Osmosis and hydrostatic pressure
Osmosis is defined as the flow of water/solvent molecules through a semipermeable membrane from a region of low to high solute concentration, until equilibrium is established.
To counter osmotic flow, some pressure must be applied to the solution in order to prevent pure solvent from going through the semipermeable membrane separating the two liquids; this is known as the osmotic pressure.
The osmotic pressure is the pressure required to counter, not sustain, osmosis.
The osmotic pressure can be approximated by using the following formula: $\Pi = i M R T$ .
U- Tube showing osmotic pressure. On the left side of the U-tube is an aqueous solution, and on the right side is pure water. The pure water is trying to dilute the solution by travelling through the semipermeable membrane. Eventually the added weight of the extra water on the left causes enough pressure to stop osmosis.
Osmotic pressure is the pressure that needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane. Osmotic pressure can also be explained as the pressure necessary to nullify osmosis. One way to stop osmosis is to increase the hydrostatic pressure on the solution side of the membrane; this ultimately squeezes the solvent molecules closer together, increasing their “escaping tendency.” The escaping tendency of the solution can be raised until it eventually equals that of the molecules in the pure solvent; at this point, osmosis will cease. The osmotic pressure is the pressure required to achieve osmotic equilibrium.
Osmotic pressure. Osmotic pressure is the pressure required to stop osmosis.
The osmotic pressure (II) of an ideal solution can be approximated by the Morse equation:
$\Pi = i M R T$
Here, i is the van ‘t Hoff factor, M is the molarity of the solution, R is the gas constant, and T is the absolute temperature in Kelvin. We can see from this equation that the amount of solute present in the solution will directly affect the osmotic pressure of the system.
Example
What is the osmotic pressure of a 1.35 M solution of NaCl at 25 $^\circ$C?
First, fill in all of the necessary information, and then solve:
i = 2 (NaCl breaks into two particles)
M = 1.35 $\frac{moles}{L}$
R = 0.0821 $\frac{L\times atm}{K \times mol}$
T = 25 $^\circ$C + 273 = 298 K
$\Pi = 2 \times 1.35 \times 0.0821 \times 298$
$\Pi = 66.1\ atm$