Weighing buoyancy effects

The table which follows gives the values of k (buoyancy reduction factor), which is the correction necessary because of the buoyant effect of the air upon the object weighed the table is computed for air with the density of 0.0012 m is the weight in grams of the object when weighed in air weight of object reduced to in vacuo = m + m/1000. 

Buoyant Effect of Air. Weighing operations performed m vacuo are not affected by buoyancy forces. An object in air, however, is subject to a buoyancy force that is equal and opposite to the gravitational force on the mass of air the object displaces (10). If the equal arm balance of Figure 1 is in balance with a test weight of mass, in one pan, and material of mass, m, in the other, m = m if they have the same density. If the densities are different, then the buoyancy forces acting on each pan affect the result. Taking moments about the center pivot point gives... 

Air buoyancy, effect on weighing, 26 242 Air classification, of wheat flour, 26 282 Air cleaners, to improve indoor air quality, 1 820, 831-834... 

In each case, the effective mass is the true mass (M or Mw, corresponding to weighing in vacuo) minus the buoyance (fl0for object, and for weights) due to the mass of the air displaced. The true mass of the weights (Mw) is always known because this information is supplied by the manufacturer. Equation 7-4 can be rewritten as... 

Corrections required when weighing volumetric flasks are somewhat different than straight volumetric readings. Both single- and double-pan balances have four common parameters which can affect the accurate weighing of liquids, but the single-pan balance has one separate parameter of its own. The common parameters are water density, glass expansion, and the buoyancy effect. 

The differences in the buoyancy effect (based on Archimedes principle) of materials in air at different barometric pressures is not as great as the buoyancy differences in water versus air, but it still exists and can affect accurate weighings. 

The problem is more easily explained by examining what happens when you place something in water (because water weighs more than air and provides a greater buoyancy effect, its effects are more dramatic). If you put a cube of metal in water, it sinks to the bottom of the container. That cube weighs less in the water than it did in air, by an amount equal to the weight of the water it displaced. On the other hand, if you put a similar-sized block of wood in the water, it would float because the amount of water that the wood displaces weighs more than the wood,... 

There are only two occasions where measured weight equals true mass, when k = 1. This occasion occurs when measurements are made in a vacuum or the density of a sample is equal to the density of the mass standard. Fortunately, the greatest differences only occur when an object s density is particularly low (0.1% for density 1.0 g/cm3 and about 0.3% for density = 0.4 g/cm3). In most situations, the effect of air buoyancy is significantly smaller than the tolerance of the analytical balance. The effects of varying densities (of objects being weighed) and varying air densities are shown in Table 2.22. 

Buoyancy Effect When a weighing is to be performed with an accuracy of 0.1% or better, the buoyancy effect should not be neglected. The equation to be used in correcting for this effect is... 

Air buoyancy - this affects the weight of everything that has a different density. Only in very specialist work is any allowance made for the air buoyancy effect on weighing, so for practical purposes this inherent error is universally accepted in analytical chemistry laboratories. 

Figure 2-5 Effect of buoyancy on weighing data (density of weights = 8 g/cm ). Plot of relative error as a function of the density of the object weighed.

The consequences of Equation 2-1 are shown in Figure 2-5, in which the relative error due to buoyancy is plotted against the density of objects weighed in air against stainless steel masses. Note that this error is less than 0.1 % for objects that have a density of 2 g/cm or greater. It is thus seldom necessary to apply a correction to the mass of most solids. The same cannot be said for low-density solids, liquids, or gases, however, for these, the effects of buoyancy are significant and a correction must be applied. 

A bottle weighed 7.6500 g empty and 9.9700 g after introduction of an organic liquid with a density of 0.92 g/cm. The balance was equipped with stainless steel masses d = 8.0 g/cm- ). Correct the mass of the sample for the effects of buoyancy. 

Of course the preceding thought-experiment, in which calibration of the balance is conducted in a vacuum, is an unrealistic example of the buoyancy effect. Consider now a realistic case where the calibration of the balance and the weighing of the nnknown object are both conducted at atmospheric pressure now the variation arises because the densities (and thus the volumes) of the standard mass and the unknown are different. The buoyancy force on the steel standard is stiU the same (equivalent to the gravitational force on 1.5 x 10 g), but in this case this buoyancy force is accounted for in the calibration procedure. Assume that the object to be weighed is a powdered or liquid chemical with density 1 g.cm and also of true mass 10.0000g, so its volume is lO.Ocm the mass of air that it displaces is thus 12 x 10 g. In other words, the upward (buoyancy) force on the sample is greater than that on the steel standard used to calibrate the balance by an amount equivalent to a mass of (12 — 1.5 = 10.5) X 10 g, and the indicated mass on... 

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