# Plate Theory and Extensions - Chromatographic Dead Volumes > Page 34

_{ }

The
expression for the thermodynamic dead volume is more complex than that for the
kinetic dead volume and will depend on the size of the solute molecule. In
common with the kinetic dead volume, it contains the volume of moving phase V_{I(m)}. However,it also includes that
portion of the interstitial volume that is size dependent (Y), together with the pore volume available
to the solute (also size dependent (W).
Equation (39) shows the major retention factor, (xK_{3}V_{S(A)}),
is also molecular size dependent ((x)
is not unity), thus, unless the values for (Y),
(W) and (x)
are available or can be determined, it is not possible to determine the
retention volume difference between two solutes accurately. This is particularly true for LC, when
porous stationary phases (supported on silica) are used and if the solute
molecules differ significantly in size. The experimental determination of (Y), (W)
and (x) is difficult, although
theoretically possible, and can be lengthy and tedious. Equation (39) has
important implications in the measurement of the capacity factor (k'). Using
equation (39) the equation for (k') can be seen to be

_{ }

which simplifies to

_{ }(40)

Equation
(40) shows that the same errors are involved in the measurement of (k') as
those in the measurement of the thermodynamic dead volume. If the solute is
well retained, *i.e.*,

_{ }

* _{
}* WK

_{2}V

_{p}

_{(2)}+ xK

_{3}V

_{S(A) >> }V

_{I(m)}+ YV

_{I(S)}+ WV

_{p}

_{(1)}

_{ }

then the corrected retention volume can be used for thermodynamic calculations with greater confidence.