Serial dilution 2026-10-14
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Serial dilution repeatedly transfers a measured portion of one well-mixed chemical solution and dilutes that portion to a new final volume. With transferred volume and final volume at step , conserved solute gives
(1)
This product follows by repeated substitution. Each step conserves the solute in the portion transferred into its receiving flask, not the entire inventory in the preceding flask. Uniform mixing makes the selected fraction representative.
Continue the original solution mass and volume bookkeeping example. A portion of the stock contains of analytical sodium chloride, corresponding to before rounding. After dilution to , its analytical concentration is . A new portion of that mixed chemical solution contains ; dilution to gives . The two factors and multiply to .
Figure 1.
Final chemical solution volume and transferred solute in a serial dilution
. Original illustrative account, not experimental data. Calibration marks denote final contained volumes; arrows denote measured portions transferred. The first arrow carries ; the second carries . Each receiving flask conserves the inventory in its incoming portion. Equal dilution factors give successively tenfold lower analytical concentrations. Details.
The remaining stock holds ; the remaining first dilution holds . Including the final flask restores the starting inventory:
(2)
This is a direct check that making a dilute final sample does not destroy the solute. Most of it remains in earlier vessels.
Serial dilution makes a small final concentration accessible using measurable portions instead of a single extremely small transfer. Its limitation is that systematic errors propagate: if each transferred volume is below its intended value while final volumes are correct, two steps give times the intended concentration, a deficit. Repeated readings alone do not remove that bias. The gain in manageable volume therefore depends on calibrated transfer and representative mixing.
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