Log-normal derived equations for the determination of chromatographic peak parameters from graphical measurements

Equations for the calculation of peak parameters (area, mean, variance, skewness, excess, number of theoretical plates (N) and maximum number of theoretical plates) from graphically measurable variables (maximum height, retention time, width and asymmetry factor) were developed by using the log-normal distribution function as a model for chromatographic peaks. The equations were tested for a series of 50 experimental peaks obtained by gas and liquid chromatography, giving parameters consistent with those obtained by direct profile integration with numerical methods. The equations were compared with those derived from the exponentially modified Gaussian function. The greatest discrepancies between the two models were found in the results from the equations for skewness and excess. The differences were small (≈ 5%) at high peak asymmetry (a > 2.5) but became important (skewness ≈ 60%, excess > 100%) for nearly symmetric peaks (a ≈ 1.1); the log-normal equations gave values closer to the parameters obtained by direct integration. The log-normal N values were 4–16% higher than those obtained with the EMG function and the log-normal model provided more realistic estimates for maximum N.