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A van Deemter plot for the separation of neutral dyes by micellar electrokinetic chromatography is shown below. \({ }^{62}\) (a) Explain why plate height increases at low and high velocities. (b) The irregular flow path term, \(A\), in the van Deemter equation should really be 0 for the ideal case of micellar electrokinetic chromatography. The observed value of \(A\) is \(2.32 \mu \mathrm{m}\), which accounts for two-thirds of the band broadening at the optimum velocity. Suggest some reasons why \(A\) is not 0 .

Short Answer

Expert verified
Plate height increases due to diffusion at low velocities and mass transfer resistance at high velocities. Non-zero \(A\) is due to practical imperfections.

Step by step solution

01

Understanding the van Deemter Equation

The van Deemter equation describes the relationship between the linear velocity of a chromatographic process and plate height, which is a measure of column efficiency. The equation is represented as: \( H = A + \frac{B}{u} + Cu \), where \(H\) is the plate height, \(u\) is the linear velocity, \(A\) accounts for eddy diffusion, \(B\) is the longitudinal diffusion term, and \(C\) is the mass transfer term.
02

Analyzing Low Velocities

At low velocities, the term \(\frac{B}{u}\) becomes significant because the velocity \(u\) is in the denominator. This term represents longitudinal diffusion, where the analyte molecules can spread out over time due to diffusion along the column. As velocity decreases, diffusion leads to greater spreading, thereby increasing the plate height.
03

Analyzing High Velocities

At high velocities, the term \(Cu\) becomes significant. This term accounts for the resistance to mass transfer between phases. At higher velocities, there is less time for the analyte molecules to equilibrate between the stationary and mobile phases, causing band broadening and an increase in plate height.
04

Investigating the Nonzero A Term

The ideal case for micellar electrokinetic chromatography suggests that the \(A\) term, representing eddy diffusion due to the irregular flow path, should be zero due to a uniform flow path. However, the observed value of \(A\) is \(2.32 \mu m\). This can be attributed to non-ideal conditions such as imperfections in the capillary, inconsistencies in the micelle sizes, or fluctuations in micelle formation, leading to irregular flow paths and non-zero \(A\) values.
05

Summary of Findings

The van Deemter equation explains why plate height is affected by low and high velocity ranges due to diffusion and mass transfer resistance, respectively. The non-zero value of \(A\) in the micellar electrokinetic chromatography is likely due to practical deviations from ideal conditions in terms of capillary and micelle consistency.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Micellar Electrokinetic Chromatography
Micellar Electrokinetic Chromatography (MEKC) is a powerful separation technique used in analytical chemistry. It combines the principles of electrophoresis and chromatography. The unique aspect of MEKC is the use of micelles, which are small, spherical aggregates formed by surfactant molecules. These micelles serve as a pseudostationary phase in the separation process, which enables the separation of neutral compounds that are not typically separable by capillary electrophoresis.

In MEKC, the sample is introduced into a capillary filled with a buffer containing surfactant. When an electric field is applied, charged particles migrate toward the electrode of opposite charge, while neutral molecules interact with the moving micelles and are separated based on their partitioning between the micelles and the aqueous phase.

MEKC is especially valuable as it combines high efficiency and speed with the ability to separate complex mixtures. However, the separation efficiency can be influenced by various factors such as micelle concentration, buffer composition, and the applied voltage.
Plate Height
Plate height is a critical parameter in chromatography, as it quantifies the efficiency of a separation column. It is often defined by the van Deemter equation: \[ H = A + \frac{B}{u} + Cu \] where
  • \(H\) is the plate height, or the height equivalent to a theoretical plate (HETP).
  • \(A\) represents the eddy diffusion term, or the multiple paths available within the column.
  • \(B\) corresponds to the longitudinal diffusion term, which describes diffusion along the length of the column.
  • \(C\) is the mass transfer resistance between the stationary and mobile phases.
Plate height provides insight into how well a chromatographic column can separate components. The lower the plate height, the more efficient the column is, and it indicates sharp and narrow bands of separated compounds. Finding the optimal plate height involves adjusting the flow velocity to achieve the best separation efficiency.
Longitudinal Diffusion
Longitudinal diffusion is a phenomenon where analyte molecules diffuse along the length of the column, affecting the separation process. It is represented by the term \(\frac{B}{u}\) in the van Deemter equation. This diffusion occurs in all directions but is most significant along the direction of the flow, due to random molecular motion.

