For ideal solution, μA=μA* +RT lnxA
ln function is an increasing function, means that the higher the xA the higher the μA......(1)
Now consider osmosis. From Atkins' Physical Chemistry Ninth Edition, page 173,
osmotic pressure, π, is the pressure that must be applied to the solution to stop the influx of solvent (into solution across a semi-permeable membrane).
Here is my interpretation and thought process:
Had you not exerted π on solution, the μ(solution)< μ(solvent) based on (1) because lnxA is negative for xA<1, so by Second Law, the osmosis is spontaneous and solvent should move from pure solvent (high μ) to solution (low μ). Sounds right.
However, during this process, μ(pure solvent) unchanged (μ is intensive, not affected by amount) but μ(solution) increases due to dilution. Based on (1), for the solution, since xA increases μ(solution) must also increase. Although the process stops when μ(solution)=μ(pure solvent), the effect is that μ increases. μ increases would in turn imply ΔG>0 which means non-spontaneous, but as far as I know osmosis is spontaneous, so where is my misconception?