Molarity is the chemist concentration unit: moles of solute per litre of solution, written M or mol/L. It connects the world of the balance, where you weigh grams, to the world of the volumetric flask, where you measure litres, through the mole, which is the bridge between mass and count. This guide works through the formula, the mass-to-moles step that precedes it, dilutions, and the neighbouring units, ppm, normality, and percent, that molarity is often confused with.

The formula, and the mass step before it

Molarity is moles divided by litres: M equals n divided by V, where n is moles of solute and V is litres of solution, not litres of solvent. The distinction matters: you dissolve the solute and then make the volume up to the mark, because the solute itself occupies volume, and adding a litre of water to a mole of salt gives more than a litre of solution.

Moles come from mass divided by molar mass: n equals m divided by Mw. Sodium chloride has a molar mass of 58.44 g/mol, from sodium 22.99 plus chlorine 35.45, so 29.22 g is 0.5 moles. Water is 18.015 g/mol, glucose is 180.156 g/mol, sulphuric acid is 98.079 g/mol, and sodium hydroxide is 40.00 g/mol. The calculator molar-mass table carries thirty common compounds, and the Advanced panel computes a molar mass from any formula.

The worked example: 0.5 moles of NaCl made up to 0.5 litres gives 0.5 divided by 0.5, or 1.0 M. The same 0.5 moles in 1 litre gives 0.5 M, and in 2 litres gives 0.25 M. Concentration falls as volume rises, because the same amount is spread thinner, which is the intuition behind every dilution.

Making a solution of an exact molarity

Decide the target molarity and volume, compute the moles, convert to mass, weigh, dissolve in part of the solvent, transfer to a volumetric flask, and make up to the mark. For 1 litre of 0.5 M NaCl: moles are 0.5 times 1, or 0.5, and mass is 0.5 times 58.44, or 29.22 g. Weigh 29.22 g, dissolve in about 800 mL of water, transfer, rinse, and make up to 1 litre.

The volumetric flask is the accuracy: a beaker measures approximately, a flask measures exactly, and the difference is the difference between a nominal and an actual molarity. Temperature matters too, because volume expands with temperature: a solution made up at 20 degrees is slightly more dilute at 30 degrees, because the same moles occupy a larger volume. Standard lab temperature is 20 degrees for this reason.

The checklist before weighing: confirm the compound and its hydration state, because a hydrate carries water in its formula weight. Copper sulphate pentahydrate is 249.68 g/mol, while anhydrous copper sulphate is 159.61 g/mol, and using the wrong one gives a solution off by more than half. Check the bottle label, not your memory, for the form you actually hold.

Dilutions: M1V1 equals M2V2

Dilution conserves moles: the moles before dilution equal the moles after, so M1 times V1 equals M2 times V2, where 1 is the stock and 2 is the diluted solution. To make 1 litre of 0.2 M from a 2 M stock: V1 equals M2 times V2 divided by M1, or 0.2 times 1 divided by 2, or 0.1 litres. Measure 100 mL of stock, transfer to a 1-litre flask, and make up to the mark.

Serial dilutions repeat the step: each stage dilutes the previous one by the same factor, so a 10-fold series from 1 M gives 0.1 M, 0.01 M, 0.001 M, and so on. The calculator serial-dilution table builds the series, and the pipetting rule is to use a fresh tip and a calibrated pipette at each stage, because errors compound down the series.

The common dilution error is adding the diluent volume to the stock volume instead of making up to the final volume. Adding 900 mL of water to 100 mL of stock gives 1 litre only if volumes add exactly, which they do not always: mixing can contract or expand. Making up to the mark in a volumetric flask avoids the assumption entirely.

Molar masses for the compounds you will actually weigh

The table gives molar masses to two decimals, enough for ordinary solution preparation. The calculator wider table carries thirty compounds.

Beyond molarity: ppm, normality, and percent

Parts per million, ppm, is milligrams per litre for dilute aqueous solutions, because a litre of water weighs about a kilogram. A 1 ppm solution contains 1 mg per litre. To convert molarity to ppm, multiply by molar mass and by 1,000: a 0.001 M NaCl solution is 0.001 times 58.44 times 1,000, or 58.44 ppm. Ppm suits trace analysis, where molarities would be tiny decimals.

Normality, N, is molarity times equivalents per mole: the number of reactive units, protons for acids, hydroxide ions for bases, electrons for redox. Sulphuric acid is diprotic, so 1 M is 2 N, while hydrochloric acid is monoprotic, so 1 M is 1 N. Normality survives in titrations because it makes the equivalence point arithmetic simple: N1V1 equals N2V2 at neutralisation.

Percent concentrations are mass or volume shares: percent weight by volume is grams per 100 mL, so a 5 percent w/v salt solution is 5 g in 100 mL. Percent weight by weight is grams per 100 g of solution, and percent volume by volume is mL per 100 mL. Always state which percent you mean, because the three differ, and a recipe that says only 5 percent is ambiguous.

Mistakes with molarity

First, using litres of solvent instead of litres of solution: make up to the mark, do not add the solvent volume. Second, forgetting the hydrate water in the molar mass, which is the largest single source of error in student preparations. Third, confusing molarity with molality, which is moles per kilogram of solvent and does not change with temperature, while molarity does.

Fourth, temperature: a solution made at 20 degrees and used at 30 is slightly more dilute, because the volume grew. Fifth, unit slips: millilitres must become litres before dividing, so 250 mL is 0.25 L, and a molarity computed with 250 in the denominator is a thousand times too small. The calculator accepts either unit and converts, which removes the commonest slip.

Frequently Asked Questions

What is molarity?

Moles of solute per litre of solution, written M or mol/L. A 1 M solution contains 1 mole of solute in each litre of solution.

What is the difference between molarity and molality?

Molarity is moles per litre of solution; molality is moles per kilogram of solvent. Molarity changes with temperature because volume changes, while molality does not.

When do I use M1V1 equals M2V2?

For dilutions: moles are conserved, so the stock molarity times stock volume equals the diluted molarity times diluted volume. Measure the stock volume, transfer, and make up to the final volume.

How do I find the molar mass of a compound?

Add the atomic masses of its atoms. NaCl is 22.99 plus 35.45, or 58.44 g/mol. The calculator table carries thirty common compounds, and the Advanced panel computes any formula.

How do I actually make a solution of an exact molarity?

Compute moles from target molarity times volume, convert to mass with the molar mass, weigh, dissolve in part of the solvent, transfer to a volumetric flask, and make up to the mark at 20 degrees.

Why does my solution molarity change slightly with temperature?

Because volume expands with temperature while moles stay fixed. A solution made up at 20 degrees is slightly more dilute at 30 degrees. Molality, per kilogram of solvent, avoids this.