Page:NIOSH Manual of Analytical Methods - 3800.pdf/24

ORGANIC AND INORGANIC GASES by FTIR Spectrometry: METHOD 3800, Issue 1, dated 15 March 2003 - Page 24 of 47

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C6. Beer's Law

Figure C6. Double Beam Absorbance Spectrum of Water

The absorbance spectrum of a sample gas is determined from single beam spectra of an infrared-transparent gas (the background spectrum) and the sample gas (see Section 5). The fundamental relationship connecting the absorbance spectrum of a sample gas to the concentrations of the compounds comprising the sample is referred to as Beer’s Law. This relationship can be written as

$A_{1}=\sum _{j=1}^{M}{L_{S}}{a_{ij}}{c_{j}}$ (Equation C1) where

$i$	=	an index labeling the frequencies of the observed absorbance values in the sample’s absorbance spectrum.
$A_{i}$	=	the observed absorbance of a sample at the ith wavenumber (abs).
$L_{S}$	=	the sample absorption pathlength (meters).
$j$	=	an index labeling the absorbing compounds comprising the sample.
$a_{ij}$	=	the absorptivity of the jth compound at the ith wavenumber (abs/ppm/meter).
$C_{j}$	=	the volumetric concentration of the jth compound (ppm).
$M$	=	the number of absorbing compounds in the sample.

The procedures described in this method are all related to the parameters which comprise Beer’s Law. The following list describes these procedures and relationships in a general context:

1) Record a reference absorbance spectrum for each interesting compound of a nitrogen-diluted sample of the pure compound, at a known concentration and pathlength, then divide the absorbance at each point in that spectrum by the product of the concentration and pathlength. This process yields the absorptivity spectrum ($a_{ij}$), or reference spectrum, for each compound.

NIOSH Manual of Analytical Methods, Fourth Edition