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Volumetric dosing accuracy
Volumetric dosing has long been recommended as a way to make doses of chemicals that require doses too low to be measured accurate on the kinds of scales that most people have available to them. In practical terms, this means anything with a dose in the single milligram range or lower and includes most novel benzodiazepines, which users frequently dose by dissolving in propylene glycol and measuring out doses by the millilitre.

But how do you know whether the volumetric solution you're making is going to provide a reasonably accurate dose?

I'll provide a formula here which can be used to work out the upper and lower doses provided by a solution given known sources of measurement inaccuracy. The numbers are the best case scenario where no other sources of inaccuracy or error have crept in. Volumetric dosing protects you against measurement errors caused by the limits of accuracy of the tools you have available - it doesn't protect you against a lack of care and attention.

First, let's define some terms, starting with things that you control and decide upon:

W = The intended weight of the chemical you want each dose to contain (mg)

Dv = The volume of the solution you intend to measure out each time as a single dose (ml)

N = The number of doses you intend your solution to contain.

And the sources of measurement inaccuracy:

Wa = The expected accuracy of the scale you're using .scales have several attributes such as linearity and precision that affect this and a scale that's readable to within 1mg isn't necessarily accurate to within 1mg. ±2mg is a reasonable assumption to make for the kinds of low-cost milligram scales that most people will have. (±mg)

Sa = The expected accuracy of the measurement you'll make for the total amount of solvent being used. (±ml)

Va = The expected accuracy of the measurement you'll make each time for measuring doses of the solution (±ml)

These last two are very simple to work out if you're using something intended for measurement of volumes of liquid. For example, if you measure out your doses using a syringe with a graduated scale on the side, then the measurement you're making involves visually inspecting the height of the liquid in the syringe and determining that it's closest to one of the marks. Each mark is between two others. You can therefore be reasonably sure that the actual volume you've measured is between those values to either side. If your measuring device is marked at each millilitre then your reading of it should be ±1ml. If it has marks indicating the halfway points, then the accuracy would be better - ±0.5ml.

With numbers in mind for all of these things you can work out the best-case range of doses that can be expected from the volumetric solution:

Low: (Dv - Va) * ((W * N) - Wa) / ((N * Dv) + Sa)

High: (Dv + Va) * ((W * N) + Wa) / ((N * Dv) - Sa)

An example:

You've received a 50mg sample the exciting new benzodiazepine analogue Nopeazolam (AKA Swimhypnol). From what you've heard, it's pretty potent so you've decided that the dose you're aiming for is 0.5mg. That's far too small to weigh out your doses. You have a scale that's cheap but decent, which you calibrated recently and believe it to be accurate within 2mg. You've found it easier to measure out single millilitres of solutions you've made in the past than to mess around with smaller amounts and use a syringe marked at each 0.1ml for dosing. You also have a beaker marked at 2.5ml increments which you'll use for measuring out the solvent itself. How accurate could your Nopeazolamepam solution be? Or will you still run the risk of getting dangerously Swimpaired and forgetting who you aren't?

(Dv - Va) * ((W * N) - Wa) / ((N * Dv) + Sa)
(1 - 0.1) * ((0.5 * 100) - 2)) / ((100 * 1) + 2.5) = 0.42mg

(Dv + Va) * ((W * N) + Wa) / ((N * Dv) - Sa)
(1 + 0.1) * ((0.5 * 100) + 2) / ((100 * 1) - 2.5) = 0.59mg

So, given the known limitations affecting the accuracy of the scale, beaker and syringe you're intending to use,
your doses can be expected to fall within the range of 0.42mg to 0.59mg, which seems acceptable, even with something like Nope'lam.

Using this calculation when considering how to make your volumetric solution allows you to check whether the decisions you're making about the number of doses and the volume of each dose make sense or if you'd be better off increasing them for better accuracy. e.g. If you were using 0.5ml doses instead of 1ml doses in the example, your doses would vary between 0.36mg and 0.66mg, which could well be too much uncertainty for you and prompt you to reconsider.

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