Molarity, or amount concentration, is the number of moles of solute in one litre of solution, written mol/L or simply M. A 1 M sodium chloride solution contains 58.44 g of NaCl in every litre of finished solution. Because chemical reactions happen between particles in fixed mole ratios, molarity is the most practical way to express concentration in the lab: multiply it by a volume and you immediately know how many moles you have dispensed.
To prepare a solution, you work backwards: decide the molarity and volume you need, calculate the mass (m = c × V × M), weigh it out, dissolve it in less solvent than the final volume, transfer it to a volumetric flask and top up to the mark. Note that the volume is that of the final solution, not of the water you add – dissolving a solid usually changes the volume a little.
Besides molarity, this calculator reports the amount in moles, the mass concentration (g/L, the same as mg/mL), the weight-per-volume percentage, and – if you enter the solution density – the mass percent and the molality, which is the concentration per kilogram of solvent.
How to use the Molarity Calculator
- Mass of solute
- Molar mass of solute — Default: sodium hydroxide NaOH. Use the formula mass including any water of crystallisation.
- Volume of solution
- Density of the solution (optional) — Only needed for mass percent and molality. About 1.00 g/mL for dilute water solutions; 1 M NaOH is about 1.04 g/mL.
- Want to work backwards? Type a value into Molarity and Mass of solute is calculated for you.
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Divide the mass of solute by its molar mass to get moles, then divide by the solution volume in litres. To find the mass needed for a target concentration, type the molarity into the result – the calculator solves backwards for the mass. Mass percent and molality use the solution density to find the mass of the whole solution.
Worked example
10 g of sodium hydroxide (NaOH, M = 39.997 g/mol) is dissolved and made up to 250 mL. n = 10 ÷ 39.997 = 0.2500 mol and c = 0.2500 ÷ 0.250 L = 1.000 M. The mass concentration is 10 g ÷ 0.25 L = 40 g/L (4% w/v). With a solution density of 1.04 g/mL the 250 mL weighs 260 g, so the solution is 10 ÷ 260 = 3.85% NaOH by mass and its molality is 0.2500 mol ÷ 0.250 kg of water = 1.000 mol/kg.
Making a solution step by step
- Choose the molarity and the final volume you need.
- Type the molarity into the result to get the mass (m = c × V × M).
- Weigh the solute and dissolve it in roughly two thirds of the final volume of solvent.
- Transfer quantitatively to a volumetric flask, rinsing the beaker into it.
- Make up to the mark at room temperature and mix by inverting the stoppered flask.
Inputs explained
| Field | What to enter |
|---|---|
| Mass of solute | Units: g, mg, µg, kg, oz, lb |
| Molar mass of solute | Units: g/mol, kg/mol, Da (u), kDa. Default: sodium hydroxide NaOH. Use the formula mass including any water of crystallisation. |
| Volume of solution | Units: L, mL, µL, m³, dm³, cm³ … |
| Density of the solution (optional) | Units: g/mL, g/cm³, kg/m³, kg/L, lb/ft³. Only needed for mass percent and molality. About 1.00 g/mL for dilute water solutions; 1 M NaOH is about 1.04 g/mL. |
What each result means
- Amount of substance = [Mass of solute] ÷ [Molar mass of solute]
- Molarity = [Amount of substance] ÷ [Volume of solution]
- Mass concentration = [Mass of solute] ÷ [Volume of solution]
- Weight per volume = [Mass of solute]÷([Volume of solution]×1000)×100
- Number of solute particles = [Amount of substance]×6.02214076e+23
- Mass percent (w/w) = ([Mass of solute]÷([Density of the solution (optional)]×1000×[Volume of solution]))×100
- Molality = [Amount of substance]÷(([Density of the solution (optional)]×1000×[Volume of solution] – [Mass of solute])÷1000)
Example values
How the main result changes when Mass of solute changes and everything else stays at the example values above:
| Mass of solute (g) | Molarity (mol/L (M)) |
|---|---|
| 5 | 0.5 |
| 7.5 | 0.7501 |
| 10 | 1.0001 |
| 12.5 | 1.2501 |
| 15 | 1.5001 |
| 20 | 2.0002 |
Formula
n = m ÷ M · c = n ÷ V = m ÷ (M × V) · m = c × V × M
Mass concentration ρ* = m ÷ V = c × M · molality b = n ÷ (ρ_solution × V − m)
Worked example
Inputs — Mass of solute: 10 g; Molar mass of solute: 39.997 g/mol; Volume of solution: 0.25 L; Density of the solution (optional): 1.04 g/mL.
Results — Amount of substance = 0.250019 mol; Molarity = 1.000075 mol/L (M); Mass concentration = 40 g/L; Weight per volume = 4 % w/v; Number of solute particles = 1.5056e23; Mass percent (w/w) = 3.8462 %; Molality = 1.000075 mol/kg.
Key terms
- Molarity (amount concentration)
- Moles of solute per litre of solution, mol/L.
- Molar mass
- Mass of one mole of a substance, g/mol.
- Mass concentration
- Mass of solute per volume of solution, g/L.
- Volumetric flask
- Flask calibrated to hold one exact volume at the mark, used to make standard solutions.
Frequently asked questions
What is molarity?
The number of moles of solute per litre of solution (mol/L, M). A 2 M solution has 2 mol of solute in every litre.
How do I calculate molarity from grams?
Divide the mass by the molar mass to get moles, then divide by the volume in litres. 5 g of HCl (36.46 g/mol) in 1.2 L: 0.1371 mol ÷ 1.2 L = 0.114 M.
How many grams do I need for a 0.1 M solution?
m = c × V × M. For 500 mL of 0.1 M NaCl: 0.1 × 0.5 × 58.44 = 2.922 g. Type 0.1 into the molarity result and the calculator finds the mass for you.
Is the volume that of the solvent or the solution?
The solution. Dissolve the solute in part of the solvent, then make up to the final volume in a volumetric flask.
What is the difference between M, mM and µM?
1 M = 1 mol/L, 1 mM = 0.001 mol/L and 1 µM = 10⁻⁶ mol/L. Use the unit menu on the result to switch.
Does molarity change with temperature?
Slightly: the solution expands when warmed, so the same moles occupy a larger volume. Water expands about 0.26% between 20 and 30 °C.
How do I convert molarity to g/L?
Multiply by the molar mass: 0.5 M glucose is 0.5 × 180.16 = 90.08 g/L.
What is the molarity of pure water?
About 55.3 M (997 g/L ÷ 18.015 g/mol at 25 °C).
Can I work backwards from the result?
Yes. Type the result you want into Molarity and the calculator finds the matching mass of solute.