# What is the molarity?

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.

- Page: https://www.acalculator.org/chemistry/molarity-calculator
- JSON spec: https://www.acalculator.org/chemistry/molarity-calculator.json
- Version: d27f4c92ac3f

## Default answer

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.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| m | Mass of solute | The mass of the substance dissolved. |
| mw | Molar mass (g/mol) | The molar mass of the solute, in grams per mole: the sum of the atomic weights in its formula. |
| v | Volume of solution | The final volume of the solution, not the volume of solvent added. |
| c | Molarity (mol/L) | The amount of solute per liter of solution, in moles per liter (M). |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| mass | Mass of solute | The mass of the substance dissolved. |
| molarMass | Molar mass (g/mol) | The molar mass of the solute, in grams per mole: the sum of the atomic weights in its formula. |
| volume | Volume of solution | The final volume of the solution, not the volume of solvent added. |
| molarity | Molarity (mol/L) | The amount of solute per liter of solution, in moles per liter (M). |
| millimolar | Molarity (mmol/L) | The same molarity in millimoles per liter (mM): mol/L × 1,000. |
| moles | Amount of solute (mol) | The amount of solute in moles: mass in grams ÷ molar mass. |
| massConcentration | Mass concentration | The mass of solute per volume of solution: mass ÷ volume. |

## Method

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).

## Assumptions

- 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

1. m = 0.05844, mw = 58.44, v = 0.001 gives c = 1, moles = 1, massConcentration = 58.44. 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.
2. c = 0.1, mw = 180.156, v = 0.00025 gives m = 0.004504, moles = 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.
3. m = 0.0106, mw = 105.988, v = 0.0005 gives c = 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.
4. m = 0.002, mw = 39.997, c = 0.5 gives v = 0.0001. Source: hand calculation in content.mdx: V = 2 ÷ (39.997 × 0.5) = 0.10001 L = 100.01 mL.

## FAQ

### 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.

## Sources

- IUPAC Compendium of Chemical Terminology (the Gold Book), amount concentration: c = n ÷ V, also called molarity. https://doi.org/10.1351/goldbook.A00295
- IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW), Abridged standard atomic weights (2021): H 1.008, C 12.011, O 15.999, Na 22.990, Cl 35.45. https://ciaaw.org/abridged-atomic-weights.htm
- NIST Special Publication 811 (2008), section 8.6.6: amount-of-substance concentration, mol/m³ and mol/L. https://www.nist.gov/pml/special-publication-811