An analytical balance with a readability of 0.1 mg appears suitable for weighing almost any quantity accurately. That is not the case. Anyone weighing out 2 mg on such a balance may have a relative uncertainty of more than 5%, while the same balance stays below 0.1% at 500 mg. The concept of minimum weight makes that difference concrete and testable.
In this article we explain what minimum weight is, how it relates to repeatability and readability, how to calculate it and which environmental influences determine it. The data you need come from a calibration of the analytical balance, provided it has been tailored to this purpose.
What is minimum weight?
The minimum weight is the smallest net quantity you can weigh out on a balance while the relative measurement uncertainty remains within your own requirement. You set that requirement yourself, for example 1% for a simple determination or 0.1% for a critical weighing of a reference substance.
The principle is simple. At small loads, a large part of a balance's uncertainty is virtually constant: a fixed number of tenths of a milligram, regardless of how much you weigh. For a large sample this uncertainty is relatively small; for a small sample it is relatively large. Somewhere there is the point at which the relative uncertainty is exactly equal to your requirement. That point is the minimum weight.
Do not confuse this with Min on the type plate of a legally verified balance. Min is a legal term that belongs to the accuracy class. The minimum weight is a user term, based on the actual performance of the balance at your workplace and on your own requirement. The two values can differ considerably.
Repeatability and readability
At small loads, repeatability is usually the main source of uncertainty. It is expressed as the standard deviation s of a series of weighings of the same weight, and is determined during a calibration according to EURAMET cg-18. For the minimum weight, a repeatability test with a small test weight, close to the quantities you actually weigh, is the most representative.
The readability d is the smallest step on the display. It forms a lower limit: a balance cannot show differences smaller than d. If the measured standard deviation is very small, smaller than what the readability can actually distinguish, a lower limit derived from d is often used in practice. This prevents an overly optimistic minimum weight.
Other contributions, such as the indication error, eccentricity and the uncertainty of the weights, increase with the load. These mainly determine the uncertainty at larger quantities and usually play a smaller role in the minimum weight.
Worked example
In the simplest approach, in which only repeatability is taken into account:
m_min = k · s / U_rel
Here k is the coverage factor, s the standard deviation from the repeatability test and U_rel the required relative expanded uncertainty, written as a decimal.
Take an analytical balance with a readability of 0.1 mg. During calibration, a repeatability of s = 0.1 mg was measured. You want a relative uncertainty of no more than 1%, with coverage factor k = 2:
- k · s = 2 × 0.1 mg = 0.2 mg
- U_rel = 1% = 0.01
- m_min = 0.2 mg / 0.01 = 20 mg
As a check: for a sample of 20 mg, the expanded uncertainty is 0.2 mg, and 0.2 mg divided by 20 mg is exactly 1%. If you weigh out more, the relative uncertainty becomes smaller. If you weigh out less, it becomes larger.
The requirement and the repeatability have a large effect, as the table shows:
| Repeatability s | Minimum weight at 1% requirement (k = 2) | Minimum weight at 0.1% requirement (k = 2) |
|---|---|---|
| 0.05 mg | 10 mg | 100 mg |
| 0.1 mg | 20 mg | 200 mg |
| 0.2 mg | 40 mg | 400 mg |
In practice, apply a safety margin. The repeatability at calibration was measured under the conditions at that moment. In daily use, with different users and under varying conditions, the spread can be larger. Many laboratories therefore deliberately weigh well above the calculated minimum weight, for example by a factor of two or more.
Some pharmacopoeias set requirements for the repeatability and accuracy of balances for quantitative determinations. If you work according to such a requirement, check for yourself which requirements and which calculation method apply, and communicate this before the calibration so that the measuring points and the reporting are aligned with it.
Environmental influences
The minimum weight is not a fixed property of a balance model. It depends strongly on where the balance is placed. The same balance can have a much smaller minimum weight in a quiet weighing room than next to a fume cupboard. The main influences:
- Draughts and air flow: air-conditioning outlets, extraction, doors and colleagues walking past cause small forces on the weighing pan. Keep the draught shield closed during weighing and place the balance out of the air flow.
- Vibrations: centrifuges, pumps, lifts and traffic transmit small movements through the floor and table. You see this as an unsteady indication and a larger spread.
- Static charge: plastic weighing boats, powders and dry air can become electrostatically charged. The indication then keeps drifting slowly. An ioniser, antistatic or metal weighing boats and sufficient humidity help.
- Temperature: a sample or vessel that is warmer or colder than the room causes air flow in the weighing chamber. Let objects come to room temperature and keep sunlight and heat sources away from the balance.
- Handling: hands in the weighing chamber, a boat that is not centred or reading too quickly all add spread.
Air buoyancy also plays a role in fine weighings, especially if the sample and the weights have very different densities. Read more in conventional mass and air buoyancy.
The weighing table and the set-up
An analytical balance belongs on a stable, low-vibration surface. An ordinary laboratory bench often flexes with the user's movements and transmits vibrations from the floor. A heavy weighing table, or a table with a separate, damped top for the balance, limits that influence. A design in which the user can lean on the worktop without the balance top moving is convenient.
Preferably place the weighing table against a solid wall or in a corner, away from doors, walkways and air outlets. Level the balance after positioning and give it sufficient warm-up time. If the balance is moved, the conditions change and with them the repeatability; have it checked again. Suitable surfaces can be found among our calibration tables.
How MASSLAB helps you
MASSLAB calibrates analytical balances and precision balances according to EURAMET cg-18, preferably in their own location, because the environment counts in the result. If you tell us in advance your requirement for the relative uncertainty and the smallest quantities you weigh, we tailor the repeatability test and the reporting of the uncertainty in use accordingly. That way, the certificate shows whether your balance is suitable at your workplace. Between calibrations, you monitor the balance with a check weight; read about this in checking your scale between calibrations. More information can be found at laboratory balance calibration.