The equations so far apply only to binary fluid mixtures. For
more than two constituents, say K, there will exist K values
of the mass ratios 
. These are not independent since the
totals of the individual masses of constituents must add up to
the mass of the mixture. Hence, because of the conservation of
mass
There are also K different values of non-advective flux
associated with the K constituents, and these are related
by
which follows from the definition of velocity and the conservation
of mass. Thus there are really only K-1 independent values of
and 
, and the functions of state such as
, 
, etc. depend therefore on K+1 variables, e.g.
There are K-1 virtual chemical potentials defined by
with the subscript 
signifying that all S except
and are held constant. These potentials are related to
the K Gibbsian partial molar chemical potentials 
as follows
...
where the 
are the molecular (or atomic) weights of the
K different constituents. These relations state that the
K Gibbs potentials are not all independent with the interdependence
expressed by Eqs. (4.201-5) being consistent with the
Gibbs-Duhem relation for systems of several components.