Molarity Calculator
M = n / V = m / (MW × V). Type the formula and the molarity calculator works out the molar mass, then any two of mass, volume and concentration give the third, with the lab steps to make it up.
Molarity
- Molarity 0.2500 mol of NaCl in 0.25 L of solution.
- 1.000 M
- Working Molarity is moles of solute per liter of solution: M = n / V, and n = m / MW. Every unit is converted to grams, liters and mol/L before dividing. The commonest slip is leaving milliliters in, which is out by a factor of 1,000.
- M = m / (MW × V) = 14.61 g ÷ (58.44 g/mol × 0.25 L) = 1.000 mol/L
- Molar mass of NaCl 22.990 (Na) + 35.45 (Cl) = 58.44 g/mol, from the IUPAC (CIAAW 2024) abridged standard atomic weights. Shown to 2 decimal places because the atomic weights are uncertain by about ±0.01 g/mol for this formula.
- 58.44 g/mol
- Moles of solute 250.0 mmol.
- 0.2500 mol
- Concentration in other units Mass concentration is molarity times molar mass. 5.844% w/v (grams per 100 mL), which is not the same as % w/w unless the solution's density is 1 g/mL.
- 1.000 M = 58.44 g/L
- How to prepare this solution General practice for a solution made to a known volume. Correct for purity if the reagent is less than 100% (divide the mass by the purity as a fraction), and follow your lab's procedures.
- Weigh 14.61 g of NaCl. Dissolve it in less than the final volume (about 200 mL of solvent), then transfer it to a 250 mL volumetric flask, rinse the beaker into the flask two or three times, then add solvent to the mark. Stopper and invert to mix. Make up to volume after the solid has fully dissolved and the solution is back at room temperature. Follow your lab's procedures.
| Element | Atoms | Atomic weight | Mass (g/mol) | Mass percent |
|---|---|---|---|---|
| Na (sodium) | 1 | 22.990 | 22.99 | 39.34% |
| Cl (chlorine) | 1 | 35.45 | 35.45 | 60.66% |
| Total | 2 | 58.44 | 100.00% |
- Molarity is per liter of SOLUTION. Dissolving 1 mol in 1 L of water gives slightly more or less than 1 L of solution, and therefore not quite 1 M. That is why the solute is dissolved first and then made up to volume.
- Molarity changes slightly with temperature because volume does. For work that must not, use molality (mol per kg of solvent).
- To dilute a stock solution to a lower concentration, use C1V1 = C2V2; the dilution calculator does that.
How the Molarity Calculator works
Molarity is moles of solute per liter of solution: M = n / V. Since moles are mass divided by molar mass (n = m / MW), the working formula is M = m / (MW × V), with m in grams, MW in g/mol and V in liters. Rearranged, the mass to weigh out for a target concentration is m = M × V × MW, and the volume to make a given mass up to is V = m / (MW × M).
A worked example, the one above: 14.61 g of sodium chloride made up to 250 mL. The molar mass of NaCl is 22.990 + 35.45 = 58.44 g/mol, so 14.61 g is 14.61 / 58.44 = 0.2500 mol. Divide by 0.250 L and the solution is 1.000 M. Going the other way, 500 mL of 0.1 M NaCl needs 0.1 × 0.5 × 58.44 = 2.922 g.
The molar mass is where the effort goes. Type a formula and this calculator reads it (element symbols, counts, brackets, and hydrates such as CuSO4·5H2O) and adds up the atomic weights. Those are the IUPAC standard atomic weights as abridged by CIAAW, the IUPAC commission responsible for them, in its 2024 table. For a handful of elements (hydrogen, carbon, nitrogen, oxygen, chlorine and others) CIAAW publishes an interval rather than a single value, because their isotopic makeup genuinely varies in nature; the abridged table gives the single value it intends for calculations, and that is what is used here. It is also why molar masses are shown to two or three decimal places and no more: the atomic weights themselves are uncertain beyond that.
Three mistakes account for most wrong molarities. The first is units: a volume left in milliliters makes the answer a thousand times too large. The second is the hydrate. Copper sulfate pentahydrate is 249.68 g/mol and anhydrous copper sulfate is 159.60; weigh one using the other's molar mass and the solution is out by more than half. Use the formula of what is actually in the bottle. The third is volume of solution versus volume of solvent. Molarity is per liter of finished solution, so the solute is dissolved in less than the final volume and then made up to the mark in a volumetric flask. Adding 250 mL of water to 14.61 g of salt does not make 250 mL of solution.
Molarity, molality and normality are easy to confuse. Molality (m) is moles of solute per kilogram of solvent, not per liter of solution. It does not change with temperature, because mass does not, which is why it is used for boiling-point elevation, freezing-point depression and other colligative properties. In dilute water solutions near room temperature the two are close; in concentrated solutions or other solvents they are not. Normality (N) is equivalents per liter: molarity multiplied by the number of reacting units per formula, so 1 M sulfuric acid is 2 N for an acid-base reaction because each molecule gives up two protons. Normality depends on the reaction, which is why its use is now discouraged in favor of molarity.
This calculator makes a solution from a solid. To make a weaker solution from a stronger one, the relation is C1V1 = C2V2 and the dilution calculator solves it. For a solid that is not pure, divide the mass by the purity as a fraction: 2.922 g at 99% purity is 2.952 g weighed.
Molarity Calculator FAQ
How do you calculate molarity?
Divide moles of solute by liters of solution: M = n / V. From a mass, first convert to moles by dividing by the molar mass, so M = m / (MW × V). 5.844 g of NaCl (molar mass 58.44 g/mol) is 0.1 mol, and in 0.5 L of solution that is 0.2 M.
How many grams do I need to make a solution of a given molarity?
Multiply molarity by volume in liters by molar mass: m = M × V × MW. For 250 mL of 0.5 M glucose (180.16 g/mol): 0.5 × 0.25 × 180.16 = 22.52 g. Weigh that, dissolve it in less than 250 mL, then make up to 250 mL in a volumetric flask.
What is the difference between molarity and molality?
Molarity is moles per liter of solution; molality is moles per kilogram of solvent. Molarity is easier to measure out with glassware, but changes slightly with temperature because liquids expand. Molality does not, which is why colligative-property calculations use it.
What is normality and how does it relate to molarity?
Normality is equivalents per liter: molarity times the number of reacting units each formula supplies in the reaction at hand. 1 M H2SO4 is 2 N as an acid because each molecule donates two protons. Because the same solution can have different normalities in different reactions, molarity is the preferred unit.
Do I use the volume of water or the volume of the solution?
The volume of the solution. The solute takes up space and changes the total volume, so dissolve it in less solvent than the target and then make up to the final volume. This is what a volumetric flask is for.