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## Thursday, December 22, 2011

### Chromatography Calculations: Resolution of Chromatography Peaks,Bed Volume

Chromatography calculations

These are the equations which is used to calculate various things during chromatography including column volume, media requirements for column, resolution etc

Total or Empty column volume

Ve = π * r2 * L or 1/4 π * d2 * L

Ve = empty column volume
r = column radius
L = length of the column (or packed bed)
D = column diameter
If r (or d) and L are expressed in mm, Ve will be in µL. If in cm, then Ve in mL.

Volumetric Flow Rate (VFR) Calculation from Linear Flow Rate (LFR)

This can be useful because the chromatographic media has certain flow rate specification at which it can be operated, for example a chromatographic media specification says use 150 cm/hr flow rate so while setting up the flow rate in peristaltic pump or in other automated system like AKTA volumetric flow rate need to be calculated, using the equation below it can be calculated.

VFR (ml/min) = LFR(cm/hr) / 60 * πr2

we need 150cm/hr and the column used has a diameter of 0.5cm or 0.25cm as radius so,

VFR = 150/60 * 3.14 * (0.25)2 ;

Volumetric flow rate will be ~ 0.5 ml/min

Linear Flow Rate (LFR) Calculation from Volumetric Flow Rate (VFR)

LFR(cm/hr) = VFR(ml/min) * 60 / πr2

Similarly we need 1ml/min and the column used has a diameter of 0.5cm or 0.25cm as radius so,

LFR(cm/hr) = 1 * 60 / ( 3.14 * (0.25)2 )

Linear flow rate will be ~ 300 cm/hr

Bed Volume

Bed volume (L) = Bed height (cm) * Column cross-sectional area (cm2) / 1000

cross-sectional area = π * r2

Packed Bed Volume

Packed bed volume (L) = Column bed height (cm) * cross-sectional area (cm2) * x10-3

cross-sectional area = π * r2

Settled chromatography medium volume

Settled chromatography medium volume (L) = Packed bed volume (L) * compression factor
compression factor can be obtained from the chromatographic media specification sheet.

Slurry volume

Slurry volume (L) = Settled chromatography medium volume (L) / (slurry concentration (%) * x 10-2)

The chromatography medium volume for HIC, IEX, Affinity, Reverse Phase

The chromatography medium volume is calculated from the formula:
The chromatography medium volume (L) =

(Quantity to be bound (g) * (1+ safety margin (%) / 100)) / (Dynamic binding capacity (g/L)

The chromatography medium volume for Gel Filtration Chromatography
The chromatography medium volume (L) =
Sample volume to be processed (L) / (Sample volume in percent of total column volume (%) / 100)

Resolution (Rs)

Chromatographic peak resolution can be calculated using the following equation

Rs = (tR1 – tR2) / 0.5(W1 + W2)

Rs – Resolution

tR1 – Retention time of the first peak

tR2 – Retention time of the second peak

w1 – Width of first peak

w2 – width of second peak

Sources & References

GE Life Sciences - Chromatography medium volume calculators

Tosoh Bioscience LLC: The Chemistry of Innovation - Technical Support – Basic Chromatographic Calculations