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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?

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(a) The tendency for the solute undergoing diffusion to occupy as large a volume as possible is similar to that of a gas filling the volume available to it and in each case the driving cause is the increase in entropy. In any distribution of particles there are more ways of distributing them in a larger volume than in a smaller one.

Recall that as the solvent enters the concentrated solution the solution volume increases and this continues until the chemical potential on either side of the semi-permeable membrane is equalised. The pressure is also increased as solution is pushed up into a column, the difference in pressure is the osmotic pressure.

(b) From the statements above you can see that reverse osmosis cannot occur without applying external energy.

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.

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  • $\begingroup$ " Recall that as the solvent enters the concentrated solution the solution volume increases and this continues until the chemical potential on either side of the semi-permeable membrane is equalised. " What about the decrease of the volume on the other side? $\endgroup$ – Abcd Aug 28 '18 at 15:33
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    $\begingroup$ Any change in the pure solvent's entropy is balanced by the opposite change of the solvent's entropy in the solution side of the semi-permeable membrane plus the increase in entropy due to the presence of the solute as the volume increases. Nothing would happen if there was no solute. $\endgroup$ – porphyrin Aug 28 '18 at 21:40

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