Question

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

Hint:

Osmotic pressure, a colligative property, is particularly valuable for determining the molar mass of large molecules such as proteins and polymers, which are difficult to analyze using other methods.

Answer 1

Osmotic pressure \( (\pi) \) is defined as the pressure needed to halt the transfer of solvent molecules through a semipermeable membrane from a less concentrated solution to a more concentrated one. This pressure can be calculated using the van’t Hoff equation: \[ \pi = C R T \] where: 
- \( \pi \) = osmotic pressure, 
- \( C \) = molar concentration of the solute in the solution, 
- \( R \) = universal gas constant \( (0.0821 \, \text{L atm mol}^{-1} \text{ K}^{-1}) \), - \( T \) = temperature in Kelvin. 
To determine the Molar Mass using Osmotic Pressure: The molar concentration \( (C) \) is described by: \[ C = \frac{n}{V} = \frac{m}{M V} \] with \( n \) being the moles of solute, \( m \) the mass of the solute, and \( M \) the molar mass of the solute. 
Rearranging the osmotic pressure equation provides: \[ \pi V = \frac{mRT}{M} \] To find \( M \): \[ M = \frac{mRT}{\pi V} \] By measuring osmotic pressure \( (\pi) \), and knowing the mass \( (m) \) and volume \( (V) \) of the solution, the molar mass \( (M) \) of the solute can be accurately calculated.