# CHM1222Chromatograph yTheory

Published on October 16, 2007

Author: Arley33

Source: authorstream.com

Introduction to Chromatography Theory:  Introduction to Chromatography Theory Bioanalytical Chemistry Spring 2004 The Theory of Chromatography:  The Theory of Chromatography Plate theory - older; developed by Martin & Synge Rate theory - currently in use today Plate Theory - Martin & Synge 1954 Nobel Laureates:  Plate Theory - Martin & Synge 1954 Nobel Laureates View column as divided into a number (N) of adjacent imaginary segments called theoretical plates within each theoretical plate complete equilibration of analytes between stationary and mobile phase occurs Plate Theory - Martin & Synge 1954 Nobel Laureates:  Plate Theory - Martin & Synge 1954 Nobel Laureates Significance? Greater separation occurs with: greater number of theoretical plates (N) as plate height (H or HETP) becomes smaller L = N H or H = L / N where L is length of column, N is number of plates, and H is height of plates N can be Estimated Experimentally from a Chromatogram:  N can be Estimated Experimentally from a Chromatogram N = 5.55 tr2 / w1/22 = 16 tr2 / w2 where: tr is retention time; w1/2 is full width at maximum w is width measured at baseline Choice of Column Dimensions:  Choice of Column Dimensions Nmax = 0.4 * L/dp where: N - maximum column efficiency L - column length dp - particle size So, the smaller the particle size the higher the efficiency! Efficiency Relative to Analysis Time:  Efficiency Relative to Analysis Time N Analysis Time, min 1970’s 300 mm L 10 um today 150 mm L 5 um today 90 mm L 3 um 10 100 First Important Prediction of Plate Theory:  First Important Prediction of Plate Theory Bandspreading - the width of bands increases as their retention time (volume) increases Problem::  Problem: A band exhibiting a width of 4 mL and a retention volume of 49 mL is eluted from a column. What width is expected for a band with a retention volume of 127 mL eluting from the same analyte mixture on the same column? ANS: 10.4 mL Second significant prediction of plate theory:  Second significant prediction of plate theory The smaller HETP, the narrower the eluted peak Plate Theory - Practical Considerations:  Plate Theory - Practical Considerations Not unusual for a chromatography column to have millions of theoretical plates Columns often behave as if they have different numbers of plates for different solutes present in same mixture Rate Theory:  Rate Theory Based on a random walk mechanism for the migration of molecules through a column takes into account: band broadening effect of rate of elution on band shape availability of different paths for different solute molecules to follow diffusion of solute along length Van Deemter Equation:  Van Deemter Equation H = A n1/3 + B/n + C n where: H is HETP (remember want a minimum!) n is mobile phase velocity A, B, and C are constants Van Deemter Equation:  Van Deemter Equation H = A n1/3 + B/n + C n first term - rate of mobile phase movement through column (often just a constant) second term - longitudinal solute diffusion; solute concentration always lower at edges of column so solute diffuses longitudinally third term - equilibration is not instantaneous Resolution:  Resolution Ideal chromatogram exhibits a distinct separate peak for each solute reality: chromatographic peaks often overlap we call the degree of separation of two peaks: resolution = peak separation average peak width Resolution:  Resolution Resolution = D tr / wavg let’s take a closer look at the significance of the problem: Resolution:  Resolution So, separation of mixtures depends on: width of solute peaks (want narrow) efficiency spacing between peaks (want large spacing) selectivity Example:  Example What is the resolution of two Gaussian peaks of identical width (3.27 s) and height eluting at 67.3 s and 74.9 s, respectively? ANS: Resolution = 2.32

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