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Reconstitution Arithmetic: Volume, Concentration and Molarity

Three calculations, one of which is almost always done from the wrong number. Worked through, with the unit error that causes most of the trouble.

8 min readUpdated

A clear solvent bottle beside a sealed vial of white powder on a pale bench

Preparing a peptide solution involves three calculations: the concentration you get from a given volume, the volume needed for a target concentration, and the conversion from mass to moles. All three are straightforward, and the error that matters is almost always in the input rather than the arithmetic.

Start from the certificate, not the label

The label is nominal. The certificate reports a measured content, and fills are generally set to meet or exceed the label, so a vial marked 10 mg frequently contains a few percent more.

Using 10 mg where the certificate says 10.4 mg builds a four percent error into everything downstream, and it is an avoidable one. Net peptide content covers why the two figures differ, and reading a certificate line by line covers where to find the right one.

Concentration from a volume

Concentration equals measured content divided by solvent volume. A vial containing 10.4 mg brought up in 2 mL is 5.2 mg/mL. Nothing else is involved, provided the volume added is the volume measured rather than the volume intended.

The powder itself contributes a little volume, which is negligible at these masses and is why solvent volume is treated as final volume in practice.

Volume for a target concentration

Volume equals content divided by target concentration. For 10.4 mg at a target of 2 mg/mL, that is 5.2 mL. The practical constraint is the vial: a 2 mL vial cannot hold 5.2 mL, so either the target changes or the material is transferred, and transferring introduces losses that why peptides stick to plastic is relevant to.

Mass to moles

Molar concentration equals mass concentration divided by molecular weight. This is where most unit errors happen, because mass is in milligrams, molecular weight is in grams per mole, and the answer wanted is usually micromolar.

QuantityUnitCommon error
Measured contentmgUsing the label instead
Solvent volumemLIntended rather than measured
Concentrationmg/mLReported without saying which number it came from
Molecular weightg/molSalt-form mass used instead of free peptide
Molar concentrationmol/L, then scaledFactor-of-1000 slip between mM and µM

The arithmetic is simple. Four of these five inputs are where the mistakes live.

A worked example

A vial whose certificate reports 10.4 mg of a compound with a molecular weight of 1419.5 g/mol, brought up in 2 mL.

  • Mass concentration: 10.4 mg ÷ 2 mL = 5.2 mg/mL.
  • In grams per litre, 5.2 mg/mL is 5.2 g/L.
  • Molar concentration: 5.2 g/L ÷ 1419.5 g/mol = 0.00366 mol/L, which is 3.66 mM.
  • A 1 in 1000 dilution of that gives 3.66 µM.

Two compounds of the same mass in the same volume give different molar concentrations, because the molecules differ in weight. Molecular weight for buyers covers where that figure comes from.

Which molecular weight to use

The free peptide mass, which is what a certificate reports and what a formula predicts. The powder weighs more because of counter-ion and residual water, but the content assay already measures peptide rather than powder, so the two are consistent with each other. Mixing a salt-corrected mass with an assayed content double-counts. TFA and acetate salt forms covers the distinction.

Serial dilution, and where it goes wrong

Reaching a working concentration from a stock usually means several steps rather than one, because a single very large dilution is hard to perform accurately with ordinary glassware. Each step multiplies, so a 1 in 10 followed by a 1 in 100 is a 1 in 1000 overall.

Two errors dominate. The first is compounding: a small systematic error at each step multiplies rather than averages out, so three sloppy steps are considerably worse than one. The second is adsorption, which bites hardest at the dilute end, because loss to a container wall is roughly fixed per unit of surface and therefore a larger share of a small quantity.

Why the final volume is not always the volume added

For a vial of lyophilised powder at these masses, solvent volume and final volume are close enough to treat as identical, and that is the convention in practice. It stops being true when a concentrated stock is diluted into a fixed final volume, where the stock contributes meaningfully to the total.

The habit that avoids the confusion is to state which convention a number uses when recording it. "Made up to 10 mL" and "10 mL added" are different operations and they produce different concentrations.

Record what you did, not what you planned

Write down the lot, the content figure used, the measured volume added, and the resulting concentration. A solution labelled only with a compound name and a concentration cannot be checked later, and cannot be tied back to a certificate at all.

For where this sits among the other molecules a catalogue carries, not everything in a peptide catalog is a peptide covers how the classes differ.

This guide is general reference for research buyers. Materials supplied by Restate Health are for laboratory research use only and are not for human or veterinary use.

Common questions

Should I use the label or the certificate figure?

The certificate. The label is nominal and the certificate reports a measured mass, which is often a few percent higher. Using the label builds that difference into every number downstream.

Does the powder add volume?

A little, and at these masses it is small enough that solvent volume is treated as final volume. The larger uncertainty is whether the volume added was measured or assumed.

Which molecular weight goes in the molarity calculation?

The free peptide mass from the certificate or the formula. The content assay already measures peptide rather than powder, so applying a salt correction as well counts the same thing twice.

Why do equal masses give different molar amounts?

Because the molecules weigh different amounts. The same mass of a small peptide contains far more molecules than the same mass of a large one.

What is the most common error?

A factor of a thousand between millimolar and micromolar, usually introduced when converting mg/mL to g/L. Writing the units at every step catches it.

All products are supplied strictly for laboratory research and development purposes. They are not for human or veterinary use and are not intended to diagnose, treat, cure, or prevent any disease or medical condition.