The Balance and the Report
You are preparing a certificate of analysis for a powder seizure. The analytical balance in your lab has a readability of 0.01 g and a calibration check that morning passed within tolerance. You weigh the powder three times: 5.02 g, 5.01 g, and 5.03 g. The balance's calibration certificate lists an expanded uncertainty of ±0.02 g at this load. A colleague's draft report states the net weight as '5.020 g' and lists purity as '98.6%' from a single injection. The defense will scrutinize significant figures and uncertainty.
1. What net weight and uncertainty should appear on the certificate, and why?
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The three readings average 5.02 g; the balance readability is 0.01 g, so reporting to the thousandth (5.020 g) overstates precision. Report 5.02 g ± 0.02 g (expanded uncertainty from the calibration certificate), matching the instrument's stated uncertainty. The replicate spread (0.02 g) is consistent with that uncertainty. Significant figures should reflect the least precise component - here 0.01 g readability and 0.02 g expanded uncertainty - so two decimals is appropriate.
2. The draft reports 98.6% purity from a single injection. What is wrong, and what should the report say?
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A single injection gives no estimate of repeatability; 98.6% to one decimal implies precision the data do not support. The report should be based on replicate injections (e.g., triplicate) with a mean and standard deviation, or the result should be reported with an explicit note that n=1 and the figure is an estimate. Also state the method's validated range and LOQ. If only one injection exists, report the value with a caveat, not as a definitive purity, and flag it for re-analysis before the certificate is finalized.