The influence of variations in atmospheric pressure on the uncertainty budget of weighing results

The various assays in quantitative analytical chemistry always include mass determinations, along with other operations, and the same is true for the uncertainty budget of such a procedure. In order to obtain an accurate weighing result it is necessary to consider air buoyancy, which depends on, besides other parameters, atmospheric pressure. In contrast to air temperature and humidity, it is not possible to control the atmospheric pressure in a conventional laboratory. Therefore, it can be necessary to consider the uncertainty of pressure in uncertainty calculations of weighing operations, depending on the mass and density of the weighed object. The theoretical relationship between pressure variations and obtained weight value are derived. Experimental confirmation was obtained on the one hand by the mass determination of five Pyrex glass bottles over a period of 6 months; these are objects with a lower density than the reference weights of the balance, thus showing a negative dependence of weight value on atmospheric pressure. On the other hand, a tungsten cylinder was weighed over several weeks; this high-density object has a positive dependence. In both cases the experimental slopes agreed with the theoretical values. The consequences on the uncertainty budget of a weighing operation are remarkable: the total uncertainty of the mass determination of a 90 g glass bottle is 0.3 mg whereas it is 4 μg for a 4.6 g tungsten cylinder. The contributions originating from the pressure variation alone are 0.3 mg and 3.5 μg, respectively, i.e., the pressure uncertainty dominates and is much more important than the uncertainty contributions of balance repeatability and linearity.