Molarity Explained: How to Calculate Concentration and Make Solutions

“Add a spoonful of salt to a pot of water” is fine for pasta. It’s useless for chemistry, where a reaction might need exactly twice as many particles of one substance as another. Chemists need a way to say how much of a substance is dissolved in a given volume, and the standard way is molarity.

The definition

Molarity (M) = moles of solute ÷ litres of solution

Its units are mol/L, usually written simply as M and read as “molar”. A 2 M solution of hydrochloric acid contains 2 moles of HCl in every litre.

Two words in that definition deserve attention:

• Solute is the thing being dissolved (the salt, the sugar, the acid).
• Solution is the finished mixture — solute and solvent together. Not the volume of water you started with.

That second point matters more than it looks, and we’ll come back to it.

Calculating molarity

You dissolve 5.844 g of sodium chloride in water and make the total volume up to 250 mL. What is the molarity?

1. Convert mass to moles. NaCl is 58.44 g/mol, so 5.844 g ÷ 58.44 g/mol = 0.1000 mol.
2. Convert volume to litres: 250 mL = 0.250 L.
3. Divide: 0.1000 mol ÷ 0.250 L = 0.400 M.

The formula rearranges to give either of the other quantities:

• moles = molarity × volume (L)
• volume (L) = moles ÷ molarity

Making a solution in the lab

The most common practical question runs the other way: how much solid do I weigh out?

Prepare 500 mL of 0.150 M potassium permanganate, KMnO₄.

1. Moles needed: 0.150 mol/L × 0.500 L = 0.0750 mol.
2. Molar mass of KMnO₄: 39.098 + 54.938 + 4(15.999) = 158.03 g/mol.
3. Mass: 0.0750 mol × 158.03 g/mol = 11.85 g.

Now the practical part. You don’t add 11.85 g to 500 mL of water. You dissolve the solid in less than 500 mL of water — say 350 mL — in a volumetric flask, then add more water until the liquid reaches the 500 mL mark. Dissolving a solid changes the volume a little, so “500 mL of water plus solid” would not give exactly 500 mL of solution, and your concentration would be slightly off.

Dilution: C₁V₁ = C₂V₂

Labs rarely make every solution from solid. They keep concentrated stock solutions and dilute them as needed. The key fact is that adding solvent changes the volume but not the number of moles of solute. Moles before = moles after, and since moles = concentration × volume:

C₁V₁ = C₂V₂

How much 12.0 M hydrochloric acid do you need to make 250 mL of 1.00 M HCl?

V₁ = C₂V₂ ÷ C₁ = (1.00 M × 250 mL) ÷ 12.0 M = 20.8 mL

Measure 20.8 mL of the concentrated acid and make it up to 250 mL total. Two useful things about this equation:

• The volumes can be in any unit, as long as both use the same one. mL on both sides is fine.
• C₂ must always be smaller than C₁. If your calculation says the dilute solution is stronger than the stock, you’ve swapped something.

Safety note: with concentrated acids, always add the acid to the water, slowly, never water to acid. Diluting strong acids releases a lot of heat, and water added to concentrated acid can boil and spatter.

Molarity of ions

When an ionic compound dissolves, it breaks into ions, and the ion concentrations can be higher than the compound’s molarity. In 0.10 M CaCl₂:

• [Ca²⁺] = 0.10 M
• [Cl⁻] = 0.20 M, because each formula unit releases two chloride ions.

This matters for pH calculations — 0.05 M Ba(OH)₂ gives 0.10 M hydroxide ions — and for anything involving colligative properties.

Molarity’s weakness

Liquids expand when heated, so a solution’s volume changes with temperature, and its molarity changes with it. For most bench chemistry that’s negligible. For precise work over a range of temperatures, chemists use molality (moles of solute per kilogram of solvent), which doesn’t change with temperature. We compare the two in molarity vs. molality.

Quick answers

What does 1 M mean? One mole of solute per litre of solution.

Is molarity the same as concentration? It’s one measure of concentration. Others include mass percent, parts per million, molality and g/L.

Why do we use litres of solution, not solvent? Because the solution’s volume is what you actually measure and dispense. Using solution volume means “10 mL of a 1 M solution” always contains exactly 0.010 mol, however it was made.

Calculate it

The molarity calculator solves for molarity, grams of solute or volume — and has a dilution mode for C₁V₁ = C₂V₂ that also tells you how much solvent to add.