Without going into an extensive treatment, it seems that this analysis
ignores osmotic pressure, and assumes that the rate of A moving upward
is exactly equal to the rate of B moving downward. The rate of movement
will be proportional to the chemical activity difference across the two
compartments. Finally, if the concentration of A is greater (than
equilibrium) below, then some of that A will react to B in the lower
compartment.
In short, if you wrote down the set of differntial equations for this
system, accounting for changes in osmotic pressure and the effect of
that on chemical activities (not concentration), then you'd find that
the whole will approach equilibrium with time, independent of the
actual values of the rate constants.
-Paul Schlosser
