Recently, I studied Prof.Suo's lecture "Advanced Elasticity", node/725.
The following is explaination about osmosis pressure in the lecture.
A bag contains a liquid of volume V, with N particles dispersed in the liquid. The particles can be of any size. When the particles are molecules, we call them solutes. When the particles are somewhat larger, we call them colloids. The bag is immersed in a reservoir of the same liquid but without any such particles. The liquid is incompressible, but we can change the volume of the liquid inside the bag by allowing the molecules of the liquid to permeate through the skin of the bag. The particles in the bag, however, cannot permeate through the skin. Such a skin is semi-permeable.
The physics of this situation is analogous to the ideal gas, provided that the concentration of the particles is dilute. Every particle is free to explore the entire volume in the bag. The liquid molecules permeate through the skin to drive the composite system (the bag and the reservoir) to reach equilibrium. Consequently, V is a variable. Recall once again the defining equation of the pressure,
p=T dlog(omega)/dV.
We obtain that
p=TN/V
This pressure is known as the osmotic pressure.
If we treat N is constant, p is inversely proportional to V. when V is larger, p is smaller?
I have hardly understood in the direct sense. when the molecules of the liquid permeate through semi-permeable skin, I think p is larger and larger in the sense because the height difference of two sides is larger and larger in the process of permeatation.
Why is it inverse to our sense? When the molecules of the liquid permeate through semi-permeable skin, V is increased , is P decreased?
Yhe lecture is available at node/885
Re: About osmotic pressure
To recap, in the equation,
p = TN/V,
p is the osmotic pression, T the temperature (in unit of energy), N the number of particles that cannot go through the skin, and V the volume of the liquid encloded by the skin.
N/V is the concentration of the particles. When the volume of liquid V is large, the concentration of particles is low, so that the osmotic pressure is small.
The osmotic pressure p is balanced by other forces. In the example used in the lecture notes, the osmotic pressure is balanced by the presure due to the difference in the heights of the liquid on the two sides of the skin.
Here is a way to see this effect. The skin separates a solution and a pure solvent. The solvent molecules can go through the skin, but the solute molecules cannot. The solvent molecules go from the side of pure solvent to the side of solution, so that the solution becomes more dilute.
the osmotic pressure in the non-balance state
Dear Prof.Suo,
Thank you for your reply. I totally agree with your explaination. but your explaination is only adequate for osmotic pressure in the balance state
what I am confused is osmotic pressure in the permeating process( I think the process is non-balance state, the formula mentioned above may be not applicable)
when the molecules of the liquid permeating through semi-permeable skin, IN THE PROCESS, the osmotic pressure p is increasing or decreasing? I think it is increasing, because the height difference of two sides is increasing in the permeating process.
the osmotic pressure p is increasing until it reached balance state.
If the formula p = TN/V is applicable to the permeating process, the osmotic pressure p is smaler and smaller because V is increasing in the process.
So, my question is, Is the formula p = TN/V applicable to the permeating process? If not, what change does the osmotic pressure p undergo in the permeating process(transient non-banlace state)? I think the osmotic pressure p is direct proportional to delta(V) [the volume change of solvent ] in the permeating process, is it right?
Thank you for your help!
best regards
Ma
Re: the osmotic pressure in the non-balance state
If you assume that solute molecules diffuse rapidly in the solution, such that the concentration of the solute reaches equilibrium rapidly within the solution, and the permeation of the solvent molecules through the skin is relatively slow, then you can use the formula p=TN/V to calculate the osmotic pressure.
The osmotic pressure in the solution drives the volume V of the solution to increase by promoting solvent molecules to permeate through the skin from the pure solvent to the solution.
A presure added mechanically by a piston on the solution has an oposite effect: the mechanical pressure added on to the solution causes the volume of the solution to decrease by pushing solvent molecules to permeate through the skin from the solution to the pure solvent.
When the osmotic pressure equals the difference in the presures due to the difference in the heights of the solution and the pure solvent, permeation stops, and equilibrium is reached.