# Osmosis, osmotic pressure, vapour pressure...

by Taturana
Tags: osmosis, osmotic, pressure, vapour
 P: 109 Why does osmosis happens? Does osmosis happens when we have osmotic pressure difference between the two solutions (that are connected by a membrane)? Does osmosis happens when we have two solutions of different concentrations? My professor told that osmosis happens because of the vapour pressure difference between the solutions. But I didn't understand what vapour pressure has to do with osmosis. Can you explain me that, please? I've been thinking too and is the vapour pressure of a solution numerically equal to the osmotic pressure of that solution? I see this relation because I know the more concentred is the solution the bigger is it's vapour pressure... that's right? How do I calculate vapour pressure? (Can I use p V = n R T?) Does density of the solutions has anything to do with osmosis? And what about hidrostatic pressure? Thank you for the help, Rafael Andreatta
 Sci Advisor P: 5,544 Osmotic pressure gradients arise from spatial changes in concentration of a solute, and usually it's in the context of aqueous solutions. I suppose it can be related to a vapor pressure, but I don't see what the advantage is. http://en.wikipedia.org/wiki/Osmotic_pressure Osmotic pressure is indeed a pressure, and can balance a hydrostatic pressure head if, for example, a semipermeable membrane is used to separate the two solutions. There's a (IIRC) Norwegian company what is trying to extract usable energy by exploiting the osmotic pressure difference between salt and fresh water, but I don't see how it's economical. Now, if you have multiple solutes and a membrane that can (as a suggestive example) distinguish between K and Na ions, it's possible to set up directed transport using the osmotic pressure gradient of either K or Na as well as use the electric potential that is established by the imbalance of ions. http://en.wikipedia.org/wiki/Gibbs-Donnan_effect
 Sci Advisor HW Helper PF Gold P: 2,532 A simple way of visualizing osmosis is to consider a saline solution and pure water separated by a membrane. The concentration of water is lower on the saline side (it has to be <100% due to the dissolved salt), so there's a driving force for water to diffuse from the pure water side into the saline solution. We can tie osmosis and vapor pressure together with the chemical potential. The chemical potential is the driving force to move matter around, just as electrical potential is the driving force to move electric charges around. Matter tends to move to where its chemical potential will be lowest. The chemical potential often increases with increasing concentration and vice versa. Since concentration is a lot easier to visualize, mechanisms like diffusion and osmosis (which are actually driven by changes in chemical potential) are often modeled as simply being driven by concentration differences. Fick's Laws of diffusion, for example, are expressed in terms of concentration gradients. The chemical potential $\mu$ is defined as $$\mu=\mu_0+RT\ln a$$ where $\mu_0$ is just a reference constant for that material, R is the gas constant, T is the temperature, and a is called the activity. It's the activity that is often approximately proportional to concentration; the activity is zero when the material is absent and one when the material is pure. Now here's the connection: if the material is in equilibrium with its own vapor, the vapor pressure p will equal the activity a. This lets us calculate the vapor pressure of any material, since the chemical potential is also equal to $H-TS$ where H is the molar enthalpy and S is the molar entropy. At equilibrium, by definition, the chemical potential of the condensed state (lets say it's a liquid) and the gas is equal: $$\mu_\mathrm{gas}=\mu_\mathrm{liquid}$$ $$\mu_\mathrm{0,gas}+RT\ln p_\mathrm{gas}=\mu_\mathrm{0,liquid}+RT\ln a_\mathrm{liquid}$$ $$RT\ln p_\mathrm{gas}=-(\mu_\mathrm{0,gas}-\mu_\mathrm{0,liquid})$$ where we've assumed the liquid to be pure ($a=1$, as stated above). This is equivalent to $$RT\ln p_\mathrm{gas}=-(\Delta H-T\Delta S)$$ where $\Delta H$ and $\Delta S$ are the change in enthalpy and entropy when the liquid boils. With a little algebra, we obtain $$p\propto\exp(-\Delta H/RT)$$ and thus see a relationship between vapor pressure, heat of vaporization, and temperature. I hope this helps answer your question. Also, I concur that vapor pressure increases with concentration, so long as the assumption holds that chemical potential increases with concentration. The density of materials comes into play because denser materials generally take more energy to melt and boil, and so $\Delta H$ is higher. Thus water, for example, has a much higher vapor pressure than aluminum, with has a much higher vapor pressure than dense osmium. Does this all make sense?
P: 176
Osmosis, osmotic pressure, vapour pressure...

 Quote by Mapes The chemical potential often increases with increasing concentration and vice versa.
I thought that chemical potential decreases, which is why water has a higher chemical potential than the solution?