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Thermodynamics
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The distribution of the solute between the mobile and stationary phase is the origin of retention of a solute in chromatography, see e.g. the animation. Under normal chromatographic conditions this distribution is approximately equal to the equilibrium distribution.

 

The equilibrium constant for the distribution is proportional to the retention factor of the solute, i.e.:

 

k = F * K

 

where

 

k = retention factor ( sometimes also called the capacity factor )

 

F = the column phase ratio

 

K = the equilibrium constant for the distribution between the mobile and stationary phase.

 

( Note: This equation is based on a number of assumptions that not will be further discussed here.)

 

The important point is that the equilibrium constant is a thermodynamic quantity. Therefore, the following relation from thermodynamics applies:

 

DG0 = DH0 - TDS               ( 1 )

 

where

 

DG0 = the standard free energy of adsorption to the stationary phase

 

DH0 = the standard enthalpy of adsorption to the stationary phase.

 

DS0 = the standard entropy of adsorption to the stationary phase.

 

T = the temperature in the system.

 

Thermodynamics also gives us the following relation between the standard free energy of adsortion and the equilibrium constant for adsorption.

 

DG0 = - RT * ln K                         ( 2 )

 

where R is the gas constant and ln the natural logarithm.

 

By combining equations 1 and 2 we see that, at a give temperature, a high value for the equilibrium constant can be achieved in two ways: a high negative numerical value for DH0 and/or a high positive value for DS0.

 

The numerical value of DH0 mainly reflects the difference in the solutes molecular interaction with the mobile and stationary phase. A high negative numerical value is obtained when the interactions in the stationary phase is much more favorable than in the mobile phase.

 

The value of DS0 reflects the change in molecular movements and disorder as the solute is transferred from the mobile to the stationary phase. A large positive value means that the magnitude of the "randomness" and "disorder" increases.

 

In many reversed phase systems the enthalpic term determines the magnitude of retention. However, it is important to note that retention also is dependent on entropy changes. An increase of entropy upon adsorption of the solute to the stationary phase also increases retention. It is well known from e.g. physical chemistry that the hydrophobic interaction ( hydrophobic effect ) is an entropic effect.

 

 

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