Page 122 - Modern Analytical Chemistry

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Chapter 5 Calibrations, Standardizations, and Blank Corrections 105
5 A Calibrating Signals

Signals are measured using equipment or instruments that must be properly cali-
brated if S meas is to be free of determinate errors. Calibration is accomplished
against a standard, adjusting S meas until it agrees with the standard’s known signal.
Several common examples of calibration are discussed here.
When the signal is a measurement of mass, S meas is determined with an analyti-
cal balance. Before a balance can be used, it must be calibrated against a reference
weight meeting standards established by either the National Institute for Standards
and Technology or the American Society for Testing and Materials. With an elec-
tronic balance the sample’s mass is determined by the current required to generate
an upward electromagnetic force counteracting the sample’s downward gravita-
tional force. The balance’s calibration procedure invokes an internally programmed
calibration routine specifying the reference weight to be used. The reference weight
is placed on the balance’s weighing pan, and the relationship between the displace-
ment of the weighing pan and the counteracting current is automatically adjusted.
Calibrating a balance, however, does not eliminate all sources of determinate
error. Due to the buoyancy of air, an object’s weight in air is always lighter than its
weight in vacuum. If there is a difference between the density of the object being
weighed and the density of the weights used to calibrate the balance, then a correc-
1
tion to the object’s weight must be made. An object’s true weight in vacuo, W v , is
related to its weight in air, W a , by the equation
é æ 1 1 ö ù
.
W v = W a ´ ê 1 + ç – ÷ ´0 0012 ú
ë ê è D o D w ø û ú
where D o is the object’s density, D w is the density of the calibration weight, and
0.0012 is the density of air under normal laboratory conditions (all densities are in
3
units of g/cm ). Clearly the greater the difference between D o and D w the more seri-
ous the error in the object’s measured weight.
The buoyancy correction for a solid is small, and frequently ignored. It may be
significant, however, for liquids and gases of low density. This is particularly impor-
tant when calibrating glassware. For example, a volumetric pipet is calibrated by
carefully filling the pipet with water to its calibration mark, dispensing the water
into a tared beaker and determining the mass of water transferred. After correcting
for the buoyancy of air, the density of water is used to calculate the volume of water
dispensed by the pipet.

5
EXAMPLE .1
A 10-mL volumetric pipet was calibrated following the procedure just outlined,
3
using a balance calibrated with brass weights having a density of 8.40 g/cm . At
25 °C the pipet was found to dispense 9.9736 g of water. What is the actual
volume dispensed by the pipet?

SOLUTION
3
At 25 °C the density of water is 0.99705 g/cm . The water’s true weight,
therefore, is
é æ 1 1 ö ù
W v = 9 9736. g ´ ê 1 + ç – 840 ÷ ´0 0012. ú = 9 9842. g
è 0 99705.
.
ë ê ø û ú