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What is the arithmetic to convert 8 mg in 5 mL into units on a U-100 scale?

Asked 3 Sept 2024Modified 20 months agoViewed 49k times
32

Numbers first: 8 mg · 5 mL.

I can do the algebra. I am not confident about the conversion factors.

If there is a standard way to lay this out, I would rather learn that than invent one.

Can someone show the working rather than just the answer?

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LS
askedlow_dead_space37k373 Sept 2024

2 Answers

Accepted answer first, then by votes
102

Accepted answer

1.6 mg/mL, so one unit carries 0.016 mg. 8 ÷ 5 = 1.6 mg/mL; one unit on a U-100 barrel is 0.01 mL; 1.6 × 0.01 = 0.016 mg per unit. To go the other way, divide your intended dose by 0.016: a 0.16 mg dose is 10 units, and a 0.32 mg dose is 20. Write both the concentration and the milligrams per unit on the vial.

The arithmetic only stops being confusing once you work it through once and see that it is straightforward.

Worked example, because the general form is easier to trust once you have seen it once. Take a 10 mg vial and add 2 mL of diluent: the concentration is 10 ÷ 2 = 5 mg/mL. A 0.5 mg dose is 0.5 ÷ 5 = 0.1 mL. On a U-100 syringe, where 1 unit = 0.01 mL, that is 0.1 ÷ 0.01 = 10 units. Change the diluent to 1 mL and the same dose becomes 5 units — same dose, half the resolution.

Breaking it down further: if a 10 mg vial has 96.5 per cent content, you have 9.65 mg of peptide. Divide that by 2.00 mL and your concentration is 4.825 mg/mL, not 5.00 mg/mL, which is a 3.5 per cent systematic error in every dose calculation.

The Arrhenius relationship for drawing kinetics means that cold solution takes noticeably longer to draw than room-temperature solution.

Worth noting: the concentration after reconstitution is not the same as the label claim, and most people do not account for the difference.

Write the arithmetic on the vial label. It costs nothing and removes the step where you reconstruct it from memory.

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LB
answered · acceptedlaminar_bench69k578 Nov 2024
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88

Write the units at every step, because units errors are the failure mode that catches everyone eventually.

The concentration you actually work with is label claim times content fraction divided by actual diluent volume, which is usually not the same as the nominal concentration because content is usually not 100 per cent and you rarely measure the diluent volume to 0.1 mL precision.

Worth being precise here: number of stopper piercings matters less than the gauge doing the piercing. A 30G or 31G needle through a butyl stopper leaves a track that reseals; a 21G or 18G drawing needle punches a core and can drop it into the solution.

The limitation is that technique reduces risk, it does not remove it, and nothing you can do outside a controlled environment makes a non-sterile preparation sterile.

If in doubt, use more diluent and accept the shorter usable window.

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JH
answeredjana_horakova10k1419 Nov 2024
7Thank you — the worked example is what makes this usable. – tare_and_weigh 4 months ago
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