Integrated Infrared Band Intensities
H. William Wilson Western Washington State College Bellingham, 98225
A physical chemistry experiment
There is probably no other technique in infrared spectronhotometrv that relies more upon ontimized instrumental parameters' and inherent operat& dexterity than the determination of apparent integrated hand intensities and absorption coefficie&. We have had a great deal of success in illustrating the role of instrumental functions in distortine band contours and the pitfalls of data handling by h a v k g junior-senior level ~ h v s i c a lchemistw students carry out routine intensity evaiuations as laboiatory experime&. The results can easily be shown to have parallels in nmr, esr, uv-vis, or anywhere where sharp spectral band features are encountered. Two methods, described in detail some years ago by R a m ~ a y ,present ~ quite different means of determining the intensitv IB) of infrared bands. The first of these. usually called Method I, is particularly useful for isolated hands that are unhindered hv underlvinc! or neighborine absorption areas. Based on the assumpcon t h a t such hand has a Lorenzian contour, Method I requires only the measurement of the maximal band absorbance, loglo (To/T),,,,, and the apparent half hand width A v ~ l zof~ the band in question. The apparent integrated intensity is then computed from the relationship
a
El
=
K 2.303 logm(T0/T)..~..&112" 2
(1)
lntegrated infrared Band intensities for the 1216 cm-1 Band of Chloroform
.
,
mole
loglo
lo5) TdT
X
Avrira mole (m-I) X 10')
. .
mole X
,
,
mole X 10')
(cm2/ nole)
1 = 0.014 cm. B, refers to the results obtained by Method I. 'Bn are results obtained by using Method I1 and a planimeter. dB',, are results obtained by using Method I1 and weighing cutouts.
where K is a constant that corrects for the resolution of pwrly resolving instruments. It has a value of 1.57 for any spectral slit width-half hand width ratio of less than 0.40. The el factor is the concentration-path length product, and To and T refer to the incident and transmitted beam intensities, respectively. The two latter values and the half hand widths are easilv and ohviouslv effected hv instrumental settings. The ease and simnlicitv . - of Method I make i t an unsuestioned choice for measuring simple bands, but where broad spectral interference or overlapping bands are found, it is of little or no value and Method I1 must be employed. Here the integral of an absorbance versus freauencv nlot must be determined hv some mechanical means such as square counting, planimetry, or even cuttine" the olots out and weiehine them aeainst a known cal" ibration area. The relationship between the measured integral and the apparent integrated intensity is simply
. -.
A
-
where the integral is taken over the whole hand. Simple hands, free of interference and containing only one fundamental mode such as the 1216 cm-l band of chloroform in carbon tetrachloride, should yield identical BI and B,, values. It soon becomes apparent to the student that such agreement is fortuitous even under the most ideal conditions and that disparities of less than *lo% between measurements are uncommon (3). Table 1 is a sampling of the values obtained under typical circumstances in the student laboratory. Both Methods I and II are compared and a further differentiation is made between values obtained by planimetric and cutout methods of integration. There is almost no limit to the number of experimental variations that the instructor can present to the student depending upon the latter's laboratory ability and the time available for the typically time consuming demands made by Method 11. It is also of considerable interest to students to carry out hand integrations of nmr bands and compare them with machine results. Although absolute values do not result, the student's awareness of data handling uncertainties is considerably sharpened.
a
392
/ Journal of Chemical Educalion
'Seshadri, K. S., Jones, R. Norman, Spectrochim. Acta, 19, 1013 (1963). 2Rarnsay, D . A . , J. Amer. Chem. Soc., 74,72 (1952). 3Scbmid, E. D., Langenbucher, F., Wilson, H. W., Speetrochim. Aeto, 19,835 (1963).
