Molarity calculator

How do I calculate molarity?

Molarity = moles of solute ÷ liters of solution, and moles = grams ÷ molar mass. 58.44 g of sodium chloride (molar mass 58.44 g/mol) in 1 L of solution is 1 mol/L, written 1 M.

How much solute do I need for a solution?

Grams = molarity × liters × molar mass. For 2 L of 0.5 M NaCl: 0.5 × 2 × 58.44 = 58.44 g.

Where do I find the molar mass?

Add up the atomic weights of the atoms in the formula from a periodic table, or read it from the chemical's label or safety data sheet.

Is it liters of water or of solution?

Of the final solution. Dissolve the solute in less water, then add water up to the final volume in a volumetric flask.

What is the difference between molarity and molality?

Molarity is per liter of solution; molality is per kilogram of solvent. Molality does not change with temperature, molarity does slightly.

How much stock solution do I need to make a weaker one?

Use C₁V₁ = C₂V₂, because diluting does not change the moles of solute (OpenStax Chemistry 2e, section 3.3). To make 5.00 L of 0.100 M KOH from a 1.59 M stock you need V₁ = 0.100 × 5.00 ÷ 1.59 = 0.314 L of stock, then water up to 5.00 L. The dilution calculator does this for any three of the four values.

What is the molarity of the individual ions?

Multiply by the number of ions each formula unit releases. A 1.0 M solution of CaCl₂ is 1.0 M in Ca²⁺ and 2.0 M in Cl⁻, because the formula has two chlorides. The calculator gives the molarity of the compound as written, which is the number on a reagent bottle.

The formula and its limits

Molarity (M) is the number of moles of solute in exactly one liter of the solution, not of the solvent (OpenStax Chemistry 2e, section 3.3). Written out, M = n ÷ V, where n = mass ÷ molar mass, so M = mass ÷ (molar mass × V). Rearranged for a recipe, mass = M × V × molar mass. The volume must be in liters and the molar mass in grams per mole. The formula describes the finished solution at the temperature where its volume was measured; because liquids expand and contract, the same solution has a slightly different molarity at another temperature, which is why chemists who need a temperature-proof unit use molality.

Worked examples

Finding molarity (OpenStax Example 3.16): 25.2 g of acetic acid, molar mass 60.052 g/mol, is dissolved in enough water to make 0.500 L of vinegar. The amount is 25.2 ÷ 60.052 = 0.4196 mol, and the molarity is 0.4196 mol ÷ 0.500 L = 0.839 M. Finding the mass (Example 3.17): how much NaCl is in 0.250 L of a 5.30 M solution? The amount is 5.30 × 0.250 = 1.325 mol, and the mass is 1.325 × 58.44 g/mol = 77.4 g. Choose “Grams needed” in the calculator, enter 58.44, 0.25 and 5.3, and it returns the same figure.

Common mistakes

Unit slips come first. The volume field is in liters, so 500 mL must be entered as 0.5; typing 500 gives 0.00084 M for the vinegar above, a thousand times too small. Second, the volume is that of the finished solution: dissolve the solute in less water, then fill to the mark of a volumetric flask, rather than adding the solute to a full liter of water. Third, use the molar mass of the substance as it is in the bottle, so a hydrate such as CuSO₄·5H₂O counts its water. Last, molarity applies to the solute as written; for a salt that dissociates, multiply by the number of ions per formula unit to get the concentration of each ion.

Sources: OpenStax Chemistry 2e, section 3.3 “Molarity” (definition, the dilution equation, Examples 3.16, 3.17 and 3.21, rounding advice), section 3.1 (molar mass) and section 11.4 (molarity versus molality and temperature). Related: dilution calculator, grams to moles calculator, molality calculator and percent to molarity calculator.