Calculating the Concentration of a Reconstituted Stock Solution

The arithmetic for preparing a laboratory stock solution is one division. Almost all of the error comes from using the wrong number in it — the figure printed on the label rather than the figure measured on the lot. This note covers the calculation, the four places accuracy is lost, and how to record it so the number can be checked later.

The calculation

Concentration is mass divided by volume. Dissolve 10 mg of solid in 2 mL of solvent and the stock is 5 mg/mL, which is also 5 µg/µL. To go the other way, volume is mass divided by the concentration you want: 10 mg at a target of 2 mg/mL needs 5 mL.

Diluting an existing stock uses the same relationship in the form C₁V₁ = C₂V₂. To make 1 mL at 1 mg/mL from a 5 mg/mL stock: V₁ = (1 × 1) / 5 = 0.2 mL of stock, made up to 1 mL total. Note “made up to”, not “plus”: 0.2 mL of stock plus 1 mL of solvent is 1.2 mL and a different concentration.

Why the label figure is usually the wrong input

The quantity on a label is normally the weighed solid. That solid includes counter-ion and residual water, so the mass of peptide in the vial is the labelled mass multiplied by the net peptide content.

A vial labelled 10 mg with a measured net content of 80% contains 8 mg of peptide. Dissolved in 2 mL, the solution is 4 mg/mL of peptide, not 5. A calculation that used the label is 25% high — larger than most of the differences people worry about on a certificate, and entirely avoidable by reading one figure.

Where the certificate gives content as a peptide-mass figure rather than a percentage, use it directly. Where no content figure exists at all, no accurate concentration can be calculated from that vial, and that is worth knowing before the solvent goes in.

Four places accuracy is lost

• Fill variation. The labelled quantity is a target. Two vials from one lot can differ by a few percent, so a concentration is only as good as the assumption that this vial matches the lot’s average.
• Added volume versus final volume. The solid occupies volume and displaces solvent. At a few milligrams in millilitres the effect is small; at high concentrations it is not, and the honest description is “dissolved in 2 mL of solvent” rather than “made up to 2 mL” unless volume was actually made up.
• Incomplete dissolution. Anything still solid is not in solution, so the real concentration is lower than calculated and unknown. Material lost to haze or precipitate counts the same way — see cloudy solutions and precipitates.
• Adsorption to surfaces. Peptides stick to glass and plastic. At low concentrations the fraction lost to the container wall and pipette tips stops being negligible, which is one reason dilute working solutions are made fresh rather than stored.

A worked example

• Label: 10 mg. Certificate for this lot: purity 99.1%, net peptide content 82%.
• Peptide in the vial: 10 × 0.82 = 8.2 mg.
• Solvent added: 2 mL. Stock concentration: 8.2 / 2 = 4.1 mg/mL.
• To obtain 0.5 mL at 1 mg/mL: (1 × 0.5) / 4.1 = 0.122 mL of stock, made up to 0.5 mL.
• The same vial calculated from the label alone would have been recorded as 5 mg/mL — a 22% overstatement carried into every dilution downstream.

What to write down

Lot number, net peptide content used, solvent, volume added, whether volume was made up, date and concentration. Six fields, one line. A stock solution whose concentration cannot be reconstructed from a record is an unknown solution, and no result obtained with it can be reported as quantitative.

All products referenced on this site are supplied for laboratory research use only, and are not for human or veterinary use. Nothing here is a recommendation for any use other than laboratory research.