Weighing Milligram Quantities in the Laboratory

A hundred milligrams of cadmium metal, weighed on a balance reading to 0.01 mg, carries a standard uncertainty of 0.05 mg. That number comes from a worked example in the EURACHEM/CITAC guide on measurement uncertainty, and it is the honest starting point for any discussion of weighing milligram quantities in the laboratory: the mass is never the number on the display, and the error is rarely where people look for it.

This guide walks the whole path a small quantity of material takes — arrival, weighing, dissolution, storage, labelling, documentation — and attaches published evidence to each step. It is about handling a substance as a laboratory material. It contains no dosing information and no guidance on use in humans, which is outside its scope entirely.

Why weighing milligram quantities in the laboratory goes wrong

A balance reading is the output of a measurement system, not a property of the sample. The EURACHEM/CITAC Guide CG 4, Quantifying Uncertainty in Analytical Measurement, decomposes the weighing step of a calibration-standard preparation into named contributors: for both the tare and the gross weighing, readability, repeatability, and a calibration function whose own sources are the sensitivity of the balance and its linearity.

Two of those deserve attention because they behave differently at small masses.

Readability is the digit resolution, and it is fixed. On a balance resolving 0.01 mg it contributes the same absolute amount whether you weigh 5 mg or 500 mg — which means its relative weight grows by two orders of magnitude across that range.
Linearity is the deviation of the calibration function across the range. The guide notes that sensitivity can be neglected when the mass is taken by difference on the same balance over a very narrow range, but linearity is counted for each of the two weighings.

That is the technical reason for weighing by difference. In the guide’s worked example the 100 mL volumetric flask itself is weighed twice, without and with the purified metal inside, and the sample mass is the difference. The sample never sits on a weighing boat that has to be transferred, so nothing is lost between vessels, and the sensitivity term drops out because both readings are taken at nearly the same load.

The guide also records what it deliberately did not correct for: buoyancy, on the grounds that the weighing results are quoted on the conventional basis for weighing in air and the densities involved were similar. That is a modelling decision, stated openly. It is a good habit to copy — write down the effects you decided to ignore and why, rather than leaving them unmentioned.

There is no universal minimum sample mass that follows from this. What follows is a rule of proportion: the smaller the aliquot, the larger the share of your final concentration that comes from the balance rather than from the chemistry.

Why purity of the starting material changes the concentration before you start

The guide writes the concentration of a prepared standard as a function of three quantities: the mass of material, its purity expressed as a mass fraction, and the volume of the solution. Purity is not a footnote in that equation. It is a multiplier.

The published example uses a high-purity metal with a purity of 0.9999 and a standard uncertainty of 0.000058 on that figure, and arrives at the following budget.

Component	Value	Standard uncertainty	Relative standard uncertainty
Purity of the material	0.9999	0.000058	0.000058
Mass of the material	100.28 mg	0.05 mg	0.0005
Volume of the flask	100.0 mL	0.07 mL	0.0007
Resulting concentration	1002.7 mg/L	0.9 mg/L	0.0009

Note what the table says about a material of that grade: the purity term is the smallest of the three contributions, an order of magnitude below the mass and volume terms. That relationship inverts as purity falls. A batch certified at 99.0 % rather than 99.99 % shifts the central value of your concentration by a full percent — not the uncertainty, the value itself — and no amount of careful pipetting recovers it.

The guide is also explicit that the cleaning procedure supplied by the manufacturer had to be carried out to obtain the purity quoted on the certificate, and that an uncertainty associated with surface contamination has to be added to the certificate value. A certificate describes the material in a defined state, not in whatever state it reaches your bench in.

Where the volumetric step adds error the balance did not

In the same worked example the volume term carries three influences, and it is worth seeing them separated because only one of them is under the operator’s control.

Calibration of the flask. The manufacturer quotes 100 mL ± 0.1 mL measured at 20 °C. The guide observes that this tolerance is given without a confidence level or distribution, so an assumption has to be made before it can enter a budget at all.
Repeatability of filling to the mark. The guide cites filling experiments on a typical 100 mL flask giving a standard deviation of 0.02 mL, used directly as a standard uncertainty.
Temperature. The flask and solution temperatures differ from the temperature at which the flask volume was calibrated.

The temperature term is the one most often forgotten in a laboratory that runs warm. A flask calibrated at 20 °C and filled at 25 °C does not contain its nominal volume of solution, and the discrepancy is systematic rather than random — it does not average out over replicates.

Choosing a stock solvent, and what dimethyl sulfoxide costs you

Dimethyl sulfoxide (DMSO) is the default stock solvent for compound collections because it dissolves a very wide range of organic structures. It also absorbs water from the atmosphere, and the screening literature has quantified what that does.

