Question

Molecular mass of NaCl determined by osmotic pressure measurement is found to be half of the actual value. Explain

Answer 1

Hint: Understand the colligative property called osmotic pressure. Identify whether NaCl dissociates or not. Along with the general formula for osmotic pressure, we need to multiply it with one more term called the Van't Hoff factor. So, understand the calculation of that as well.

Complete Solution :
Let us first find the relation between molecular mass, osmotic pressure and colligative properties.
- Osmotic Pressure is the pressure applied to stop the flow of solvent molecules through a semipermeable membrane from a diluted solution to concentrated solution.
Mathematically it is given as:
$\mathrm{\Pi }$ =CRT
Where,
$\mathrm{\Pi }$ = osmotic pressure
C= Molar concentration of the solution
R= Universal gas constant
T= Temperature

Molar concentration of a solution containing $w_2$ grams of solute whose molar mass is $M_2$, and the total volume of the solution is V litres, can be expressed as:
C = ${\displaystyle \frac{w_2}{V\times M_2}}$
 - So we can now write the osmotic pressure as:
$\mathrm{\Pi }$= ${\displaystyle \frac{w_{2}RT}{V\times M_2}}$
On rearranging the above equation we get,
$M_2$= ${\displaystyle \frac{w_{2}RT}{\mathrm{\Pi }V}}$

- NaCl undergoes complete dissolution into $N{a}^{+}$ and $C{l}^{-}$ ions. So, the total number of particles will be 2 times the number of molecules of NaCl.
- As we know that the colligative properties are directly proportional to the number of particles. Hence molar mass is inversely proportional to the number of particles.
So the molecular mass of NaCl determined by osmotic pressure measurement is found to be half of the actual value.

Note: It is important to understand that the colligative properties are dependent only on the number of particles and not on the nature of the compounds. For example, 100 g of glucose and 100 g of urea will cause the same change in colligative properties irrespective of their nature and working mechanism.