Question

How molar mass of a solute is determined from osmotic pressure measurements?

Answer 1

Hint: Osmotic pressure is directly proportional to the amount of solute present in a volume of a solution.

Complete step by step answer:
Osmotic pressure is the pressure developed on the solution side due to the net flow of the solvent molecules through a semipermeable membrane. As we know that a solution of its own has only vapour pressure, it will develop osmotic pressure only when osmosis (osmosis always occur from a dilute solution into concentrated solution) takes place by placing it in contact with a solvent or less concentrated solution through a semipermeable membrane. Thus we can say that the osmotic pressure is the pressure required to prevent osmosis.
According to Boyle-Van’t Hoff Law, the osmotic pressure ($\pi $) of a dilute solution is directly proportional to its molar concentration at constant temperature.
$\pi \,\alpha \,C$ (at constant temperature)
We know that,
$C = \dfrac{n}{V}$ (where$n$is the number of moles of the solute dissolved in $V$ volume of the solution)
According to Gay-Lussac Van’t Hoff Law, the osmotic pressure of a dilute solution is directly proportional to the temperature $T$ (Kelvin), with concentration remaining the same.
$\pi \,\alpha \,T$
Combining the two laws we get,
$\pi \,\alpha \,CT$
$\pi \, = R\,CT$
Where,$R$ is a constant called solution constant.
Since, $C = \dfrac{n}{V}$
$
  \pi = \dfrac{{nRT}}{V} \\
   \Rightarrow \pi V = nRT \\
 $
Osmotic pressure is a colligative property because it depends upon the number of moles of the solute $(n)$dissolved in a given volume $(V)$of the solution.
Let, $n = \dfrac{{{W_B}}}{{{M_B}}}$
where,${W_B} = $ mass of the solute and ${M_B} = $ molar mass of the solute
$\pi V = (\dfrac{{{W_B}}}{{{M_B}}})RT$
Therefore, the molar mass of the solute, ${M_B} = \dfrac{{({W_B} \times R \times T)}}{{\pi \times V}}$
Hence, the observed molar mass can match the normal molar mass, provided that the solute is non-volatile, the solution is dilute and also the solute does not undergo association or dissociation in the solution.

Note:
We know that all the colligative properties are helpful in determining the observed molar mass of the solute. Out of these, osmotic pressure is the best although it is sometimes inconvenient to prepare different semi permeable membranes. In fact, osmotic pressure can be determined at room temperature whereas other colligative properties such as elevation in boiling point and depression in freezing point cannot be evaluated at room temperature. It is particularly useful for biomolecules and polymers with high molecular masses such as proteins because in their dilute solutions both elevation in boiling point ($\vartriangle {T_b}$) and depression in freezing point ($\vartriangle {T_f}$) are too small to be measured accurately. Moreover, the polymers and biomolecules are generally not stable at higher temperature.