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Alternative Approach: Rate Theory Based on the principal of the summation of variances.

Alternative Approach: Rate Theory Based on the principal of the summation of variances. σ T 2 = σ 1 2 + σ 2 2 + σ 3 2 + … So all contributions to the broadening of a peak can be combined in this way. σ T 2 = σ 1 2 + σ 2 2 + σ 3 2 + …

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Alternative Approach: Rate Theory Based on the principal of the summation of variances.

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  1. Alternative Approach: Rate Theory Based on the principal of the summation of variances. σT2 = σ12 + σ22 + σ32 + … So all contributions to the broadening of a peak can be combined in this way

  2. σT2 = σ12 + σ22 + σ32 + … σ1, σ2, etc. are individual contributions to peak width σT

  3. Rate Theory Considers 3 main sources of peak broadening: 1. Eddy Diffusion (A) 2. Longitudinal Diffusion (B) 3. Resistance to Mass Transfer (C)

  4. 1. Eddy Diffusion (A): Particular pathways may differ in length. This mechanism is independent of flow rate (A)

  5. 2. Longitudinal Diffusion (B): A plug of solute in a liquid will tend to spread out into neighboring solvent. This mechanism is proportional to the inverse of the flow rate (B/u)

  6. 3. Resistance to Mass Transfer (C): Different analyte molecules may encounter more random interactions with the stationary phase. This mechanism is directly proportional to the flow rate (Cu)

  7. Rate Theory All 3 will contribute to the height (H) of a theoretical plate depending on the rate of flow (u) H = A + B/u + Cu “Van Deemter Equation”

  8. Historical “Van Deemter Equation” H = A + B/u + Cu uopt uopt

  9. Modern “Van Deemter Equation”: H = B/u + Csu + Cmu

  10. u (cm/s) upractical uopt Rule of Thumb: Save time by using u ≈ 2 uopt

  11. Review of Chromatographic Quantities K = Partition Coefficient, Distribution Coefficient N = Total number of theoretical plates in a column H = Height Equivalent to one Theoretical Plate (mm) L = Length of a chromatographic column (mm) tr = Retention Time for a chromatographic peak (min) W = Base width of a chromatographic peak (min) σ = standard dev. in a chromatographic peak (min) F = Mobile phase flow rate (mL/min) u = linear velocity of mobile phase (mm/min)

  12. Some Useful Derived Quantities H ≡ σ2/L = L/N = A +B/u + Cu = B/u + Csu + Cmu N = (tr/σ)2 = 16(tr/W)2 = 5.54(tr/W1/2)2 k′ = K(Vs/Vm) = (tr – t0)/t0 α = KB/KA = k′B/ k′A = (tB – t0)/(tA – t0) where: tB>tA Rs = (tB – tA) / (WB+WA)/2 = 2(tB – tA)/W where: WB ≈ WA u = L/t0 Vm = t0F W = 4σ W1/2 = 2.35σ

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