As the velocity of the mobile phase decreases, the time the analytes spend in the column increases. Longer residence time allows for greater diffusion, leading to band spreading and increased plate height. This is why the longitudinal diffusion term becomes more pronounced at low velocities.

Understanding and controlling longitudinal diffusion is crucial for optimizing separation performance, particularly in techniques like MEKC where efficient separation is a top priority.
Mass Transfer Resistance
Mass transfer resistance is related to the challenges molecules face when moving between the stationary and mobile phases in chromatographic separation. It is expressed as the term \(Cu\) in the van Deemter equation.

When the velocity of the mobile phase is high, there is insufficient time for equilibrium to be established between the liquid phase and the micelles. This results in less effective separation due to the analytes not fully interacting with the stationary phase. As a consequence, band broadening occurs, and the plate height increases.

Strategies to minimize mass transfer resistance include optimizing the velocity of the mobile phase and selecting appropriate stationary phases to ensure efficient interaction and transfer between phases. Efficient mass transfer is essential for achieving high-resolution separations in MEKC.

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Most popular questions from this chapter

The observed behavior of benzyl alcohol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{OH}\right)\) in capillary electrophoresis is given here. Draw a graph showing the number of plates versus the electric field and explain what happens as the field increases. $$ \begin{array}{cc} \text { Electric field }(\mathrm{V} / \mathrm{m}) & \text { Number of plates } \\\ \hline 6400 & 38000 \\ 12700 & 78000 \\ 19000 & 96000 \\ 25500 & 124000 \\ 31700 & 124000 \\ 38000 & 96000 \end{array} $$

Molecular mass by sodium dodecylsulfate-gel electrophoresis. Ferritin is a hollow iron-storage protein \({ }^{61}\) consisting of 24 subunits that are a variable mixture of heavy (H) or light (L) chains, arranged in octahedral symmetry. The hollow center, with a diameter of \(8 \mathrm{~nm}\), can hold up to 4500 iron atoms in the approximate form of the mineral ferrihydrite \(\left(5 \mathrm{Fe}_{2} \mathrm{O}_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\right)\). Iron(II) enters the protein through eight pores located on the threefold symmetry axes of the octahedron. Oxidation to Fe(III) occurs at catalytic sites on the H chains. Other sites on the inside of the \(\mathrm{L}\) chains appear to nucleate the crystallization of ferrihydrite. Migration times for protein standards and the ferritin subunits are given in the table. Prepare a graph of \(\log (\) molecular mass \()\) versus \(1 /\) (relative migration time), where relative migration time \(=\) (migration time)/(migration time of marker dye). Compute the molecular mass of the ferritin light and heavy chains. The masses of the chains, computed from amino acid sequences, are 19766 and \(21099 \mathrm{Da}\). $$ \begin{array}{lll} \text { Protein } & \begin{array}{l} \text { Molecular } \\ \text { mass }(\text { Da }) \end{array} & \begin{array}{l} \text { Migration } \\ \text { time }(\mathrm{min}) \end{array} \\ \hline \text { Orange G marker dye } & \text { small } & 13.17 \\ \alpha \text {-Lactalbumin } & 14200 & 16.46 \\ \text { Carbonic anhydrase } & 29000 & 18.66 \\ \text { Ovalbumin } & 45000 & 20.16 \\ \text { Bovine serum albumin } & 66000 & 22.36 \\ \text { Phosphorylase B } & 97000 & 23.56 \\ \beta \text {-Galactosidase } & 116000 & 24.97 \\ \text { Myosin } & 205000 & 28.25 \\ \text { Ferritin light chain } & & 17.07 \\ \text { Ferritin heavy chain } & & 17.97 \end{array} $$

