Why does my 10 mg vial only yield about 9.2 mg of usable draws even with low-dead-space syringes?

I switched to fixed-needle U-100 insulin syringes after reading that dead space costs a fortune with luer fittings, and my yield improved a lot. But I still cannot account for all the material. Working it through, a nominal 10 mg vial seems to give me somewhere around 9.2 mg of usable draws, not 9.5 and certainly not 10.

The 0.3 to 0.8 mg gap bothers me because I cannot name where it goes. I can see three candidates and I do not know how to weight them:

• Content assay. The COA on this lot says peptide content 96.5 %. I do not know whether that is already reflected in the "10 mg" claim or applied to it.
• Unrecoverable residue. There is clearly some solution I cannot get out — the needle cannot reach the last bit even with the vial tilted.
• Dead space. Small per draw but there are twenty draws.

Can someone build the full accounting from 10 mg down to what actually leaves the vial, with each term separated? I want to know which terms are worth attacking and which are irreducible. A percentage answer is not enough; I want to see where each fraction of a milligram goes.

Research use only, and I am aware label claim and content are different quantities.

Adding the term the accepted answer explicitly sets aside, because in practice it is often larger than the dead space: error in the diluent volume you actually added.

The accepted answer assumes 2.00 mL of diluent was added. Suppose you measured it with a 3 mL luer-lock syringe graduated in 0.2 mL increments. Realistically you can read that to about ±0.05 mL, and there is a systematic component too — if you drew to the 2.0 mL graduation with the hub already full of water, you delivered 2.0 mL; if you drew to the graduation with an air-filled hub and then expelled, you delivered less. Work the consequence:

1. Intended 2.00 mL, actually delivered 1.90 mL. Concentration = 9.65 / 1.90 = 5.079 mg/mL instead of 4.825.
2. Each 100 µL draw now delivers 0.508 mg instead of 0.4825 mg — a 5.3 % overdelivery per draw.
3. Draws available: 1900 − 40 residue = 1,860 µL, at 102 µL per draw = 18 draws. So you get one fewer draw, each 5 % larger.
4. Total delivered = 18 x 0.508 = 9.14 mg. Yield essentially unchanged.

Note what this shows: diluent volume error barely affects yield but directly affects dose accuracy. Total mass out of the vial is nearly conserved regardless of how much water you put in; what changes is how it is divided. That is the opposite of dead space, which affects yield strongly and dose accuracy not at all. Two error sources, two different consequences, and they are constantly conflated.

Practical consequences:

• Measure diluent with the most accurate device you have, not the most convenient. A 1 mL syringe graduated in 0.01 mL used twice beats a 3 mL syringe graduated in 0.2 mL used once.
• Read to the same feature every time — bottom of the plunger seal, consistently — and read at eye level, because parallax on a syringe graduation is worth several percent.
• Write the volume you actually added on the vial, not the volume you intended. Every downstream calculation depends on it and your memory will not be reliable in three weeks.

One accounting term nobody has mentioned, which is small but real and shows up as a slow drift rather than a fixed loss: evaporative and adsorptive loss over the in-use life of the vial.

Two components:

• Adsorption to the container. Peptides adsorb to glass and to the elastomer of the stopper. The quantity is small and saturable — a monolayer over the wetted area — but for a low-concentration solution it is a non-trivial fraction. Rough scale: a monolayer of a 4 kDa peptide over an internal wetted area of a few square centimetres is in the microgram range, so at 5 mg/mL it is a rounding error. At 0.1 mg/mL, in a dilute working solution, the same absolute loss becomes percent-level. This is why dilute stocks behave worse than concentrated ones for reasons unconnected to stability.
• Volume loss through the septum. Very small over weeks for an intact butyl closure, but a septum that has been pierced twenty times has twenty tracks in it. Over a long in-use period this shows up as a fill level slightly lower than your arithmetic predicts, and it concentrates the remaining solution rather than diluting it, so late draws deliver marginally more than early ones.

Neither term is worth putting in your accounting for a 5 mg/mL vial used over four weeks. Both are worth knowing about if you are working at low concentration or over long periods, because they run in opposite directions — adsorption removes peptide, evaporation removes solvent — and neither is visible.

The practical version: at working concentrations of a few mg/mL over a few weeks, the accepted answer's four-term accounting is complete to better than a percent. Do not add terms you cannot measure to a calculation whose largest uncertainty is the content figure on the COA.