Molarity Calculator From Mass: Grams, Molar Mass and Volume

This calculator gives the molar concentration of a solution made by dissolving a weighed solid. Enter the mass of solute in grams, its molar mass and the final volume of the solution in millilitres; you get the molarity in mol/L, the same value in millimolar (mM) and the moles of solute.

Formula

c = m ÷ (M × V), with V in litres: V(L) = V(mL) ÷ 1000.

• c: molarity, moles of solute per litre of solution (mol/L, written M)
• m: mass of solute in grams
• M: molar mass of the solute in g/mol
• V: final volume of the whole solution, not the volume of water added
• 1 mol/L = 1000 mM

Worked Example

2.922 g of sodium chloride (M = 58.44 g/mol) made up to 250 mL in a volumetric flask.

1. Moles: n = 2.922 ÷ 58.44 = 0.0500 mol
2. Volume in litres: 250 ÷ 1000 = 0.25 L
3. c = 0.05 ÷ 0.25 = 0.2000 mol/L
4. In millimolar: 0.2 × 1000 = 200.00 mM

Assumptions

• The volume is the final volume after the solid has dissolved and the solution has been made up to the mark, as in a volumetric flask.
• The solute is pure and fully dissolved; for a hydrate, use the molar mass of the hydrate you weighed.
• The temperature is near the one the flask is calibrated for (usually 20 °C); molarity changes slightly as the solution expands with heat.

How to read the result

Molarity tells you how many moles are in each litre, so multiplying it by any volume in litres gives the moles in that volume. A 0.2 M solution holds 0.02 mol in 100 mL. If you need the mass for a target molarity instead, use m = c × V × M, or find the moles first and convert them with the moles to grams calculator. To make a weaker solution from this one, use the dilution calculator.

Limits and common mistakes

• Adding the solid to 250 mL of water gives more than 250 mL of solution and a slightly lower molarity; make up to the final volume instead.
• Forgetting to convert mL to L makes the answer 1000 times too small.
• Molarity is per litre of solution, molality is per kilogram of solvent; for that, use the molality calculator.

Frequently Asked Questions

What is the molarity of 2.922 g NaCl in 250 mL?

0.2 mol/L (0.2 M), using M = 58.44 g/mol.

What is the formula for molarity from mass?

Molarity = grams ÷ (molar mass × volume in litres).

What is the difference between M and mM?

1 M is 1 mol/L; 1 mM is one thousandth of that, 0.001 mol/L.

Can I use the volume of water I added?

Only as an approximation for very dilute solutions. Strictly, V is the final volume of the solution.

in m | Mass of solute | g | 2.922 | 0
in mm | Molar mass of solute | g/mol | 58.44 | 0.001
in v | Final volume of solution | mL | 250 | 0.000001
out c | Molarity | mol/L | m / (mm * v / 1000) | 4
out cmm | Concentration in millimolar | mM | c * 1000 | 2
out n | Amount of solute | mol | m / mm | 4