TECHNICAL INFORMATION
395
Calibration of Volumetric Ware
TECHNICAL INFO. CALCULATION FROM APPARENT WEIGHT CALIBRATION WITH WATER
To obtain it, the nominal capacity can be used for V T , without introducing an appreciable error.
The true capacity of a glass vessel at a standard temperature can be obtained from the apparent weight of the liquid container or delivered at any other temperature. To do this, it is necessary to take into account four factors for single pan balances having built in weights — the buoyant effect of the air on the liquid and weights; the change of density of the liquid; the change of volume of the glass with temperature; and the apparent mass of the built-in weights as compared to their true mass. Details for this deviation of these corrective factors are covered in NIST IR 74-461, “The Calibration of Small Volumetric Laboratory Glassware”. Buoyant Effect When a body is weighed in air, it does not weigh the same as it would in a vacuum, because both the weights and the body itself are buoyed up by the air. This is in accordance with the principle of Archimedes, which states that any body immersed in a gas or a liquid is pushed upward by a force equal to the weight of an equal volume of the gas or liquid. The density of air varies according to the height above sea level and even in any one place from time to time depending on the weather. As a result, the apparent weight of a volume of water also may vary due to changes in the forces acting on it and on the weights. In order to be able to compare weighings, it is necessary to take into account changes in the density of air. The best solution is to calculate the net upward thrust at the time of weighing and add it to the apparent weight. The result is the true weight and is the same as if the weighing actually had been made in a vacuum (“in vacuo”). Since this establishes all weighings on a common basis, the results of several weighings at different times or places can be compared. For very accurate calibration of volumetric glassware, the actual density of the air at the time of weighing is determined. However, if it is assumed that the barometer reading is 760 mm, the relative humidity is 50%, and the carbon dioxide in the air is 0.04% by volume, then densities of air for various temperatures calculated on this basis will be sufficiently accurate for most purposes. Further assumptions usually made are that the air and the liquid are at the same temperature and that weighings are made with brass weights having a density of 8.4 grams per mL. The difference between the mass and the apparent weight of one mL of water is called the buoyancy constant. This constant multiplied by the volume of water expressed in milliliters is the buoyancy correction, and it must be added to the apparent weight of a volume of water to get the true mass of the water. The exact volume may not be known, but the use of the approximate or nominal value will not introduce any significant error. Change of Density of the Water The volume of a liquid at any temperature is equal to its mass divided by the mass of one mL of the liquid at that temperature. The maximum weight of one mL of water is one gram at 4 °C. At all other temperatures water is lighter, and, consequently, athe volume is a larger number than the mass. The difference between volume and mass for one mL at any temperature is equal to one minus the density at that temperature. If this difference is multiplied by the nominal volume of water, a density correction is obtained which can be added to the mass of the water to give the actual volume of the glass vessel at the temperature of weighing. Here, too, the nominal volume can be used to determine the correction. Change in Volume of Glass Glass also changes volume with temperature change. To find the capacity of a glass vessel at the standard temperature from its capacity at the temperature of weighing, use the following formula:
Apparent Mass of Built-In Weights When, under specified ambient conditions, an unknown object exerts the same force on a balance as the mass of a specified hypothetical reference material, the object is said to have an apparent mass versus the reference material. The specified ambient conditions are 1) temperature = 20 °C, and 2) air density = 0.0012 g/cm 3 . The hypothetical reference material is completely specified by its density at 20 °C. For the older apparent mass scale, this specified density at 20 °C, D 20 is 8.3909 g/cm 3 , and for the more recent scale, 8.0. (Quotation from NIST IR 74-461.)
CORRECTION TABLES FOR 33 EXPANSION BOROSILICATE GLASS WHEN SINGLE PAN BALANCES ARE USED
Tables 1, 2, & 3 on page 397 give the sum of all four corrections — buoyant effect, water density, glass expansion, and apparent mass of built-in weights. Table 1 is to be used for KIMAX® apparatus, made of 33 expansion borosilicate glass (ASTM E- 438, Type I Class A); Table 2 is for apparatus made of Kimble® soda lime glass (ASTM E438, Type II); and Table 3 is for apparatus made of Kimble® 51 expansion borosilicate glass (ASTM E438, Type I, Class B). The example below illustrates the use of the Tables. a) Nominal Capacity of vessel (33 expansion borosilicate glass) = 25 mL b) Temperature of weighing = 22.5 °C c) Barometric Pressure of weighing = 760 mm Hg. d) Weight recorded on balance before filling receiver = 28.841 g. e) Weight recorded on balance after filling receiver = 53.761 g. f) Apparent or hypothetical weight of water at 22.5 °C and 760 mm Hg (e – d) = 24.920 g. g) Corrective factor at 22.5 °C and 760 mm Hg from Table 1 1.00327 + 1.00349 = 1.00338 g. 2 h) Volume of vessel at 20 °C and 760 mm Hg. (f x g) = 25.004 mL
ERRORS CAUSED BY USING TABLES 1, 2, & 3 ON PAGE 397 WITHOUT CORRECTING FOR ACTUAL CONDITIONS
The size of errors introduced into calibrations by ignoring actual air conditions and glass expansion is indicated below.
Variation in Density of the Air TEMPERATURE. For each 1 °C difference between air and water temperatures, the error is to 0.004 mL per liter. Volumes will be too large when the air is hotter than the water, and vice versa. PRESSURE. For each 10 mm that the barometer departs from 760 mm, the error amounts to 0.014 mL per liter. Volumes will be too small if the actual pressure is greater than 760 mm, and vice versa. RELATIVE HUMIDITY. If the relative humidity differs from 50%, errors of 0.001 to 0.004 mL per liter may occur, depending on the actual humidity and temperature. Expansion of Glass For each 0.000001 change in the cubical coefficient of expansion, the change in corrections amounts to 0.001 mL liter/1 °C. The effect of this on the calculated volume at 20 °C is shown in Table 1.
V T = V 20 (1 + α (T T – T 20 )
Where V 20 = capacity at standard T 20 , V T = capacity at temperature of weighing T T , and α = cubical coefficient of expansion of the glass. 1 + α (T T – T 20 ) = the temperature correction of the glass vessel.
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