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264 Modern Analytical Chemistry

applied across a quartz crystal, an oscillatory vibrational motion is induced in the
crystal. Every quartz crystal vibrates at a characteristic resonant frequency that is a
function of the crystal’s properties, including the mass per unit area of any material
coated on the crystal’s surface. The change in mass following adsorption, absorption,
or binding of the analyte, therefore, can be determined by monitoring the change in
the quartz crystal’s characteristic resonant frequency. The exact relationship between
the change in frequency and mass is determined by a calibration curve.

8D.2 Quantitative Applications
Particulate gravimetry is commonly encountered in the environmental analysis
of water, air, and soil samples. The analysis for suspended solids in water samples, for
example, is accomplished by filtering an appropriate volume of a well-mixed sample
through a glass fiber filter and drying the filter to constant weight at 103–105 °C.
Microbiological testing of water also is accomplished by particulate gravimetry.
For example, in the analysis for coliform bacteria an appropriate volume of sample
is passed through a sterilized 0.45-mm membrane filter. The filter is then placed on
a sterilized absorbent pad saturated with a culturing medium and incubated for
22–24 h at 35 ±0.5 °C. Coliform bacteria are identified by the presence of individual
bacterial colonies that form during the incubation period. As with qualitative appli-
cations of precipitation gravimetry, the signal in this case is a visual observation
rather than a measurement of mass.
Total airborne particulates are determined using a high-volume air sampler
equipped with either cellulose fiber or glass fiber filters. Samples taken from urban
environments require approximately 1 h of sampling time, but samples from rural
environments require substantially longer times.
Grain size distributions for sediments and soils are used to determine the
amount of sand, silt, and clay present in a sample. For example, a grain size of 2 mm
serves as a boundary between gravel and sand. Grain size boundaries for sand–silt
and silt–clay are given as 1/16 mm and 1/256 mm, respectively.
Several standard methods for the quantitative analysis of food samples are
based on measuring the sample’s mass following a selective solvent extraction. For
example, the crude fat content in chocolate can be determined by extracting with
ether for 16 h in a Soxhlet extractor. After the extraction is complete, the ether is al-
lowed to evaporate, and the residue is weighed after drying at 100 °C. This analysis
has also been accomplished indirectly by weighing a sample before and after ex-
tracting with supercritical CO 2.
Quartz crystal microbalances equipped with thin-film polymer or chemical
coatings have found numerous quantitative applications in environmental analysis.
Methods have been reported for the analysis of a variety of gaseous pollutants, in-
cluding ammonia, hydrogen sulfide, ozone, sulfur dioxide, and mercury. 10 Bio-
chemical particulate gravimetric sensors also have been developed. For example, a
piezoelectric immunosensor has been developed that shows a high selectivity for
human serum albumin and is capable of detecting microgram quantities. 11

Quantitative Calculations The result of a quantitative analysis by particulate
gravimetry is just the ratio, using appropriate units, of the amount of analyte to the
amount of sample.