Determination of molar IR absorptivities and their errors

• Published in: Journal of molecular structure 1984, Vol.114, p.297-300
• Main Authors: Staat, H., Korte, E.H.
• Format: Article
• Language: English
• ISSN: 0022-2860; 1872-8014
• DOI: 10.1016/0022-2860(84)87148-3

Molar absorptivities of band maxima of acetonitrile, n-heptane, benzene, and toluene were determined from difference spectra. The statistical and most important systematic errors are given. Recently, we studied statistical and systematic errors occuring in the determination of IR absorptivities ε of liquids (ref. 1). Considerable systematic errors are caused by reflection losses at the outer and inner surfaces of the cell windows. It was shown that these are compensated for if the ratio of two transmittance spectra (T 1, T 2) due to different sample thicknesses (d 1, d 2) is used: In such a case Bouguer—Lambert-Beer's laws leads to ▪ where c denotes the concentration. The reliability of the absorptivities derived in this way, is mainly affected by the statistical error comprising the standard deviations of the transmittance measurements as well as by the systematic errors from multiple beam interference within the cell (the fringes do not compensate for each other because of their different periods) and from the finite slit width. Experimental conditions can be chosen so that errors from beam convergence, polarization, temperature variations, and thermal emission are negligible. The influences on the transmittance measurement by drift, unwanted radiation, reliability of wavenumber reading, and non-linearity of the detector system are not considered. The molar absorptivities of band maxima of acetonitrile, n-heptane, benzene, and toluene have been determined using equation (1) and are listed in the Table. The values ofΔd employed were in the order of 10 μm to 40 μm, therefore, the strongest bands could not be evaluated. The statistical error was calculated from ▪ and the systematic error due to finite spectral slit width (s) from ▪ with the band half-width 2γ. The deviation of the cell from planoparallel shape has been taken into account quantitatively, this is different to the method used previously (ref. 1). If the cell is wedge shaped so that its thickness varies linearly from (d 0 - δ) to (d 0 + δ), the interference pattern of a cell filled with a compound of refractive index n s is described by ▪ where φ = 4 π n s ν d and r denotes the reflectance, T the true transmittance, and ν the wavenumber. Since n s( ν ) is not known precisely, only a range can be given for T A limited by the values for cos φ = ± 1. For the absorptivities derived from a difference spectrum this uncertainty is ▪ but only as far as the average refractive index n s is a sufficient a