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Molarity Calculator

Convert between mass, moles, volume and molar concentration of a solution — solve for molarity, the mass to weigh out, or the volume to make up.

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Result

100 mM

Moles: 100 mmol

Formula: M = (mass / molar mass) / volume

M = (mass / molar mass) / volume. Moles n = mass / molar mass. Concentration is moles of solute per litre of solution.

How to use

  1. Pick what to solve for: molarity, mass, or volume.
  2. Enter the molar mass of the solute (g/mol) and the two known quantities with their units.
  3. Read the result and the number of moles involved.

About this tool

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Three ways round the same relationship: find the molarity from a mass and a volume, the mass you need for a target concentration and volume, or the volume that a given mass will make up to a given concentration. Mass takes mg, g or kg, volume takes mL or L, concentration takes mM or M, and the molar mass defaults to 58.44 g/mol, which is sodium chloride — so the starting figures, 5.844 g made up to 1 L, describe a 0.1 M saline.

The arithmetic is three lines long; what the arithmetic cannot tell you is the part that ruins solutions. Molarity is moles per litre of solution, not per litre of solvent — and the distinction is the whole game. Adding 1 mol of solute to 1 L of water does not give you 1 M, because the solute takes up room of its own — you dissolve it in less water and then bring the total up to the mark in a volumetric flask. The tool's volume field means final volume throughout, and if you read it as "water added" every result is quietly too dilute.

Two more traps sit in the molar mass rather than the volume. It has to match the form you are actually weighing: copper(II) sulfate is 159.60 g/mol anhydrous but 249.68 as the familiar blue pentahydrate, so weighing the pentahydrate against the anhydrous figure leaves you at 63.9% of the concentration you wanted. And because molarity is defined per unit volume, it drifts with temperature while the mass does not — water is about 2.6% less dense at 80 °C than at 20 °C, so a solution made up to 1.000 M on the bench reads near 0.974 M once it is hot. Where that matters, molality, in moles per kilogram of solvent, is the quantity that holds still.

Frequently asked questions

What is molarity?

Molarity is moles of solute per litre of solution (mol/L, written M). A 1 M solution contains one mole of solute in each litre.

How do I calculate molarity?

M = n / V, where n = mass / molar mass and V is volume in litres. For example 5.844 g of NaCl (molar mass 58.44 g/mol) in 1 L is 0.1 mol / 1 L = 0.1 M.

How much solute do I weigh for a target molarity?

mass = molarity × volume × molar mass. To make 2 L of 0.5 M NaCl you need 0.5 × 2 × 58.44 = 58.44 g.

Where do I find the molar mass?

Sum the atomic masses of every atom in the formula. NaCl is 22.99 (Na) + 35.45 (Cl) = 58.44 g/mol; many periodic-table references list it directly.

Is molarity per litre of solvent or per litre of solution?

Of solution — the finished volume, after the solute is dissolved. That is why you dissolve the solid in less water than the target and then top up to the mark rather than adding a litre of water to it. Dissolving changes the volume, so the two routes do not give the same concentration.

Does molarity change with temperature?

Slightly, because volume does. A solution made up at room temperature is a little less concentrated when warmed, since the same moles now occupy more litres. It rarely matters at bench precision, and where it does, molality — moles per kilogram of solvent — is used instead because mass does not expand.

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