3 Assume for simplicity that the HPLC plate height, H, can be given by Equation26-23

Chapter 28, Problem 28-23

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3 Assume for simplicity that the HPLC plate height, H, can be given by Equation26-23 aswhere C = Cs + CM'(a) By using calculus to find the minimum ll, show that the optimal velocity uop,can be expressed as(b) Show that this leads to a minimum plate height Hmin given byllmin = 2VlfC(c) Under some conditions for chromatography, Cs is negligible compared toCM' For packed HPLC columns, C" is given bywd~ eM =--DMwhere w is a dimensionless constant, dp is the particle size of the columnpacking. and D" is the diffusion coefficient in the mobile phase. The B coefficientcan be expressed as where y is also a dimensionless constant. Express uop, and Hmm in terms ofDM, dp' and the dimensionless constants y and w.If thc dimensionless constants are on the order of unity, show that "op, andH min can be expressed asUnder the preceding conditions, how could the plate height be reduced byone third? What would happen to the optimal velocity under these conditions?What would happen to the number of theoretical plates N for thesame length column?For thc conditions in part (e), how could you maintain the same number oftheoretical plates while reducing the plate height by one third?The preceding discussion assumes that all band broadening occurs withinthe column. Name two sources of extracolumn band broadening that mightalso contribute to the overall width of HPLC peak