What is osmotic pressure? How will you determine molar mass of solute from osmotic pressure?

Answer: \(M_2 = \dfrac{W_2RT}{\pi V}\)

Osmotic pressure is the excess hydrostatic pressure that must be applied to the solution to just stop the flow of solvent into it (osmosis) through a semipermeable membrane separating it from the pure solvent. It is denoted by \(\pi\).

For dilute solutions, the van't Hoff equation is \(\pi = CRT\), where C is the molar concentration: \(C = \dfrac{n_2}{V}\).

If \(W_2\) g of solute of molar mass \(M_2\) is dissolved in V dm\(^3\) of solution, \(n_2 = \dfrac{W_2}{M_2}\):

\(\pi = \dfrac{W_2RT}{M_2V}\quad\therefore\quad M_2 = \dfrac{W_2RT}{\pi V}\)

Measuring \(\pi\) at temperature T for a known mass of solute in a known volume of solution gives the molar mass. The method is useful for polymers and proteins because it works at room temperature and \(\pi\) is large even for dilute solutions.