The Determination of the Areas of Resolved and Partially Resolved Chromatography Peaks

Abstract

Gas chromatographic peaks were demonstrated to have the form of normal distribution curves. A mathematical treatment has been developed which permits the calculation of the areas of these curves from the statistical parameters, height of the mode (peak height), and standard deviation u. The standard deviation equals the width of the peak a t 0.882 of peak height. Methods given for the evaluation of the mutual effects of overlapping peaks have made it possible t o obtain corrected peak heights. The standard deviation of the gas chromatography peak has been found to vary linearly with the retention time, thus permitting the graphical estimation of u for use with corrected peak heights in the calculation of true areas for overlapping peaks. The method has also been extended to the treatment of skewed, overlapping pealts. The variation of u with retention time, its constancy, and its relationship t o the number of theoretical plates are discussed. INTRODUCTIONIn quantitative gas chron~atography using a differential detector, the area under the peak corresponding to a colnpound is proportioilal to the aiuount of that compound present in tlie gas stream. Area measurements are therefore fundamental.Various procedures have been proposed for the measurement of peak areas. The integrator built into the recorder is the least laborious, but suffers from obvious disadvantages if there is a base-line drift or if there are overlapping peaks. The triangulation procedure (1) gives a good first approximation. Another procedure which has been widely used is to cut out the pealrs or a tracing of the pealts, and to weigh the cut paper. Planimeter tracing has also been used. With all these procedures, precision and accuracy suffer when the peaks are very narroxv or if two or more peaks have a moderate overlap. AREA OF SYiLIMETRICAL PE-AKS ( a ) Isolated PeaksI t has been pointed out and developed theoretically (2, 3, 4) that the peaks obtained with a well-designed chromatograph closely approxiinate a nornlal or Gaussian distribution curve as ~1 1 0~~1 1 in Fig. 1. The equatioii for this type of curve is given by Goulden (5) as where Y is the height of tlie curve measured a t a distance x from tlie mean, i V is the number of variates, which, for our purposes may be tal<en as the area, -4, and u is tlie standard deviation. At the mean or central peal; of the curve, x = 0, Y = h or peal; height, and equation [I] becomes l~lfa

Essential Oils and Their Constituents: Xxix. The Essential Oil of Marihuana: Composition of Genuine Indian Cannabis Sativa L.

“…Quantitative results were obtained from measuretllel~ts of peak areas, as previously reported (7,8).…”

Prostaglandins: Their role in egg-laying of the cricket Teleogryllus commodus

“…Each sample was chromatographed three times. Quantitative estimation ofpeak areas was done by the method of Bartlet and Smith (8). Individual peaks were identified by logarithmic plots of relative retention times and by comparison with runs ofauthentic standards (single and mixed 99% pure fatty acids) interspersed between experimental runs.…”

Column and Gas Chromatographic Analysis of Oil of Wild Ginger: Identification and Estimation of Some New Constituents

“…Constituents were identified by comparison of retention times on both columns as well as infrared characteristics with those of authenticated reference standards aild determined by the sigma method developed in this laboratory (5,6). …”