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I know that in a mixture of different gases, we can assign every type of gas molecules a partial pressure so that the total pressure is the sum of all partial pressures. This can be extended to gas molecules dissolved in a liquid when there is a liquid phase next to a gaseous phase.

Can we also assign partial pressure to a solid that is dissolved in a liquid? For example, can we define partial pressures for ions in a $\ce{NaCl}$ solution so that

$$p_\mathrm{tot} = p(\ce{Na+}) + p(\ce{Cl-}) + p(\ce{H2O})?$$

This question came up to me when I tried to come up with an intuitive explanation for osmosis. If such a partial pressure phenomenon would exist, a solution with high concentration of solids would have a lower partial water pressure than a solution with low concentration of solids, assuming both solution have the same total pressure. This would result in a net flow of water from low concentration to high concentration if both solutions were divided by a selectively permeable membrane.

The usual explanations for osmosis I found on the internet using the chemical potential were quite unintuitive to me since chemical potential is quite an abstract concept to me. It would be nice to have an explanation on a basic level.

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    $\begingroup$ No. That is not intuitive at all. If you remove water, the dissolved stuff would simply fall at the bottom of the container,. Even with water, the only P exerted is hydrostatic. I do not see how this kind of forced analogy helps as compared to the right description of the phenomenon. $\endgroup$
    – Alchimista
    Commented Oct 25, 2021 at 11:25
  • $\begingroup$ Such an analogy would help me. I want to understand osmosis more on a molecular level. Simply accepting the mathematics does not make me feel like I truly understand whats going on. But I see your point that the analogy to the gas does not make sense. Still, there has to be some explanation whats happening on a molecular level, without refering to abstract observables from statistical mechanics, or no? $\endgroup$
    – Pehliks
    Commented Oct 25, 2021 at 11:50
  • $\begingroup$ You can explain the osmosis with pressure exerted by molecules to each other. But that is far to be an analogy to partial pressure of ideal gases. Perhaps try reading first the article Chemical potential and then Osmosis at Wikipedia. - I see that while writing this comment the answer has been added. $\endgroup$
    – Alchimista
    Commented Oct 25, 2021 at 12:00
  • $\begingroup$ But unfortunately it is not quite correct except for the part in the link. $\endgroup$
    – Alchimista
    Commented Oct 25, 2021 at 12:10

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The vapor pressure of ions like $\ce{Na+}$ and $\ce{Cl-}$ is effectively zero compared to the vapor pressure of water, so your equation is essentially correct though $p_{\mathrm{total}} = p_{\ce{H2O}}$ (assuming the system has no air). The ions do lower $p_{\ce{H2O}}$ compared to a system with pure water, and the effect (the change in pressure) is proportional to the mole fraction of ions.

As for assigning a pressure to a solution in the context of osmosis, there exists the concept of osmotic pressure, which is defined as

$$\Pi = cRT$$

Where $\Pi$ is the osmotic pressure, $c$ is the solute concentration (often multiplied by $i$, the Van't Hoff factor), $R$ is the universal gas constant and $T$ is the absolute temperature.

Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane.

In the absence of such external pressure in the semipermeable membrane system, solvent will move from the region of lower to higher osmotic pressure, i.e. the presence of solute generates an inward flux of solvent. The osmotic pressure is not related to the total pressure (like in your equation).

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  • $\begingroup$ The second part is acceptable but the first section has the defect of mixing different things and ideas, including a reference to vapour pressure. And in the second part, it is rather a P acting on the liquid and not on the pressure of ions or solute. Which is ultimately affected by the presence of the latter. $\endgroup$
    – Alchimista
    Commented Oct 25, 2021 at 12:09
  • $\begingroup$ OP asked about partial pressures and gas pressures and included an equation that adds them up to the total pressure, so I decided to mention the effects of ions on vapor pressure (which are indeed related to the total pressure) since this is where I think OP's confusion might be. As for the second part, I see that osmotic pressure is a property of the solution, not of individual solutes (I'll try to improve the answer). $\endgroup$
    – Vinícius Godim
    Commented Oct 25, 2021 at 12:42
  • $\begingroup$ Yes I think that the way the question is posed makes everything more difficult. Just saying that it is almost nonsensical won't be polite enough. I even suspect that playing enough one can create connections between the various phenomena we have already mentioned in terms of (if would be there) mechanical pressure. All this won't help OP neither. And myself I cannot write a better answer than those commonly found, as in the Osmosis page on Wikipedia etc. Perhaps you can stress the last line. In particular adding solute suck liquid inwards. The picture of OP can't even work as for it would.... $\endgroup$
    – Alchimista
    Commented Oct 25, 2021 at 13:14
  • $\begingroup$ .... require the liquid to move in order to increase its pressure. And there is no such a principle. $\endgroup$
    – Alchimista
    Commented Oct 25, 2021 at 13:18

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