Balance drifting, or reading below its minimum weighable mass

Lifted from measurement and uncertainty, which works the arithmetic below and states plainly what the course could not source.

What you see

Two different faults that present as one complaint — “the balance will not give me a number”.

Drift. The display creeps while you watch it, or settles and then moves again, or jumps when you touch the bench. Repeated weighings of the same object disagree.

Below the minimum weighable mass. The display is perfectly steady and the number is meaningless, because the quantity is too small for the instrument. This one does not look like a fault at all, which is what makes it the more dangerous of the two.

Likely causes

1. A draught, an unlevel or unstable surface, a leaning elbow, or a balance standing on a fridge or a drainer.
2. Static, which makes light powders creep and is worst in dry air and with plastic weighing vessels.
3. A quantity below what the balance can resolve. Weighing 0.20 g of phenidone on a 0.01 g balance is the standard case in this course.

What is happening: the chemistry and physics

Three properties get called by one word, and separating them is most of the diagnosis.

• Resolution is the smallest change the display can show. That is a fact about the display.
• Repeatability is how closely repeated weighings of the same object agree. You can measure this yourself in five minutes.
• Accuracy is how close the reading is to the real mass. You cannot measure it at all without a mass you already trust.

Drift is a failure of repeatability — a random error, scattered about the right answer, reduced by better technique or averaged down by repeating. A balance that reads half a gram heavy every time is a systematic error instead, repeatable and repeatably wrong, found only by comparison with a reference. Only one of the two is fixed by buying a better instrument.

🧮The same balance, three very different measurements

Take the convention that the last displayed digit is uncertain, so a 0.01 g balance carries a nominal ±0.01 g.

• 100 g of sodium sulfite — 0.01 / 100 = 0.01 per cent. Irrelevant; your spatula carries away more.
• 2.00 g of metol — 0.01 / 2.00 = 0.5 per cent. Comfortable.
• 0.20 g of phenidone — 0.01 / 0.20 = 5 per cent, and that is the floor from the display alone, before repeatability, drift, draughts or static are counted.

A kitchen scale reading to 1 g, used to weigh 0.5 g, gives 200 per cent. That is not a measurement with a large error in it. It is not a measurement.

!What the course will not quote

Laboratory practice expresses the second fault as a minimum weighable quantity derived from a balance’s repeatability rather than from its display. This course could not read a manufacturer’s repeatability or linearity specification for the inexpensive balances sold to photographers, and therefore quotes no minimum weighable mass and no rule of thumb. The arithmetic above is a floor - your balance is at least this uncertain and probably worse.

Diagnostic questions

• Weigh the same object ten times, lifting it off the pan between weighings. What is the spread? That number is your balance’s repeatability, and it is about your balance rather than about balances in general.
• Is the error scattered or one-sided? Scattered is drift and technique; one-sided is a systematic error and needs a reference mass.
• Does the reading move when you touch the bench, lean on it, or open a door? That is the environment, not the instrument.
• What fraction of the target quantity is the balance’s resolution? If it is more than a per cent or so, stop, because no amount of care with the pan will rescue it.

Corrective action

For drift — level, still surface; let the balance settle before zeroing; tare with the empty vessel on the pan; add the solid slowly, because you cannot take it back and scraping some out again puts it into the air; and weigh by difference for anything hygroscopic, expensive or static-prone, which also defeats the creeping powder.

For a quantity below the balance’s reach, the answer is not care but arithmetic. Weigh a larger mass of the substance into a stock solution and measure out a portion of that solution, which moves the precision from your balance to your pipette. The alternative is a 0.001 g balance for the small ingredients.

Prevention

Run the balance check in the balance and thermometer procedure before a session that depends on a small weighing, and record its result rather than remembering it.

Transfer quantitatively — rinse the weighing vessel into the mixing vessel with some of the water the recipe already calls for, because what stays in the beaker is missing from the solution.

Write the reading down before you do anything else — the actual reading, not the number you were aiming at. “2.03 g” and “2 g” are different records, and only one of them lets you explain a result later.