# Chromatography

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Chromatography

## 1. Concept

### 1.1. Second Law of Thermodynamics

1.1.1. Entropy increases (opposite of separation)

### 1.2. Separation

1.2.1. Differential transport of compounds from one region (shared) to another

1.2.2. Allowing dilution to take place

### 1.3. Theories

1.3.1. Plate Theory vs. Rate Theory

## 2. GC vs. HPLC Categories

### 2.1. Gas Chromatography

2.1.1. Gas-Solid Chromatography

2.1.1.1. Best used with gases

2.1.2. Gas-Liquid Chromatography

2.1.2.1. Best used with organic compounds that are high volatile

### 2.2. High-Performance Liquid Chromatography

2.2.1. Hydrophilic interaction

2.2.1.1. Best used with small polar organic compounds

2.2.2. Reverse Phase Chromatography

2.2.2.1. Best used with small nonpolar organic compounds

## 3. Analytical Separation Calculations

### 3.1. Measure of column efficiency

3.1.1. Plate Height (H or HETP)

3.1.1.1. Distance along the column corresponding to a theoretical separation step (N)

3.1.1.2. H = L / N (L is column length, N is theoretical plate number)

3.1.2. Therefore, plate height and theoretical plate number are inversely proportional

3.1.2.1. When H decreases, more steps (N) are possible, resulting in better separation and narrower peaks

### 3.2. Relationship of Diffusion Peak to Gaussian Peak

3.2.1. Einstein equation: Lambda^2 = 2DT

3.2.1.1. D = diffusion coefficient, t = time

3.2.2. N = 16(tr/W)^2

3.2.2.1. tr = Retention Time

3.2.2.2. W = Peak Width

3.2.3. The two above equations can be combined, when w = 4*Lambda (in the Gaussian Peak width calculation), and due to the fact that distance and time are proportional

### 3.3. Width at Base vs. Half-Height

3.3.1. Base: N = (16*(tr-tm)^2)/Wb

3.3.2. Half Height: N = (5.54*(tr-tm)^2)/Wh

3.3.3. tm = minimum time, without any interaction with column

3.3.4. W is peak width, either base or half height

### 3.4. Resolution of Peaks

3.4.1. Resolution (Rs) is proportional to square root of N

3.4.2. Rs1/Rs2 = ((N1)^(1/2))/((N2)^(1/2))

3.4.3. Rs is equal to the change in retention time divided by the average peak width at the base

## 4. Rate Theory of Chromatography

### 4.1. Consisting of various potential equations (hence, why it is a theory)

4.1.1. All equations bring about a hyperbolic function that can then predict minimum plate height at optimum velocity (maximum efficiency)

4.1.2. In terms of normal operating velocities (relative to most tests conducted), the Van Deemter equation provides the best experimental fit

### 4.3. A Term: Eddy Diffusion

4.3.1. Linearly proportional to particle quality and particle diameter

4.3.2. Molecules could travel unequal distances

4.3.2.1. Also, independent of velocity

### 4.4. B Term: Longitudinal Diffusion

4.4.1. B = 2y*Dm

4.4.1.1. y is the Impedance Factor from the packing

4.4.1.2. Dm is the molecular diffusion coefficient

4.4.1.3. Lower velocity leads to heightened plate height, higher velocity leads to lesser plate height

### 4.5. C Term: Mass Transfer

4.5.1. Relates mass transfer of sample components between mobile and stationary phases

4.5.2. Stationary and mobile phase mass transfers expressed with Cs and Cm respectively

4.5.3. Higher velocity leads to heightened plate height, lower velocity leads to lesser plate height