JOURNAL O F CHEMICAL EDUCATION
BEER'S LAW I N ANALYTICAL CHEMISTRY HERMAN A. LIEBHAFSKY and HEINZ 6. PFEIFFER General Electric Company, Schenectady, New York
HAVING concluded that Beer used amount (not concentration) of absorbing material in the law often called by his name,' we now wish to suggest that this law be formulated in terms of the number of absorbing centers, which is proportional in the simplest ease to the amount of the sample containing the absorbing material. Although the suggestion represents a welcome return to Beer's point of view, it is not made as a matter of historical pedantry. The fact is that concentration has become far too restrictive a variable for the needs of modern analytical chemi~try.~A brief summary of experience gained in this laboratory will suffice to make this clear. Over 15 years ago, it was discovered that hafnium or zirconium in macrogram amounts could be determined spectrophotometrically in a mn-homogeneous system comprising a hydroxyanthraquinone lake suspended in the solution of the dye in ethyl alcohol.3 4. Surprisingly enough, Beer's law was obeyed reasonably well. Some years later the rate of pitting of stainless '
the depth steel was measured radiographically."ere of the pit, which depends upon the amount of metal removed, was obtained by densitometering a negative. At about the same time, it proved possible to place the or-benzoin oxime spot test for copper on a quantitative basis.' This could be done because the absorbance (but not the reflectance) of such spots as measured on a General Electric recording spectrophotometers was propptional to the amount of ropper present. More recently, the study of analytical methods based upon X-ray absorption has involved samples in each state of matter." lo Here each atom or ion must be regarded as an absorhing center, and m a s s (not concentration) of absorbing material has always been recognized as a logical variable. The table shows the diversity of these various analytical methods. Comments on definitions and related matters are in order here. Absorbance is log,, In/I, where I and I" represent the flux of radiant energy reaching the detector in the presence (I)or absence (Io)of the absorhing centers, other things equal. Owing to the complexity
PFEIFFER, H. G., AND H. A. LIEBHAFSKY, J. CBEM.EDUC.,28, 123 (1951). s LIEBHAFSKY, H. A., paper presented a t the Pittsburgh Con-
ARTY, AND
ferenee on Analytical Chemistry and Applied Spectroscopy, Pittsburgh, Pennsylvania, February 15 to 17, 1950. LIEBHAPSKY. H. A., AND E. H. WINSMW,J. Am. C h .Sac.,
1338 (1949).
60, 1776 (1938). %IEBHAFRKY,
H. A.,
AND
E. H. WINSWW,ibid., 69, 1130
(1047).
FLAW.J. F.. H. A. LIEBHAFSKY, AND E. H. WINSLOW, ibid., 71, 3G30 (19401.
LIEBHAFSKY, H. A., J. T. MIRELES-MALPICA, C. D. MomA. F. WINSLOY, General Electric Research Laboratory Report No. 510, April, 1951. ' WINSLOW,E. H., A N D H. A. LIEBHAFSKY, Anal. Chem., 21, MICHAELSON, J. L.,
AND
H. A. LIEBHAWKY, Gm. Elec. Rev.,
39, 445 (1936). O LIEBHAPBKY, H. A., H. M. SMITH,H. E. TAXIS,A N D E. H. WINSLOW, Anal. cham., 19,861 (1947). lo LIEBHAPSKY, H. A,, ibid., 21, 17 (1949).
SEPTEMBER, 1953
451 Range of Photometric Methods i n Analytical Chemistry
KO. I 2 3 4
Method
Spwtn,photomctric I'hovmrtric .
