JEE Main 2026 — Solutions Question with Solution

The osmotic pressure $\pi$ of the solution is balanced by the hydrostatic pressure of the liquid column.

$\pi =\rho gh$

Given:
Density of solution, $\rho =1000{\text{ kg m}}^{-3}$
Acceleration due to gravity, $g=10{\text{ m s}}^{-2}$
Height difference, $h=80.0\text{ mm}=0.08\text{ m}$

$\pi =1000\times 10\times 0.08=800\text{ Pa}=0.8\text{ kPa}$

From the van 't Hoff equation for osmotic pressure:
$\pi =CRT=\frac{n}{V}RT$

Given:
Volume of solution, $V=1\text{ L}=1{\text{ dm}}^3$
Gas constant, $R=8.3{\text{ kPa dm}}^3{\text{ K}}^{-1}{\text{mol}}^{-1}$
Temperature, $T=300\text{ K}$

Substituting the values:
$0.8=\frac{n}{1}\times 8.3\times 300$

$n=\frac{0.8}{2490}\text{ mol}$

The mass of hemoglobin is $w=20\text{ g}=0.02\text{ kg}$.
The molar mass $M$ in ${\text{kg mol}}^{-1}$ is:
$M=\frac{w}{n}=\frac{0.02}{\frac{0.8}{2490}}$

$M=\frac{0.02\times 2490}{0.8}=\frac{49.8}{0.8}=62.25{\text{ kg mol}}^{-1}$

Rounding to the nearest integer, we get $62$.

Answer: $62$