Molarity & Dilution
Make or change a solution: dilute a known stock (C₁V₁ = C₂V₂), prepare from a solid, plan a serial-dilution series, or interconvert percent, molarity and ppm. The substance (MW, density) carries across modes.
How to use this tool
This is the Concentration & Dilution workspace, four modes for making or changing a solution. Dilute a stock to a working strength, Make a solution from a dry solid, plan a Serial dilution series, or Convert between w/w%, w/v%, molarity and ppm. The compound's molecular weight and density carry over when you switch modes.
Dilute (C₁V₁ = C₂V₂)
Enter the stock and target concentrations and the volume you want, get the stock volume to measure and the diluent to add.
Make (from solid)
Enter the compound, molecular weight, target molarity, volume and reagent purity, get the mass to weigh and a step-by-step recipe with a safety note.
Serial
Enter the stock, dilution factor, step count and working volume, get the concentration and transfer/diluent volumes for every tube.
Convert
Enter density and molecular weight, pick the unit you know, and read the same solution in w/w%, w/v%, molarity and ppm at once.
Worked example
Diluting 12 M HCl down to 1 M and making 500 mL: measure 41.67 mL of stock, then add 458.33 mL of water.
Dilute stock
Dilution Recipe
The numbered recipe is your bench procedure. In dilution mode V₁ is the stock to measure and the remainder is diluent; when diluting concentrated acids, always add acid to water, never the reverse.
Methodology
Dilute
Conservation of moles gives C₁V₁ = C₂V₂; we solve for V₁ when you fix the other three.
Make (from solid)
Mass to weigh is m = M · V₍L₎ · MW ÷ (purity/100), the purity correction accounts for hydrates and technical grades. Safety notes are generated from the compound name (acids, bases, oxidisers).
Serial
Each step transfers V / f of the previous tube into V − V/f of fresh diluent; after step n the concentration is C₀ / fⁿ.
Convert
w/w% is mass of solute per 100 g solution; w/v% is mass per 100 mL. With density ρ in g/mL, w/v% = ρ × w/w%. Molarity M = (w/v% × 10) / MW. ppm = w/v% × 10 000 for a solution of density 1.
Sources
- Atkins, Physical Chemistry, 11th ed., ch. 5.
- Skoog, West & Holler, Fundamentals of Analytical Chemistry.