I was studying osmosis and I came across the formula for osmotic pressure. I decided to see the derivation for osmotic pressure in a dilute solution. The derivation involved an equation involving the chemical potential, fugacity and so on, which I am not familiar with. I have been introduced to very little thermodynamics. So I decided to come up with my own justification regarding the osmotic pressure formula. I want to know is there any thing wrong in my explanation.
Suppose we take a u-tube containing pure water. The level of water in both arms of the u-tube will be the same and hence also the pressure in both of the limbs. Now suppose I take a u-tube containing pure water and a dilute aqueous solution separated by a semi permeable membrane. The pure water from one limb will flow towards the other limb through the semi permeable membrane until equilibrium. In equilibrium the side of the u-tube containing the dilute solution will have a higher pressure (as seen due to greater rise in height). This extra pressure is due to the dissolved solute particles (if solute particles were not there both arms of the u-tube would have the same pressure). This extra pressure due to the solute particles is the osmotic pressure. Since the solution is very dilute, the solute-solute interactions can be neglected and we consider the solute particles as an ideal gas occupying the volume of the solution. Thus to find the pressure exerted by the solute particles we can use the ideal gas law. Hence this pressure is the osmotic pressure.
