Science & Weather · Chemistry

Molarity & Dilution Calculator — Mass to Weigh, C₁V₁ = C₂V₂

Make up and dilute solutions: find the molarity of a solution from the mass dissolved, the mass to weigh out for a target concentration and volume, the volumes for a dilution (C₁V₁ = C₂V₂), or convert between percent weight/volume and molarity. Enter the molar mass directly or type the formula and it's worked out for you.

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Mass to Weigh

2.922 g

For 100 mL of 0.5 M solution

Molar Mass Used: 58.44 g/mol (NaCl)
Moles: 0.05 mol
How to Make It: Dissolve 2.922 g in less than 100 mL of solvent, then top up to exactly 100 mL.

How this is calculated

Molarity = moles ÷ litres = mass ÷ (M × V) · mass = C × V × M · C₁V₁ = C₂V₂ · molarity = (% w/v × 10) ÷ M

M: Molar mass (g/mol)
C, V: Concentration (mol/L) and volume (L)

Molarity is moles of solute per litre of solution. To make a solution, multiply the target concentration by the volume (in litres) to get moles, then by the molar mass to get the grams to weigh. When diluting, the moles of solute don't change, so concentration × volume is the same before and after: C₁V₁ = C₂V₂. A % w/v solution has that many grams per 100 mL, i.e. ten times that per litre.

Assumptions & sources

Volume is the final volume of solution, not of solvent added.
The solute is fully dissolved; hydrates must be entered with their water (e.g. CuSO4·5H2O) if that's what you weigh.

1Standard atomic weights (abridged values) — IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW)
2Concentration of solutions — molarity and dilution — NCERT Chemistry, Class 12 — Solutions

Calculator ID SCI-MOLARITY-001 · version 1.0.0

Common questions

How much NaCl do I need for 100 mL of 0.5 M solution?

0.5 mol/L × 0.1 L × 58.44 g/mol = 2.922 g, made up to 100 mL.

How do I dilute 1 M stock to 0.1 M?

Use C₁V₁ = C₂V₂: for 250 mL of 0.1 M, take 0.1 × 250 ÷ 1 = 25 mL of stock and add 225 mL of water.

What molarity is 0.9 % saline?

0.9 g per 100 mL = 9 g/L ÷ 58.44 g/mol = 0.154 M (154 mM).