# Entropy as the driving force for osmosis

How is entropy responsible for osmosis and is movement of solvent possible from its higher concentration to lower concentration?

By concentration, I will be referring to the concentration of solvent molecules below.

I understand that the entropy of the universe tends to increase. But I do not understand how this principle applies to osmosis. Basically, in osmosis the solvent moves from its higher concentration to lower concentration. Here, it appears that the entropy of the lower concentration side is increasing and the entropy of the higher concentration of solvent side is decreasing. How can we claim that the net change is increase in entropy?

Also, is the reverse process i.e. movement of solvent molecules from lower concentration side to their higher concentration side ever possible (= thermodynamically favorable) without the presence of external driving forces?

Notes: The change in entropy of a gas with volume is $\displaystyle \frac{\partial S}{\partial V}=\frac{R}{V}$. In a dilute solution the mole fraction $x_s \sim 1/V$ where $V$ is the volume of the solvent (or solution) with one mole of solute. As $G-G^0=-T S = RT\ln(x_s)$ then $\displaystyle \frac{\partial S}{\partial V}=\frac{R}{V}$. Thus the change in entropy is the same for the dilution of a gas as for the solute in a dilute solution.