# Terms and equations used in HPLC explained

Here is an overview of the definition of terms and equations most commonly used in HPLC.

### Back pressure

The pressure required to pump the mobile phase through the column. According to the following equation, it is influenced by the viscosity of the mobile phase (ɳ), the flow rate (F), the column length (L) and the column inner diameter (dc), as well as the particle size (dp):

Back pressure (psi) = (250LɳF) / (dp2dc2)

L = column length (cm)
ɳ = mobile phase viscosity
F = flow rate
dp = particle size (µm)
dc = column inner diameter (cm)

### Capacity factor (k)

It is a measure of the level of retention of an analyte relative to a non retained component, where tR is the retention time of the sample peak and t0 is the retention time of a non retained component. A measurement of the capacity helps to determine whether changed in retention levels are due to the column (the capacity factor changes with the change in retention time) or to the system (the capacity factor remains constant with change in retention time).

k = (tR - t0) / t0

### Efficiency (N)

A measure of peak width for an analyte in a separation, determined by various methods, some of which are sensitive to peak symmetry. The most common are listed here, commencing with the peak shape which is most sensitive first:

5-Sigma               N = 25(tR/W

W = peak width at 4.4 % peak height

4-Sigma               N = 16(tR/W

or                      W = peak width at 13.4 % peak height

Tangent line method

Half peak height method        N = 5,54(tR/W

W = peak width at 50 % peak height

### Elution volume (VR)

The volume of the solvent (mobile phase) required to elute the analyte from the column at maximum concentration (peak).

VR = F*tr

### HETP

Height equivalent to a theoretical plate (HETP) is derived from the distillation theory, measuring the efficiency of a column. For a typically well packed HPLC column with 5 µm particles, the HETP (or H) values are usually between 0.01 and 0.03 mm.

HETP = L/N

where L ist the column length in millimeters and N the number of theoretical plates.

### Linear velocity

The flow rate through the column. This influences the column performance and is directly related to the column pressure. The linear velocity is measured by dividing column length L by the retention time of a non-retained component t0:

µ = L / t0

### Resolution (Rs)

It is the ability of a column to separate chromatographic peaks. Resolution can be improved by increasing the column length, reducing the particle size, changing the temperature, changing the eluent or the stationary phase.

Rs = ¼√N(k((1+k))(α-1)/α)

It can also be expressed as the difference in retention of adjacent peaks divided by their average band width:

Rs = (t2-t1)/(0,5(W1+W2))

### Selectivity (α)

It is a measure of relative difference in retention of two substances and is determined by a certain stationary phase and the composition of the mobile phase. k1 and k2 are the respective capacity factors.

α = k1/k2

### Tailing factor (T)

A measure of the symmetry of a peak, which is determined by the following equation, where W0.05 is the peak width at 5 % of height and f is the distance from the front slope of the peak to the apex at 5 % height. Ideally, the peaks should be Gaussian or completely symmetrical.

T = W0,05/2f

### Van Deemter equation

An equation used to explain band broadening in chromatography. It represents the height equivalent of a theoretical plate (H) of a chromatographic column to the various flow and kinetic parameters which cause peak broadening. The term A is known as the multiple paths term, which allows for the different paths a solute might take when passing over particles of different sizes. Term B represents the molecular diffusion or longitudinal diffusion of the solute as it passes through the column. The term C, resistance to mass transfer is the transfer rate of the analyte between the stationary and the mobile phase. u is the linear velocity of the mobile phase as it runs through the column.

H = A + B/u + Cu