find the molar mass?
Add up the standard atomic weights of every atom in the formula. For glucose, C₆H₁₂O₆: 6 × 12.011 + 12 × 1.008 + 6 × 15.999 = 180.156 g/mol. For a hydrate such as CuSO₄·5H₂O, include the water, because you weigh it too.
What is the difference between molarity and molality?
Molarity is moles per liter of solution. Molality is moles per kilogram of solvent. Molarity changes a little with temperature, because the volume does; molality does not.
Why use the final volume and not the volume of water?
Because the solute takes up space too. Dissolve the solute in less solvent than you need, then add solvent up to the mark of a volumetric flask. The concentration is the amount divided by that final volume.