1	Chapter 26: An Introduction to Chromatographic Separations Column Chromatography Migration Rates Distribution Contstants Retention Times Selectivity Factor Zone Broadening & Column Efficiency Optimizing Performance Resolution
2	Intro to Chromatography Chromatography is a separation technique HPLC & GC are our primary focus Also discuss low pressure column chromatography & TLC (thin layer) All chromatographic techniques have Stationary phase – solid or viscous liquid phase typically in a column Mobile phase – moves sample in contact with stationary phase
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4	"Partitioning = type of equilibrium..." Partitioning = type of equilibrium where the analyte divides itself between two phases For liquid-liquid extraction – two liquids For chromatography – mobile vs. stationary phases Define a partition ratio K (or distribution constant) C_swhere C_s & C_M are K = ------- C_M concentrations of analyte in stationary & mobile phases
5	"Prefer if K is constant..." Prefer if K is constant over conc. range If not constant we can work in a narrow range where it is constant This is linear chromatography Example of non-linear chromatography Pour aqueous solution of A & B on column Allow water to drain out, both A & B stick Wash column with 50% MeOH, A removed Wash column with 100% MeOH, B removed Used extensively for sample cleanup in GC
6	"From now on everything is..." From now on everything is linear chromatography In linear chromatography a constant flow rate of mobile phase moves through column K is typically constant or nearly constant Elution = process by which analyte is flushed through the column by mobile phase (which could be a liquid or a gas)
7	"Overview of" Overview of chromatographic process – packed column - Inject at t_o - Separate t₁ to t₃ - Detect at t₄ Resulting chromatogram
8	"A & B retained by..." A & B retained by column differently B has higher K B takes longer to elute from column Detector sees A first then B Peak heights & peak areas are proportional to conc. Band broadening
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12	"Define n as average linear..." Define n as average linear rate of solute migration & L as column length, then L distance n = ----- ------------ = velocity t_R time Similarly if define µ as average linear rate of movement of molecules of mobile phase L µ = ----- t_M
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14	"Relating retention time t_R to..." Relating retention time t_R to K (= C_s/C_M) n = µ x fraction of time analyte is in mobile phase moles of analyte in mobile phase n = µ x --------------------------------------------- number of moles of analyte C_M V_M 1 n = µ x -------------------- = µ x --------------------- C_M V_M + C_s V_s 1 + C_sV_s/C_MV_M Substituting K = C_s/C_M 1 Gives n = µ x ------------------ 1 + K V_s/V_M
15	"More useful relationships - capacity..." More useful relationships - capacity factor k’ (comes from K) K in concentration, k’ in moles amount of analyte in stationary phase k’ = ---------------------------------------------- amount of analyte in mobile phase K_AV_s n_sn = # of So for A à k_A’ = ---------- = ------ moles V_M n_M
16	"From previous" From previous equation à Can plug in n = L/t_R & µ = L/t_M Rearrange t_R – t_M k_A’ = ----------- and get t_M Now have k_A’ in terms of something easily measured in chromatogram Compares how long it takes a species to move through system compared to unretained species Relative because ratio, Numerator = Net Retention
17	"One step further à Selectivity..." One step further à Selectivity factor (a) describes differential migration For two K_B k_B’ a = ------ = ------- components K_A k_A’ And from (t_R)_B - t_M a = --------------- chromatogram (t_R)_A – t_M Allows calculation of the resolving power of a chromatographic system (i.e. column with A & B)
18	Chromatographic Plate Theory vs. Rate Theory Plate theory based in liquid-liquid extraction (successive extractions) K = C_org/C_water Chromatographic column can be thought of in the same way (only continuous process) K = C_s/C_M
19	"Divide chromatographic column up into..." Divide chromatographic column up into steps or segments called theoretical plates The theoretical concept is that these theoretical plates are equilibrium units for K = C_s/C_M The more theoretical plates a column has, the more efficient it is If column length = L & N = number of plates, then H = height equivalent to theoretical plate
20	"Gausian" Gausian peaks – statistical distribution of molecules W_b = 4s
21	"Gausian distribution (bell curve" Gausian distribution (bell curve) W = 4s
22	"Can derive" Can derive N = number of plates N = 16 (t_R/W_b)²W_b = base width N = 16 (t_R/4s)²= (t_R/s)² N = 5.54 (t_R/W_½)²W_½ = width at half height Column manufacturers use N to characterize column – N varies widely
23	"Shortcomings of Plate Theory" Shortcomings of Plate Theory Assumes K is independent of concentration Assumes equilibration is rapid relative to velocity of mobile phase – not true, in reality solute may pass a plate without entering Assumes no longitudinal diffusion (= non ideal effect that causes band broadening) Does not address several factors caused by mobile phase velocity (fast or slow) Rate Theory Assumes discrete units or plates for equilibrium rather than a semi continuous process through the column