## Hplc column volume calculator

Calculating the column volume and thereby determining the column void volume and capacity factors are having supreme priority and primitive relevancy in HPLC method development.

Firstly we have to understand that Column is a Cylinder contains packed material. **So the formula for Volume of the cylinder(Hallow) is**

Volume of hallow cylinder=**pi × r2× h**

But LC column contains Packed material.Generally it occupies 65% to 70% of the column volume.Hence we need to the correction for the calculation. The formula will be like this then in that case:

**Volume of the Column(V Zero)**=(Pi×r2×l×pore volume)

Here r and l are in Cms;Pi=3.14

- r=Radius and l=Length or height of the column.

I will try to give an example calculation:

Assume Column Dimensions:250mmX4.6mm,5um

then Volume of Column=3.14*0.23*0.23*0.7 gives the result of 2.908mL(If r and l were taken as Cms) and 2908uL(If r and l were taken as mms)

Here we assumed pore volume as 70%(=0.7).ie interstitial pores of the silica and middle cavity of the column together as **pore volume**.

From this if you have the Retention time(tR) of the un retained compound(Generally Uracil for RP columns and 1,3,5-Tri-t-butyl benzene for Normal phase columns we can calculate **Void time or Dead Time(t zero)**

If tR of Uracil if for eg: 5 mins and Flow rate is 1.5ml/min then

t zero(t0) =Void volume/Flow rate

=2.908mL/1.5ml/min=1.94min.

**Retention factor(k):**

=(t R-t 0)/t0

=(5–1.94)/1.94=1.58

The retention factor (k) is another measure of retention. It is the ratio of the amount of time a solute spends in the stationary and mobile phases (carrier gas).For example, a solute with a k = 6 is twice as retained by the stationary phase (but not the column) as a solute with a k = 3. The retention factor does not provide absolute retention information; it provides relative retention information. An unretained compound has k = 0.

V zero,t zero and Retention factor are interlinked one to each other

The following equations are for the novice chromatographer. More advanced calculations can be found on the system suitability and pressure-flow pages.

1. Calculation of total column volume (also used for calculating bed volume)

2. Calculation of empty column linear flow rate from volumetric flow rate

3. Calculation of volumetric flow rate from empty column linear flow rate

**1. Calculation of total column volume (also used for calculating bed volume):**

Where: *V* = calculated column volume*r* = column radius*L* = length of the column (or packed bed)

**2. Calculation of empty column linear flow rate from volumetric flow rate:**

Where:*u* = Linear flow rate (cm/hr)*F* = volumetric flow rate (mL/hr) [multiply mL/min x 60 min/hr]*r* = column radius (cm)

**3. Calculation of volumetric flow rate from empty column linear flow rate**

Where:*F* = volumetric flow rate (mL/hr) [divide by 60 min/hr to get mL/min]*u* = Linear flow rate (cm/hr)*r* = column radius (cm)

The term column volume, typically abbreviated CV, is a value used to help determine separation quality and loading capacity. But how can this concept and its definition be better understood? Bob Bickler explains it all on the Flash Purification Blog.

Some chemists think the internal volume of the cartridge *without* packing material inside is the column volume. While useful in determining scale-up factors, the empty column’s volume is not the CV. The CV of any column or cartridge is the volume inside of a packed cartridge *not* occupied by the media. This volume includes both the interstitial volume (volume outside of the particles) and the media’s own internal porosity (pore volume). Combined, the two volumes constitute 70% to 80% of the packed cartridge’s volume. Of course this means that the media only occupies 20% to 30% of the space in the cartridge.

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