What is a Molarity & Dilution Calculator?
This calculator computes molarity (M), solution dilution (M₁V₁ = M₂V₂), and ppm conversion.
How it's calculated
Molarity M = moles of solute ÷ volume of solution (L)
Dilution: M₁V₁ = M₂V₂
1 ppm = 1 mg/L
Variable definitions
| Variable | Meaning | Unit |
|---|---|---|
| M | Molarity | mol/L |
| V | Solution volume | L |
| Subscripts 1, 2 | Before (1) / after (2) dilution | - |
Assumptions
This assumes the moles of solute remain constant before and after dilution — a straightforward mass balance. In real experiments, solution volume can shift slightly with temperature (thermal expansion), so precise analytical work requires temperature correction.
Worked example
Diluting 500mL of 1M HCl down to 0.1M
- M₁V₁ = M₂V₂ → 1 × 500 = 0.1 × V₂
- V₂ = 5,000 mL
- Add water to the 500mL stock solution until it reaches a total volume of 5L.
Why the dilution formula works
Adding water doesn't change how much solute is actually dissolved — only the total volume increases, which lowers concentration. That single idea — the amount of solute stays constant — is the entire basis of M₁V₁ = M₂V₂, exactly the same logic used for saltwater concentration problems.
Good to know
- Always add acid to water, never water to acid. Adding water to concentrated acid can cause violent local boiling and splashing — remembered by English speakers with the rhyme 'Do what you oughta, add acid to water.'
- Molarity (M) and molality (m) are different. Molarity is based on solution volume, molality on solvent mass — since volume changes with temperature but mass doesn't, precision chemistry often uses molality.
- 1 mole = 6.022×10²³ particles — a hard number to grasp intuitively, but it's roughly the number of molecules in 18g of water (about one sip).
- ppm (parts per million) is used for things like residual chlorine in tap water or atmospheric CO₂ concentration, which has risen from about 280 ppm pre-industrial to over 420 ppm today.
- A reagent bottle labeled '35% hydrochloric acid' is a mass percentage, not molarity — converting to molarity requires knowing the solution's density (concentrated HCl is roughly 12M).
Frequently asked questions
Q. How do I dilute 100mL of 1M solution to 0.1M?
Using M₁V₁=M₂V₂: 1×100 = 0.1×V₂, so the final volume should be 1,000mL — add 900mL of water.
Q. Is ppm the same as mg/L?
In dilute aqueous solutions, density is close enough to 1 g/mL that they're effectively equal. Precise work requires density correction.
Q. How do I convert molarity to percentage concentration?
You need the solution's density and the solute's molecular weight — it can't be converted directly without them.