What is osmotic pressure?

From a purely conceptual point of view, let's assume that there is a tank of distilled water that I want to use to demonstrate osmotic pressure. I would find a small diameter (e.g., 2 cm) clear cylinder, that is relatively tall (e.g., 1 m). On one end of the cylinder, I would fasten a semi-permeable membrane that allows water to freely pass through it, but does not allow a bigger molecule, such as sugar to pass through it. Note that this membrane must be attached in a way that it is tightly sealed on the edges of the tube.

Next, I would mix up a moderately concentrated solution of sugar-water, put food coloring in it, and pour this solution into the tube to a height of 10 cm. The tube would then be placed in the tank of distilled water, such that the initial liquid level of the tube contents was at the same level as the water level in the tank. In other words, the bottom of the tube, with the semi-permeable membrane on the bottom, is at a depth of 10 cm in the water tank.

At a molecular level, water and sugar are trying to pass through the membrane, but sugar is blocked from doing so. A particular water molecule does not know which side of the membrane it is on, and that molecule is free to pass through the membrane. Since there is a higher concentration of water molecules on the outside of the tube, in the distilled water, there is a higher rate of water molecules hitting the membrane from the outside of the tube than from the inside of the tube, which has a lower of concentration of water molecules due to the dissolved sugar that is in the water on the inside of the tube. Because of this, the rate at which molecules from the outside of the tube pass through the membrane to enter the tube is higher than the rate at which water molecules pass through the membrane and exit the tube. This leads to a net flow of water molecules from an area of high concentration (the outside of the tube) to an area of lower concentration (the inside of the tube). Because of this, the liquid level inside the tube rises substantially above its initial height.

As the water inside the tube rises, the pressure on the inside and at the bottom of the tube rises due to the difference in height between the levels on each side of the tube, and due to the different densities of the liquids inside and outside the tube. As this happens, the rate of water molecules striking the membrane from inside the tube increases. At some point, the pressure inside the tube becomes high enough for the rate of water molecules inside the tube to exit the tube as fast as the water molecules from outside the tube are entering the tube. This pressure, which is the difference in pressure across the membrane, is what is referred to as osmotic pressure.

Imagine you have a U-shaped tube filled with pure water, with a semipermeable membrane that only water can go through and that separates the left and right parts of the U. (I am taking as a reference the image below, from the Wikipedia article you linked)

Now if you pour some solute in say the left branch, some of the water will move from right to left, in order to balance the difference in concentration between the two parts. It is as if a pressure $pi$ is pushing water from right to left; $pi$ increases with the concentration of the solution and it turns out to follow an ideal-gas-like behaviour: $$pi V = n R T $$ where $n$ is the number of moles of solute. This law can also be written (dividing both sides by $V$) as: $$pi = M R T$$ where $Mequiv {nover V}$ is the molarity.

Now to explain the two sentences you have referred:

• if you wanted to prevent this process from happening you would have to apply an extra pressure equal to $pi$ on the left solution;

• you can also think of $pi$ as the difference between the hydrostatic pressures on the right and left part of the membrane at equilibrium, due to the different levels of the liquids.