Molarity & Dilution Calculator

Frequently Asked Questions

What is molarity?

Moles of solute per litre of solution, M = n / V. From a mass, n = mass / molar mass, so M = mass / (molar mass × litres).

How does the dilution formula work?

C1V1 = C2V2: concentration times volume is conserved when you add solvent. Solve for the unknown to find how much stock or water to use.

What is the difference between molarity and molality?

Molarity is per litre of solution (volume, temperature-dependent); molality is per kilogram of solvent (mass, temperature-independent). This tool uses molarity.

How do I prepare a solution of a given molarity?

Mass needed = molarity × volume (L) × molar mass. Dissolve, then add solvent to the final volume - not before - so the volume is correct.

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How This Calculator Works

This tool covers the two everyday solution calculations. Molarity is concentration measured as moles of solute per litre of solution: M = n ÷ V. Knowing any two of molarity, moles, and volume fixes the third, and if you do not know moles directly you can enter mass plus molar mass since n = m ÷ Mᵣ. Dilution uses the conservation of moles: when you add solvent the amount of solute does not change, so the product of concentration and volume stays constant: C₁V₁ = C₂V₂. Supply any three of those four quantities and the calculator solves the fourth, then reports the volume of diluent (pure solvent) you must add as V₂ − V₁. Use any consistent volume unit on both sides of the dilution equation - mL with mL, L with L - because the units cancel.

Worked Example: Making 0.5 M NaCl, Then Diluting

To prepare 2 L of 0.500 M sodium chloride: moles = M × V = 0.500 × 2 = 1.00 mol. With molar mass 58.44 g÷mol that is 58.44 g of salt dissolved and topped up to 2 L. Now dilute it: take 100 mL of that 0.500 M stock and dilute to 500 mL. C₁V₁ = C₂V₂ → (0.500)(100) = C₂(500), so C₂ = 50 ÷ 500 = 0.100 M. You added 500 − 100 = 400 mL of water. Note the concentration fell by exactly the 5× dilution factor, matching V₂÷V₁.

Where These Equations Are Used

Lab bench: every buffer, reagent, and standard solution starts from a molarity calculation; serial dilutions build standard curves for spectrophotometry.

Titrations: the equivalence point uses M᳍V᳍ = M᳛V᳛ (scaled by stoichiometric ratio) to back out an unknown concentration.

Pharmacy & biology: preparing media, antibiotic stocks, and IV fluids all rely on C₁V₁ = C₂V₂ from a concentrated stock.

Industry: cleaning concentrates, electroplating baths, and water treatment dosing are dilution problems at scale.

Common Mistakes & Edge Cases

Using millilitres for V in M = n÷V - molarity is per litre; 250 mL is 0.250 L. Mixing units inflates concentration 1000×.

Adding solvent "to" a volume vs. adding a fixed volume: dilution math assumes you bring the solution up to final volume V₂, not add V₂ of water.

Confusing molarity (per L solution) with molality (per kg solvent) - they diverge for concentrated or temperature-sensitive solutions.

Forgetting molar mass when only mass is known: 5 g of glucose is not 5 mol; divide by 180.16 g÷mol first.

Trying to solve volume with zero molarity, or solving C₁ with V₁ = 0 - both divide by zero and are rejected.

Related Concepts & Limits

This model treats volumes as additive and ideal, which is excellent for dilute aqueous solutions but slightly off for highly concentrated or non-ideal mixtures (mixing 50 mL ethanol with 50 mL water yields under 100 mL). For temperature-independent work prefer molality or mole fraction. The molarity step depends on an accurate molar mass - compute it with the Molar Mass calculator first, then carry it here. Related quantities include normality (equivalents per litre, important for acid÷base and redox), parts-per-million for trace work, and the dilution factor V₂÷V₁ that links serial dilutions to final concentration. All results display six significant figures, ample for bench preparation.

Molarity & Dilution Calculator

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