The following substances were separated on a gel filtration column. Estimate the molecular mass of the unknown. $$ \begin{array}{lll} \text { Compound } & V_{\mathrm{r}}(\mathrm{mL}) & \text { Molecular mass (Da) } \\ \hline \text { Blue Dextran 2000 } & 17.7 & 2 \times 10^{6} \\ \text { Aldolase } & 35.6 & 158000 \\ \text { Catalase } & 32.3 & 210000 \\ \text { Ferritin } & 28.6 & 440000 \\ \text { Thyroglobulin } & 25.1 & 669000 \\ \text { Unknown } & 30.3 & ? \end{array} $$

Optimizing a separation of acids. Benzoic acid containing \({ }^{16} \mathrm{O}\) can be separated from benzoic acid containing \({ }^{18} \mathrm{O}\) by electrophoresis at a suitable \(\mathrm{pH}\) because they have slightly different acid dissociation constants. The difference in mobility is caused by the different fraction of each acid in the anionic form, \(\mathrm{A}^{-}\). Calling this fraction \(\alpha\), we can write $$ \begin{array}{ll} \mathrm{H}^{16} \mathrm{~A} \rightleftharpoons \mathrm{H}^{+}+{ }^{16} \mathrm{~A}^{-} & \mathrm{H}^{18} \mathrm{~A} \rightleftharpoons \mathrm{H}^{+}+{ }^{18} \mathrm{~A}^{-} \\ { }^{16} \alpha=\frac{{ }^{16} K}{{ }^{16} K+\left[\mathrm{H}^{+}\right]} & { }^{18} \alpha=\frac{{ }^{18} K}{{ }^{18} K+\left[\mathrm{H}^{+}\right]} \end{array} $$ where \(K\) is the equilibrium constant. The greater the fraction of acid in the form \(\mathrm{A}^{-}\), the faster it will migrate in the electric field. It can be shown that, for electrophoresis, the maximum separation will occur when \(\Delta \alpha / \sqrt{\alpha}\) is a maximum. In this expression, \(\Delta \alpha={ }^{16} \alpha-{ }^{18} \alpha\), and \(\bar{\alpha}\) is the average fraction of dissociation \(\left[=\frac{1}{2}\left({ }^{16} \alpha+{ }^{18} \alpha\right)\right] .\) (a) Let us denote the ratio of acid dissociation constants as \(R={ }^{16} K /{ }^{18} K\). In general, \(R\) will be close to unity. For benzoic acid, \(R=1.020\). Abbreviate \({ }^{16} K\) as \(K\) and write \({ }^{18} K=K / R\). Derive an expression for \(\Delta \alpha / \sqrt{\alpha}\) in terms of \(K,\left[\mathrm{H}^{+}\right]\), and \(R\). Because both equilibrium constants are nearly equal ( \(R\) is close to unity), set \(\bar{\alpha}\) equal to \({ }^{16} \alpha\) in your expression. (b) Find the maximum value of \(\Delta \alpha / \sqrt{\alpha}\) by taking the derivative with respect to \(\left[\mathrm{H}^{+}\right]\)and setting it equal to 0 . Show that the maximum difference in mobility of isotopic benzoic acids occurs when \(\left[\mathrm{H}^{+}\right]=(K / 2 R)(1+\sqrt{1+8 R})\). (c) Show that, for \(R \approx 1\), this expression simplifies to \(\left[\mathrm{H}^{+}\right]=2 K\), or \(\mathrm{pH}=\mathrm{p} K-0.30\). That is, the maximum electrophoretic separation should occur when the column buffer has \(\mathrm{pH}=\mathrm{p} K-0.30\), regardless of the exact value of \(R .{ }^{63}\)

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