Well, we all learned at one time or another that systems tend
towards equilibrium, and since only water can cross the selectively
permeable membrane in these simulations, this tendency towards
equilibrium "causes" osmosis. Continuing this line of
reasoning, water molecules, like solute molecules, seem to diffuse
down their own "concentration gradient", producing osmosis.
If we consider a "concentration gradient" to be equivalent
to a "gradient of mole fractions", this equilibrium
statement is accurate and, moreover, correctly indicates the direction
of water movement. Why isn't such an explanation completely satisfactory?
For one thing, it's unwieldy: the "concentration of water"
is difficult to measure and hard to relate in any meaningful way
to osmosis. Also, something significant is missing from the explanation!
The equilibrium approach is unsatisfactory for two more fundamental
reasons. First it brings us no closer to understanding what causes
osmosis in a molecular sense, that is, how random water movement
produces the difference in volume. Why? Because equilibrium
statements provide no information about mechanisms.
(In more technical jargon, answers couched in "equilibrium"
terms deal only with the initial and final states of a system
and are independent of the path taken between the states. Scientists
interested in mechanisms, however, investigate and characterize
the various paths involved!) Secondly, and as you perhaps have
already guessed, the equilibrium approach tells us the direction
osmosis takes when two compartments approach equilibrium, but
it doesn't provide any means for predicting the magnitude of osmosis
or for measuring such important parameters as the velocity of
solvent diffusion.
Fortunately, these issues are interrelated: understanding the
underlying mechanism will help us forge a quantitative description
of osmosis, and vice-versa.