Infrared absorptions occur over a range of frequencies, and absorption coefficients measured at any single frequency may not express the true intensity of a molecular transition. The integrated absorption coefficient is the sum of the absorption coefficients for all such frequencies in the band A = ∫ ε(v) dv. Integrated absorption coefficients have been used for a variety of applications, for the most part ignoring any inherent differences in molar absorptivity for molecules in different states of aggregation. Eischens and Jacknow have used a system using combined gravimetry and spectroscopy to calculate the ε for adsorbed species; that is, the extinction coefficient for a functional group of a molecule adsorbed on another surface. They also report that the ε for carbon monoxide on a surface vs. the same compound in solution can be assumed to be the same within the experimental accuracy; whether this conclusion can be generalized is not known.
M. S. Akhter, A. R. Chughtai, and D. M. Smith, "Determination of the Integrated Molar Absorptivity for C-ONO and C-NO2 Groups, Using FT-IR Spectroscopy," Appl. Spectrosc. 40, 1068-1069 (1986)