Molarity Calculator

Molarity (mol/L) = moles of solute ÷ litres of solution · moles = mass in grams ÷ molar mass

molarity

Moles of solute per litre of solution, written M. It is a property of the finished solution, not of the solute

mass

The mass of solute you weigh out, in grams. This is the number a balance gives you

molar mass

Grams per mole of the solute, from the reagent label or a formula

volume

The volume of the finished solution in litres — made up to the mark in a volumetric flask, not the volume of water you started with

M

Shorthand for mol/L. One millimolar is 0.001 M, written mM

Use it when a protocol gives a concentration and you need a mass to weigh, or when you have weighed something and need to know how strong the solution is. It is the right page whenever the question involves a volume of solution; if there is no volume in the question, the moles are all you have and the grams-to-moles page is the shorter route. It is not the page for concentrations expressed per kilogram of solvent — that is molality, and it uses a different denominator.

1. Making 100 mL of 1 M sodium chloride

   1. Moles needed: 1 mol/L × 0.1 L = 0.1 mol
   2. Mass: 0.1 mol × 58.44 g/mol = 5.844 grams of sodium chloride
   3. Weigh 5.844 grams and dissolve it in less than 100 mL of water
   4. Then make the volume up to exactly 100 mL — the last step is what makes it 1 M rather than approximately 1 M

   Dissolving 5.844 grams in 100 mL of water is not the same as making 100 mL of solution: the salt takes up space, so the finished volume would come to a little over 100 mL and the concentration a little under 1 M — around 2% low at this strength, and far more than that at 5 M, where the solute is a large fraction of the total. That gap is why the volumetric flask matters.

2. Working backwards: what to weigh for 250 mL of 0.5 M

   1. Moles needed: 0.5 mol/L × 0.25 L = 0.125 mol
   2. Mass: 0.125 mol × 58.44 g/mol = 7.305 grams
   3. The molarity box was left empty, so it is the concentration that gets reported back
   4. Halve the volume and the mass halves with it — 0.5 M is half of 1 M, and 250 mL is half of 500 mL

   Two halvings cancel: 250 mL of 0.5 M holds exactly the same 0.125 moles as 500 mL of 0.25 M. Concentration and volume trade off against each other, which is the whole content of the dilution equation C₁V₁ = C₂V₂.

Molarity is defined per litre of solution, not per litre of water, and that distinction is the one this page cannot make for you. Adding a solute changes the volume, so the amount of water to use is not the volume you asked for: to make 1 L of 1 M sodium chloride you dissolve 58.44 grams and then fill to the mark, which takes slightly less than a litre of water. Volume also changes with temperature — a solution made up at 4°C and used at 25°C is a little less concentrated than its label says — while a concentration quoted per kilogram of solvent does not move at all, which is why molality exists. This page assumes the solute is pure and anhydrous, so a hydrated salt such as CuSO4·5H2O carries water in its own formula weight and needs correspondingly more of it; the reagent chart below gives the figure for the hydrated form. The concentration field accepts molarity between 0.00001 M and 100 M and offers only M and mM, because the answer is always displayed in M to five decimals: micromolar and nanomolar solutions are real, but they would render here as 0.00000, and a number that reads as zero is worse than a refusal. Finally, molarity is not normality. For sulfuric acid or any other substance that donates more than one equivalent per formula unit, the two differ by that factor.

What is molarity?

Moles of solute per litre of solution, written M and read as molar. One litre of a 1 M solution holds exactly one mole of the dissolved substance; 0.1 M means one tenth of that. It describes the finished solution rather than the solute, so the same 58.44 grams of sodium chloride makes 1 M in 1 litre and 2 M in half a litre. The SI unit is the mole per cubic metre, which is numerically a thousand times smaller — 1 mol/m³ is 0.001 M.

How do I calculate molarity from grams?

Divide the mass by the molar mass to get moles, then divide by the volume of solution in litres. For 5.844 grams of sodium chloride in 100 mL: the molar mass is 58.44 g/mol so that is 0.1 moles, and 0.1 ÷ 0.1 L = 1 M. The two divisions can be written as one: molarity = mass ÷ (molar mass × volume). That single expression is what this page solves, in whichever direction you leave a box empty.

How much sodium chloride do I need for 500 mL of 1 M?

29.22 grams. Half a litre at 1 M holds 0.5 moles, and 0.5 × 58.44 = 29.22 grams. The reagent chart below lists the same figure for sodium chloride along with five other common reagents, in two bench quantities: what to weigh for 500 mL of a 1 M solution and for 1 litre of a 0.1 M solution. The two are not the same amount: half a litre at 1 M takes 0.5 moles and 1 litre at 0.1 M takes 0.1 moles, so the two weighings differ by a factor of five.

Why does it want three values?

Because the four quantities are tied together by one equation, molarity = mass ÷ (molar mass × volume), so any three determine the fourth. Nothing in the page needs a mode switch: leave one box empty and that is the one solved for. If you fill in all four and they contradict each other by more than 1%, the calculation stops rather than quietly picking a winner — four numbers from four different places disagreeing usually means one of them belongs to another substance.

Can I enter a concentration in micromolar?

Not through the concentration field, which offers M and mM only. The answer is always displayed in M to five decimal places, so 1 µM would print as 0.00000 and look exactly like zero; the field therefore starts at 0.00001 M, which is 10 µM. Working below that is real chemistry, but it is not chemistry this page can show you honestly. Enter such a solution through the mass and volume instead and read the answer from those.

• SI Units — Amount of Substance: the mole and the mole per cubic metre — National Institute of Standards and Technology (NIST)
• Standard Atomic Weights — abridged to four significant figures — Commission on Isotopic Abundances and Atomic Weights (CIAAW), IUPAC