2.4Weight and Mass

cation of four classes was devised by the International Organization of Legal Metrology (OIML), and they are shown in Table 2.21.

Balances can be calibrated or verified for accuracy with special weights, called calibrated weights, whose specific mass is known. Calibrated weights* vary in quality and tolerance. They are classified by type, grade, and tolerance.^All calibrated weights are compared directly or indirectly to the international prototype one-kilogram mass to verify their accuracy.

2.4.2 Weight Versus Mass Versus Density

It is fair to say that an object weighing a ton is heavy and that few, if any, people could move or lift it. However, on the moon the same object would weigh only a bit over 300 lb—although the average person would still be unable to move the object. If we were on the space shuttle in a free-fall environment, anyone could move the object around with relative ease. When we weigh an object, we are measuring its inertia to Earth's gravitational pull. That measurement is its weight, not its mass. The weight of an object, not its mass, will change depending upon its inertia.

Unlike weight, which varies relative to its inertia (such as gravity), mass is an inherent and constant characteristic of any object. In any given gravitational environment, an object with a lot of material (mass) will weigh more than an object of the same type, but less material. Because of this quality, we can make calculations of, and about, an object's mass from its gravitational weighing.

Density is not directly related to mass or weight, but is calculated from an object's weight divided by its volume (g/m3). For example, a large object of little mass (such as foam rubber) is considered to have little density. On the other hand, a small object of tremendous mass (such as a neutron star) has tremendous density. Density refers to the amount of space ("volume") a given amount of mass

Table 2.21 Classifications of Weighing Equipment9, 10

' n = number of intervals.

'Calibrated weights are verified to weigh what they say they do within a given tolerance. The smaller the tolerance of a calibrated weight, the better the quality and the more expensive it will be.

trThese parameters are discussed further in the section on calibrated weights (see Sec. 2.4.13).

preventing the wood from sinking. The same phenomena occurs in air, which is why helium balloons rise and wood balloons fall.

Even if an object's density and size change, its mass does not. Thus, it is possible for two objects to have the same mass but weigh different amounts due to the effects of air buoyancy caused by the weight of air. This principle can be demonstrated by taking a calibrated weight whose density is 8.0 g/cm3 and weight (in air) is 100.000 g, then using it to weigh an equal weight of pure water whose density is 1.0 g/cm3. Because their densities are different, they will occupy different volumes of air: Their volumes are 12.5 cm3 and 100 cm3, respectively. If you were to weigh each object in a vacuum to eliminate the air buoyancy factor,* the calibrated weight would now weigh 100.015 g and the pure water would now weigh 100.120 g.

Factors that affect buoyancy are the density of a sample, ambient air pressure, and relative humidity. Thus, a barometer and humidity indicator should be located within any balance room where highly accurate readings are required. The counterbalance weights within single-pan balances are also affected by air buoyancy, but in equal amounts to the sample, so they should cancel each other out. The exact amount of the buoyancy effect varies depending on the density of the material being weighed and the density of the air at the time of weighing. This phenomenon was studied in detail by Schoonover and Jones,11 and by Kupper.12

The formula for converting a weighing result to true mass is given in Eq. (2.1):

'"if

where m = mass of the sample

M = weighing result, i.e., the counterbalancing steel mass

da = air density at time of weighing1^

D = density of mass standard, normally 8.0 g/cm3

d = density of sample

k = ratio of mass to weighing result for the sample

To calculate the density of the air, use the formula in Eq. (2.2):

where T = Temperature in °K (Centigrade plus 273.15)

B = Barometer reading in millimeters of mercury

'instead of making the weighings in a vacuum, you can also make use of Eq. (2.1) and Eq. (2.2). +For the density of moist air, see the Handbook of Chemistry and Physics, The Chemical Rubber Company, published annually.

122 Measurement

There are only two occasions where measured weight equals true mass, when it = 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.

One approach to avoiding the problem of air buoyancy is to weigh an object in a vacuum (known as "weight in vacuo"). Such readings provide an object's true mass as opposed to its apparent mass. There are a variety of vacuum balances made precisely for this purpose. However, vacuum balances are expensive, require expensive peripheral equipment (such as vacuum systems), and are neither fast nor efficient to use.

2.4.4 Accuracy, Precision, and Other Balance Limitations

The amount of accuracy required in a balance, like most things in the lab, depends the balancing of your needs versus the capacities of your pocketbook. You do not need great accuracy if all you are doing is weighing letters. On the other hand, weighing volumetric flasks to calibrate volume requires tremendous accuracy. Not only is the cost greater for a more accurate balance, but the support equipment and personnel for the maintenance of such equipment are also greater. When analyzing the different attributes and characteristics that help to define the quality and capabilities of balances, many different terms are used. The following terms (and concepts) are used to describe various features of all balances:

The greater the accuracy of a balance, the closer the balance will read the nominal weight* of a calibration weight. If the calibration weight reads 10 mg, the balance should read 10 mg. If, for example, the balance reads 10.5 mg, it has less than desirable accuracy, and if it reads 12 mg, it has poor accuracy.

The precision of a balance is related to how well it can repeatedly indicate the same weight over a series of identical weighings under similar environmental conditions. Precision is not a measure of how accurately a scale can make a single weight reading. The index of precision is the standard deviation for a collection of readings. If the index of precision is greater than the readability of the balance, accuracy is significantly jeopardized.

Readability refers to the smallest measurement that a balance can indicate and that can be read by an operator when the balance is being used as intended. Generally, triple-beam balances have a readability of ±0.1 g, centigram balances have a readability of ±0.01 g, and analytical balances have a readability of ±0.0001 g.

"The nominal weight of a calibrated mass is the calibration that is printed on, or stamped into, its surface.