How do you calculate molarity?

Molarity, written M or mol/L, is the number of moles of solute in one liter of solution. It is the usual concentration unit in the lab because it links directly to moles, and reactions consume moles. Molarity has two inputs, the amount of solute and the volume of the final solution, so the calculation is two divisions.

What is the formula for molarity?

M = n / V

• M is molarity in mol/L
• n is moles of solute, which is the mass in grams divided by the molar mass in g/mol
• V is the volume of the solution in liters

Combining the two steps gives M = (mass / molar mass) / V. Molar mass comes from the chemical formula and the atomic masses, which you can look up or compute from a periodic table. For sodium chloride, Na is 22.990 and Cl is 35.45, so NaCl is 58.44 g/mol.

Volume must be in liters. Convert milliliters by dividing by 1,000.

What is the molarity of 4.383 g of NaCl in 500 mL?

Find the molarity of a solution made by dissolving 4.383 g of sodium chloride and making it up to 500 mL.

1. Convert the volume: 500 mL = 0.500 L.
2. Find the moles: 4.383 g / 58.44 g/mol = 0.0750 mol.
3. Divide by the volume: 0.0750 mol / 0.500 L = 0.150 mol/L.

The molarity is 0.150 M. To check it, reverse the steps: 0.150 M × 0.500 L = 0.0750 mol, and 0.0750 mol × 58.44 g/mol = 4.383 g.

A second example starts from a larger mass. Dissolve 10.0 g of sodium chloride and make it up to 2.00 L:

• Moles: 10.0 g / 58.44 g/mol = 0.1711 mol
• Molarity: 0.1711 mol / 2.00 L = 0.0856 M

The same formula covers both cases. Only the mass and the final volume change.

What mistakes do people make when calculating molarity?

Using the solvent volume. Molarity uses the volume of the final solution, which is the volume once the solid has dissolved and the flask is filled to the mark. The volume of water added before the solid dissolved is not the right number. The difference is small for dilute solutions and grows as the solute concentration rises.

Mixing up milliliters and liters. Entering 500 for the volume when it should be 0.500 L makes the molarity 1,000 times too small. In the mass formula, the same slip makes the required mass 1,000 times too large.

Using the wrong molar mass. A hydrate such as CuSO4·5H2O has a much larger molar mass than the anhydrous salt, because it includes the water. Use the formula on the label. The same applies to a reagent of less than 100% purity, which needs a larger mass to deliver the same moles.

Confusing molarity with molality. Molality is moles per kilogram of solvent. Molarity is moles per liter of solution. The two are close for dilute aqueous solutions, but they are not the same measure.

How do I convert molarity to grams per liter or percent w/v?

Molarity converts to other common units with the molar mass:

• Grams per liter: g/L = M × molar mass
• Percent weight per volume: % w/v = g/L / 10

For 0.150 M NaCl, that gives 8.766 g/L, or 0.8766% w/v.

How do I calculate molarity in a spreadsheet?

Set up the inputs in four cells. Put the solute mass in grams in B1, the molar mass in B2, and the final volume in milliliters in B3. Then use these formulas:

• Moles: =B1/B2
• Molarity: =(B1/B2)/(B3/1000), which gives 0.0856 for 10.0 g, 58.44 g/mol and 2,000 mL
• Mass needed for a target molarity: enter the target in E1 (0.150) and the final volume in mL in E2 (500), then use =E1*E2/1000*B2, which gives 4.383 g

For the molar mass itself, type the element masses into the formula, such as =22.990+35.45 for NaCl. The molar mass calculator builds the molar mass from an element count, and the solution and dilution calculator covers the mass needed and the dilution volumes. For the mass to weigh, purity and hydrate corrections, and the C1V1 method, see molarity, dilutions and C1V1 = C2V2.