The distribution of a solute, S, between the mobile phase and stationary phase can be represented by an equilibrium reaction

**Capacity Factor**

The distribution of a solute,
S, between the mobile phase
and stationary phase
can be represented by an equilibrium reaction

S_{m} < = = = = > S_{s}

and its associated partition coefficient, *K*_{D}, and distribution ratio, *D,*

12.2

where the subscripts m and s refer to the mobile
phase and stationary phase, respec-
tively. As long as the
solute is not
involved in any
additional equilibria in either the mobile phase or stationary phase, the equilibrium partition coefficient and the dis- tribution ratio will be the same.

Conservation of mass requires that the total moles of solute
remain constant throughout the separation, thus

(moles S)_{tot} = (moles S)_{m} + (moles S)_{s }**â€¦â€¦â€¦â€¦..12.3**

Solving equation 12.3 for the moles of solute in the stationary phase and substitut- ing into equation 12.2 gives

where *V*_{m} and *V*_{s} are the volumes
of the mobile and stationary phases. Rearranging
and solving for the fraction of solute in the mobile
phase, *f*_{m}, gives

Note that this equation is identical to that describing the extraction of a solute
in a liquidâ€“liquid extraction. Since the volumes
of the sta- tionary and mobile
phase may not be known,
equation 12.4 is simplified by dividing
both the numerator and denominator by *V*_{m}; thus

is the soluteâ€™s **capacity factor.**

A soluteâ€™s capacity
factor can be determined from a chromatogram by measur- ing the columnâ€™s void time, *t*_{m}, and the soluteâ€™s
retention time, *t*_{r} (see
Figure 12.7). The mobile
phaseâ€™s average linear
velocity, *u, *is equal
to the length of the column, *L, *divided by the time
required to elute
a nonretained solute.

12.7

By the same reasoning, the soluteâ€™s average
linear velocity, *v, *is

12.8

The solute can
only move through
the column when
it is in the mobile
phase. Its average linear velocity, therefore, is simply the product of the mobile phaseâ€™s aver- age
linear velocity and the fraction
of solute present
in the mobile phase.

*v *=
*uf*_{m }**â€¦â€¦â€¦â€¦â€¦â€¦12.9**

Substituting equations 12.5, 12.7, and 12.8 into equation 12.9
gives

Finally, solving this equation for *k*â€™ gives

12.10

where *t*_{r}â€™ is known as the **adjusted retention time.**

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Modern Analytical Chemistry: Chromatographic and Electrophoretic Methods : Capacity Factor - Theory of Column Chromatography |

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