PARTITION CHROMATOGRAPHY, AN ISENTROPIC SEPARATION PROCESS A. KLINKENBERG N. V. De Bataafsche Petroleum Maatschappij (Royal Dutch-Shell Group), The Hague, Holland
TEE result of a partition-chromatographic separation under ideal conditions may be expressed in a diagram showing concentrations against effluent volume, as follows: CONCENTRATION
I; I
i
1
>
j
j:
I, 1
!
(OUT)
I
The solvent originally associated with the solutes will appear after a volume V has passed through the column, V simply being the hold-up of moving phase in the column. A solute will be retarded. If the volume of stagnant phase in the column is v and the partition coefficient over stagnant and moving phase is K, the volume v of stagnant phase is equivalent to a volume Kv of moving phase, i. e . , the solute will appear after a volume V Kv has passed. BY a snitable choice of solvents tn.0 components, A and B, may be given differentK values and may thus be separated. After the separation the column is back in its original state. We then have separated two solutes without doing any work. The friction in the column clearly has no influence because it is the same as would be observed for the pure solvent. One is now tempted to conclude that the separation as described is a reversal of a diffusion process. Such diffusion, however, according to the second law of thermodynamics, should be irreversible. The purpose of this communication is to draw attention to this paradox and to give its solution. The process is indeed an isentropic process under the ideal conditions postulated, when a concentration profile does not change when passing through the column. These ideal conditions include immediate equilibrium, i. e., an infinite number of ideal stages, so that all transfer takes place with an infinitely small driving force, i. e., under reversible conditions. Also, other irreversibilities, such as diffusion and eddy diffusion, are assumed to be absent.
Indeed, the laws for the entropy of solutes in solution show the entropy in the mixed solution to be equal to the sum of the entropies in the separated solutions. I t is interesting to note that by feeding the separated solutions with an appropriate time lag to the same column, we may, again isentropically, restore the original state. The solution of the paradox is that the process is not the reversal of a diffusion process. If we mix the separated solutions by diffusion the mixture has double the original volume. We must therefore concentrate the separated solutions, that is, decrease their entropies, before we can restore the original state by diffusion. Thus. Isentropic chromatagraphy
-
Original mixture Scale
R
Separated solutions at original concentrations
+
/
J
\
Concentrating
Irreversible tmpies diffusion
/
Separated solutions each a t double the original concentration
+
hi^ reasoning is perfectly analogous to the one used in the well knom derivation of the entropyof gaseous mixtures with the aid of semipermeable membranes:
T ent"pies
Air at 1 atm.
2
Irreversible diffusion
-- Isentropic separation -
Oxygen s t 0 . 2 atm. Nitrogen at 0.8 atm.
J
Compression
Oxygen a t 1 atm. \Nitrogen a t 1 atm.'g
Students of thermodynamics often find the derivation of the entropy of a gaseous mixture rather difficult. Perhaps the impossibility of experimental realization of the membranes is partly responsible for this. It should therefore be of interest that the separation of gases has its analogy in partition chromatography. I t is true that ideal partition chromatography cannot be realized. However, in actual partition chromatography the result is so close to the ideal one, that the idealization of the concentration profiles, as shown in the figure, is considered acceptable xithout comment.
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