Dilutions and Buffers

Track solute through serial transfers, then see why the same pH can hide very different buffer reserves.

Same solute, more solvent

Transfer a measured portion into fresh diluent. Follow the concentration and the liquid left behind as each tube supplies the next.

Swipe the diagram horizontally to see every tube.

0 / 3 tubes mixed

Stock concentration1,000 µM

Transfer into each tube100 µL

Fresh diluent per tube900 µL

Number of tubes3

Ready to mix tube 1.

For tube 1, take 100 µL at 1,000 µM and add 900 µL of solute-free diluent. The mixed volume is 1000 µL.

C₁V₁ = C₂V₂: 1,000 × 100 = 100 × 1000 = 100,000 pmol

1:1,000planned cumulative dilution at the final tube

1 µMplanned final-tube concentration

2,700 µLtotal fresh diluent for the series

Volume left after the complete series. The last tube does not transfer onward.
Tube	Concentration	Cumulative dilution	Volume left
1	100 µM	1:10	900 µL
2	10 µM	1:100	900 µL
3	1 µM	1:1,000	1000 µL

Complete mixing, additive volumes, no loss or reaction, and an adequate stock are assumed. Removing an aliquot from a well-mixed tube changes its remaining volume and amount of solute, not its concentration. This example tracks one solute; solvent compatibility and measurement uncertainty are not modelled. Changing a setup control restarts the mixing sequence.

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Quick reference

Concentration is amount per volume

Adding solute-free diluent preserves the solute in the aliquot while increasing volume: C₁V₁ = C₂V₂. In a serial dilution, successive dilution factors multiply. Taking an aliquot from a fully mixed tube lowers its remaining amount and volume proportionally, leaving its concentration unchanged.

Neutralise first, estimate pH second

Strong base converts weak acid HA to conjugate base A−; strong acid reverses that balance. Subtract and add moles before using pH ≈ pKₐ + log₁₀(nA−/nHA). This approximation requires both partners to remain appreciable. Near exhaustion, equilibrium changes, water and excess strong titrant need explicit treatment; this tool then withholds an invalid logarithm.

A ratio does not tell you the reserve

Diluting both partners equally preserves their ratio and approximately preserves pH, while lowering buffering capacity per volume. Local buffer capacity describes resistance to a small pH change; finite additions change the ratio and consume a partner. The examples use acetate at 25 °C, additive volumes and ideal concentration approximations. They do not replace checking a prepared solution.

Check your understanding Optional

An ideal buffer is diluted tenfold while its acid-to-base ratio stays unchanged. What follows approximately?

Similar pH, but lower buffering capacity per volume.The pH becomes ten times smaller.The same pH means the same reserve against added acid.

At the bench

Use the practical dilution planners and buffer temperature calculations after exploring the assumptions behind their arithmetic.

Open Lab Calculators

Sources and model notes

These interactive examples explain selected relationships using the assumptions shown beside their controls. Calculated quantities and illustrative inputs are identified in each tool; use the linked Drybench app to work with your own data.

OpenStax · Molarity and dilution

Official open textbook derivation of dilution from conservation of solute.

OpenStax · Buffers

Stoichiometric accounting for strong-acid/base additions followed by buffer equilibrium, and the limits of buffer capacity.

Goldberg, Kishore & Lennen · Buffer thermodynamics

NIST evaluated data, Table 8: acetate pKₐ 4.756 at 298.15 K in the standard state. The tool uses the same source table as Lab Calculators.