Semin and colleagues, reporting in the Journal of Biomolecular Screening in 2005, developed near-infrared (NIR) spectroscopy to measure water content in DMSO compound stocks inside polypropylene microtubes, benchmarking it against Karl Fischer titration. They report a correlation coefficient of 0.985 over a range of 1 % to 10 % water in DMSO by weight, and state plainly why the measurement matters: water content affects solubility, degradation and freeze–thaw behaviour.

Cheng and colleagues, in the same journal in 2003, tested the candidate causes of instability for compounds held at 10 mM in DMSO — water, oxygen, freeze/thaw cycling and storage container material — using liquid chromatography with ultraviolet and mass spectrometric detection against an internal standard. Their accelerated study found most compounds stable for 15 weeks at 40 °C, and reached a conclusion worth memorising: water is more important than oxygen in causing compound loss.

Wet DMSO is not automatically fatal, though. Engeloch and colleagues reported in 2008 that a deliberate 90/10 DMSO/water mixture was adopted as the standard storage solvent at Novartis, and that monitoring the purity of 1404 compounds from ongoing medicinal chemistry projects showed 85 % of them stable over a two-year period at 4 °C. The published position is therefore not “water ruins stocks” but “water is a variable you must know the value of”.

Three practical consequences follow for a small laboratory. Keep the solvent bottle closed and consider its open-bottle history part of the experiment. Record which bottle and which lot a stock was made from. Treat the water content of a shared DMSO bottle that has been opened daily for months as unknown rather than as the specification on the label.

How many freeze-thaw cycles a stock solution survives

This question has been studied directly, and the two published designs differ enough that the numbers are not interchangeable.

Kozikowski and colleagues prepared 320 structurally diverse compounds as 20 mM DMSO solutions, stored them at 4 °C under argon in pressurised canisters to simulate a low-humidity environment, and subjected the plates to 25 freeze/thaw cycles — deliberately exposing them to ambient atmosphere after each thaw, to reproduce what happens during normal liquid handling. Compound remaining was quantified every fifth cycle by high-performance liquid chromatography–mass spectrometry with evaporative light-scattering detection, over a seven-week window chosen to limit time-dependent degradation. The stated purpose was to determine the maximum number of cycles compatible with acceptable compound integrity.

Cheng and colleagues ran their freeze/thaw arm differently: freezing at −15 °C and thawing under nitrogen at 25 °C, with two redissolution methods compared, agitation and repeated aspiration/dispense. They report no significant compound loss after eleven cycles under those conditions.

The difference between “exposed to ambient atmosphere after each thaw” and “thawed under nitrogen” is the entire point. The cycle count is not a property of the compound. It is a property of the atmosphere the vial meets on the way back to room temperature.

The operational answer is to remove the variable rather than to budget for it: aliquot a fresh stock into single-use volumes at the moment of preparation, so that no vial is ever thawed twice, and record the cycle count on any vial that is.

What belongs on the label of a milligram vial

Two labels exist on a small container and they answer to different authorities.

The supplier label is regulated. Under Regulation (EC) No 1272/2008 (CLP), Article 29(1) covers packaging so small or so shaped that the full label cannot be applied in the required languages; the label elements may then be carried on fold-out labels, tie-on tags or outer packaging. Annex I section 1.5.1.2 sets the floor for the inner packaging in that case: at least the hazard pictograms, the product identifier, and the name and telephone number of the supplier. Section 1.5.2.1 then addresses packages whose contents do not exceed 125 ml, where certain hazard and precautionary statements may be omitted for the listed hazard categories. A sparse label on a small vial can therefore be fully compliant, and the outer packaging or tag is where the rest of the information lives — which is an argument for not discarding it.

The internal label you write on a prepared stock is unregulated, which is exactly why it fails. A label that reads only “10 mM, 12/03” is unusable six months later. A usable one carries the substance identity, the supplier batch or lot, the solvent and its lot, the actual mass and volume used rather than the nominal ones, the calculated concentration, the date of preparation, the initials of whoever prepared it, and the freeze–thaw count if the vial is not single-use.

The instruction to record actual rather than nominal values is not pedantry. If the balance read 4.83 mg and the protocol called for 5.00 mg, the stock is 3.4 % weaker than its label claims, and an entire dataset can be quietly rescaled by that number.

What to check when the material arrives

Receipt is the cheapest quality gate in the whole chain, because it is the only point at which a discrepancy can still be someone else’s problem.

The safety data sheet that accompanies the shipment has a fixed structure. Annex II to Regulation (EC) No 1907/2006 (REACH), as replaced by Commission Regulation (EU) 2020/878, prescribes sixteen numbered sections, and four of them carry the information that governs how you store and handle a small sample.

