The dilution equation
C₁V₁ = C₂V₂ — moles of solute are conserved when you dilute. Enter any three values and the fourth falls out: V₁ = C₂V₂ ÷ C₁ (how much stock to take) or C₂ = C₁V₁ ÷ V₂ (what you end up with). Units don't matter as long as they match on each side — the ratio is unit-agnostic.
Example: 5 M stock → 0.1 M in 1000 mL needs 0.1 × 1000 ÷ 5 = 20 mL of stock, made up to 1 L.
Serial dilutions
A serial dilution repeats the same factor step by step: 1 M → 0.1 M → 0.01 M… Each step transfers into (factor − 1) × transfer of diluent, so each tube ends at factor × transfer total volume. The generator outputs the full table: tube number, concentration, and the exact pipetting recipe (transfer X μL into Y μL).
- Mix thoroughly at each step — serial dilution errors compound; a 5% pipetting error at step 1 becomes 50% by step 10.
- Change tips between tubes to avoid carryover.
- Discard the pipette tip after mixing — don't pipette from the tube you just mixed into the next one without a fresh tip.
- Log the protocol: concentration, date, who pipetted. Lab notebooks forgive nothing.
Common gotcha
"Add 20 mL stock to 1000 mL water" is not the same as "dilute to 1000 mL" — the first gives about 1.02× the intended final volume (so roughly 2% lower concentration). Always make up to final volume (add diluent to the mark), never "add stock to a pre-measured diluent" unless your protocol says so.