Question

Which of the following colligative properties can provide molar mass of proteins (or polymers or colloids) with the greatest precision?
A. Osmotic pressure
B. Elevation in boiling point
C. Depression in freezing point
D. Relative lowering of vapour pressure

Answer 1

Hint: Osmotic pressure, elevation in boiling point, depression in freezing point and relative lowering of vapour pressure all are colligative properties. Osmotic pressure depends on the initial concentration of solute particles and temperature. From the concentration, we can calculate the mass of the solute.

Formula: Formula of osmotic pressure is-
$\ \prod\ =\ iCRT$; where; ∏ = is the osmotic pressure
i = van’t Hoff factor
C = molar concentration (solute)
R = Universal gas constant
T = temperature

Complete Step by Step Answer:
The minimum pressure is applied to a solution so that solute particles flow from a higher concentration solution to a lower concentration solution through a semipermeable membrane to equalise the concentrations on both sides of a semipermeable membrane is called osmotic pressure. The formula of osmotic pressure is:
$\prod\ =\ iCRT → C=\frac{\prod\ }{iRT}$ …………………………(i)
Now, with the help of osmotic pressure, we will calculate molar mass:
The formula for molar concentration (C):
$C=\ \frac{n}{v}$ ……………(ii)
where; v = volume of solution
n = moles of solute

Now from equations (i) and (ii)
$\frac{n}{v}=\frac{\prod\ }{iRT}$ …………….(iii)

The Formula of molar mass (M) is:
$M=\ \frac{m}{n} → n=\ \frac{m}{M} $ ………… (iv)
where; m = mass of salute
M = molar mass
From equation (iii) & (iv)
$\frac{m}{vM}=\frac{\prod\ }{iRT}$
$M=\frac{iRTm\ }{\prod{v}}$
This is the formula for molar mass which can be calculated with the help of osmotic pressure.

Thus, Option (A) is correct

Note: Semipermeable membrane is a thin membrane made up of biological substances like cellulose , cellulose nitrate etc. It allows some specific size of a molecule to pass through it.