Section	Title	What to read it for
7	Handling and storage	Storage conditions and incompatibilities before the vial goes anywhere
8	Exposure controls / personal protection	National exposure limit values applicable in your own Member State, with their legal basis
9	Physical and chemical properties	Properties to cross-check against what the material looks like in the vial
10	Stability and reactivity	Conditions and materials to avoid

Two formal checks take seconds. Annex II requires the date of compilation on the first page, and for a revised sheet a “Revision: (date)” marking on the first page together with an indication of which version it replaces, with the changes brought to the recipient’s attention in Section 16. Annex II also prohibits a specific class of reassurance: statements such as “may be dangerous”, “no health effects”, “safe under most conditions of use” or “harmless” must not be used, nor any statement inconsistent with the classification. A sheet containing one of those phrases is defective on its face and is a reason to query the supplier before opening the container.

Alongside it, the certificate of analysis should identify the batch, name the analytical methods used and carry a date. A bare percentage with no method attached cannot be compared against anything, including the same supplier’s next batch.

Record all of it at receipt: date received, batch, appearance, storage location, who logged it. A stock solution prepared eight months later is only traceable if that entry exists.

Frequently asked questions

How small a sample can an analytical balance weigh reliably?

There is no single figure, because it depends on the balance’s readability, repeatability and linearity rather than on the sample. The useful way to think about it is proportional: readability contributes a fixed absolute amount, so its share of a 5 mg weighing is a hundred times its share of a 500 mg weighing. Establish the operating range for your own instrument rather than assuming one.

Why is weighing by difference used for small samples?

Because it removes two error sources at once. The receiving vessel is weighed empty and then with the sample inside, so nothing is lost transferring material between a weighing boat and a flask. The EURACHEM/CITAC guide also notes that the balance sensitivity term can be neglected when mass is taken by difference on the same balance over a very narrow range.

Does water in DMSO cause compound degradation?

Published screening-repository work says water matters more than oxygen. Cheng and colleagues tested water, oxygen, freeze/thaw cycling and container material as causes of instability for compounds at 10 mM in DMSO and concluded that water is more important than oxygen in causing compound loss. A separate Novartis study nonetheless found 85 % of 1404 compounds stable in a 90/10 DMSO/water mixture over two years at 4 °C.

How many freeze-thaw cycles can a DMSO stock take?

It depends on what the vial is exposed to while thawing, not on a universal cycle count. One published study froze at −15 °C and thawed under nitrogen at 25 °C and reported no significant compound loss after eleven cycles. Another deliberately exposed plates to ambient atmosphere after each of 25 thaws, precisely because that is what happens in routine handling. Single-use aliquots remove the question.

Why does the purity of the starting material affect the final concentration?

Because purity enters the concentration equation as a mass fraction multiplier alongside mass and volume. A material certified at 99.0 % rather than 99.99 % moves the calculated concentration by about one percent, and that is a shift in the value itself, not in its uncertainty. Weighing more carefully does not compensate for it.

What information should a laboratory vial label carry?

Substance identity, supplier batch or lot, solvent and solvent lot, the actual mass and volume used rather than the nominal ones, the calculated concentration, preparation date, preparer’s initials, and the freeze-thaw count if the vial is not single-use. Recording actual rather than nominal values matters: a 4.83 mg weighing against a 5.00 mg protocol makes the stock 3.4 % weaker than its label states.

Is a sparse label on a small vial a compliance problem?

Not necessarily. CLP Article 29(1) covers packaging too small or oddly shaped for a full label, allowing the elements to appear on fold-out labels, tie-on tags or outer packaging, with the inner packaging required to carry at least the hazard pictograms, the product identifier and the supplier’s name and telephone number. Annex I section 1.5.2.1 addresses packages not exceeding 125 ml separately.

What should you check when a chemical shipment arrives?

Read safety data sheet sections 7, 8, 9 and 10 before storing the container, check the date of compilation and any revision marking on the first page, and confirm the certificate of analysis names the batch, the methods and the date of analysis. Then log receipt date, batch, appearance, storage location and the person logging it, because later traceability depends entirely on that record.

References

Research use only. Nonsensia Lab supplies analytical reference standards for laboratory and research applications. This article is published for scientific and educational purposes. It is not medical advice, it does not describe any use in humans, and nothing in it should be read as a recommendation to administer any substance to a person or animal.

Filed under: Laboratory Practice

Nonsensia Lab supplies the compounds discussed in this guide as analytical reference standards for laboratory and research use.

Working With Milligram Quantities: A Practical Laboratory Guide