Molarity calculator
This molarity calculator finds the molarity of a solution from the grams or moles of solute and the volume. It also works backward to the mass to weigh out, the volume to make, or the moles in a solution.
- Solve for molarity, mass, volume or moles
- Grams or milligrams, liters, mL or µL
- Each step written out with your numbers
Last updated
How to use the molarity calculator
- Choose what to solve for: molarity, the mass to weigh out, the volume of solution, or the moles.
- For molarity or volume, say whether you know the solute as a mass (grams) or as moles.
- Enter the values you know and pick their units. The field you are solving for fills in by itself.
- Get the molar mass from the chemical formula, adding the atomic masses from a periodic table (NaCl: 22.99 + 35.45 = 58.44 g/mol).
The molarity formula
Molarity (M) is the number of moles of solute in one liter of solution. Its unit is moles per liter, written mol/L or M.
M = n ÷ V and n = mass ÷ molar mass
Put together, M = mass ÷ (molar mass × V). Rearranged: mass = M × V × molar mass, V = n ÷ M, and n = M × V. Volume must be in liters, so divide milliliters by 1,000 first. V is the volume of the finished solution, not the volume of water you start with.
Worked example
What is the molarity of 29.22 g of sodium chloride (NaCl, molar mass 58.44 g/mol) dissolved in water to make 500 mL of solution?
- Moles of NaCl: 29.22 g ÷ 58.44 g/mol = 0.5000 mol.
- Volume in liters: 500 mL ÷ 1,000 = 0.5000 L.
- Molarity: 0.5000 mol ÷ 0.5000 L = 1.000 M.
Working backward, 1.000 M × 0.5000 L × 58.44 g/mol = 29.22 g, the mass to weigh out to make the same solution.
How to make a solution of a set molarity
- Find the mass you need: mass = M × V (in liters) × molar mass. For 250 mL of 0.100 M NaCl that is 0.100 × 0.250 × 58.44 = 1.46 g.
- Weigh the solute and dissolve it in less water than the final volume.
- Transfer it to a volumetric flask and add water up to the mark, then mix.
Making up to the final volume matters because the solute takes up some space. Adding 1.46 g of NaCl to exactly 250 mL of water gives slightly more than 250 mL of solution.
Concentration units
| Unit | Meaning | Same as |
|---|---|---|
| M (molar) | moles per liter of solution | 1 M = 1,000 mM |
| mM (millimolar) | millimoles per liter | 1 mM = 1,000 µM |
| µM (micromolar) | micromoles per liter | 1 µM = 1,000 nM |
| mg/mL | milligrams per milliliter | 1 mg/mL = 1 g/L; divide by molar mass for M |
| m (molal) | moles per kilogram of solvent | not the same as molarity |
Common questions
What is the formula for molarity?
Molarity = moles of solute ÷ liters of solution (M = n ÷ V). 0.50 mol of NaCl in 2.0 L of solution is 0.25 M.
How do you calculate molarity from grams?
Divide the grams by the molar mass to get moles, then divide by the volume in liters. 29.22 g of NaCl is 29.22 ÷ 58.44 = 0.5000 mol; in 0.500 L that is 1.000 M.
How do you convert mg/mL to molarity?
mg/mL is the same as g/L, so divide by the molar mass in g/mol. A 5.844 mg/mL NaCl solution is 5.844 g/L ÷ 58.44 g/mol = 0.1000 M.
How many grams do I need for a 1 M solution?
For 1 liter, the molar mass in grams. One liter of 1 M NaCl needs 58.44 g, made up to 1 L. For other volumes, multiply by the volume in liters: 500 mL needs 29.22 g.
What is the difference between molarity and molality?
Molarity is moles per liter of solution; molality is moles per kilogram of solvent. Molarity changes slightly with temperature because the volume does, while molality does not.
How do I dilute a solution to a lower molarity?
Use C₁V₁ = C₂V₂. To make 100 mL of 0.1 M from a 1.0 M stock, take 0.1 × 100 ÷ 1.0 = 10 mL of stock and add water up to 100 mL. The dilution calculator does this for you.
Sources
- OpenStax Chemistry 2e, 3.3 Molarity. Definition of molarity (moles of solute per liter of solution), mass and dilution examples, NaCl molar mass 58.44 g/mol
- OpenStax Chemistry 2e, 11.4 Colligative Properties. Molality (moles per kilogram of solvent) and why molarity, unlike molality, changes with temperature
- IUPAC CIAAW: Standard atomic weights. Na 22.990; Cl 35.446 to 35.457, usually rounded to 35.45
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