Page 199 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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Encyclopedia of Physical Science and Technology EN007C-340 July 10, 2001 14:45

810 Infrared Spectroscopy

for the “zero sample” condition and use that for the back- Another ratio method is the internal standard method. In
ground point. This can be used but is somewhat subjective this method a known amount of an internal standard mate-
and may not be very reproducible. An alternative is to use rial is added to the sample mixture. The internal standard is
a line tangent to the spectrum at the band wings or even chosen so that it has no absorption at the analytical wave-
connecting some more distant points. The more closely length for the sample and vice versa. Again from Beer’s
the line approaches the true background, the better, but it Law, the absorbance ratio is
is not necessary that the tangent line and the true back-
A ac a s A
ground coincide exactly. A consistent base line construc- = and c = c s (22)
A s a s c s aA s
tion should yield a reproducible measured absorbance for
a given concentration, and the absorbance should vary where the subscript s denotes the internal standard. Here
linearly with concentration. Again, this is calibrated with the internal standard concentration c s is known, and the
standards. One of the advantages of the method is that it constant ratio a s /a can be determined from one sample of
can reduce or eliminate a correction for the finite back- known concentration, after which the concentration can
ground absorption of the solvent or major component. be calculated from the absorbance ratio.
Some care should be taken in choosing the tangent points
for the base line. These points should not be too sensitive
G. Gas State Analysis
to concentration variations of other components that may
be present. In a quantitative analysis involving gases, the concentra-
tion term c in Beer’s law is replaced by the pressure or
partial pressure p of the gas being measured. Beer’slaw
F. Ratio Methods reads

In most solid-state spectra, the sample film thickness and A = abp. (23)
the amount of sample in a KBr disk or a Nujol mull are
In this case, the measurement of the background ab-
not known. It is still possible to do quantitative analysis by
sorbance is usually that of the evacuated cell or the cell
the ratio method. This is based on the fact that, in a given
filled with nonabsorbing gas such as nitrogen. There is a
mixture, the absorbance ratio of any two bands in one
complication in the use of Beer’s law in the vapor phase
spectrum should be independent of the sample thickness.
that is called pressure broadening. Not only is the ab-
Consider a two-component mixture, each component of
sorbance of a gaseous component a function of its partial
which has an analytical band with no interference from
pressure; it is also a function of the total pressure. This
the other component. The absorbance ratio for the two
means that the absorbance of a gaseous component with a
analytical bands is, from Beer’slaw,
fixed partial pressure can be changed by introducing an-
other completely nonabsorbing gas such as nitrogen. The
A 1 a 1 b 1 c 1 A 1 a 1 c 1
= or = . (19)
A 2 a 2 b 2 c 2 A 2 a 2 c 2 rotational fine structures of gas-phase bands are broadened
by collisions between the molecules of the component be-
The b values are identical and cancel since the absorbances
ing measured, and other gas molecules and collisions vary
aremeasuredforthesamesamplepreparation.Sincea 1 /a 2
infrequencyandseverityasthepressureincreases.Forthis
is a constant, the absorbance ratio is proportional to the
reason the total pressure is often kept constant in a quanti-
concentration ratio. One can also write
tative analysis of gases. The desired partial pressure of the
100 gas to be analyzed is introduced into an evacuated cell.
c 1 = (20) Then the total pressure is increased to a standard value
1 + c 2 /c 1
such as 760 mm Hg by introducing nitrogen, for example,
which, when multiplied out simply states that the sum of before measuring the absorbance.
the two concentrations c 1 and c 2 is 100%. In this equa-
tion the ratio c 2 /c 1 is replaced by its equivalent from the
previous equation to give H. Multicomponent Analysis
In the most general case for quantitative analysis, one
100
c 1 = . (21) wishes to measure several components of the mixture and
1 + (a 1 /a 2 )(A 2 /A 1 )
there are no isolated wave numbers. This means that, at
The a 1 /a 2 ratio is a constant that can be determined by the best analytical wave number for one component, the
measuring A 2 /A 1 for one standard of known concentra- other components have finite absorption that interferes
tion. Once a 1 /a 2 is evaluated, the concentration c 1 of an with the measurement. Fortunately, Beer’s law is addi-
unknown can be calculated from the absorbance ratio. tive, which means that at any given wave number in the