Calculate osmotic pressure of 0.1 M aqueous solution of an electrolyte at 300 K if van't Hoff factor is $1 \cdot 125 .\left[\mathrm{R}=0.0821 \mathrm{~atm} \mathrm{dm}^3 \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$

The osmotic pressure $\pi$ of an electrolyte solution is given by $\pi = iCRT$, where $i = 1.125$ is the van't Hoff factor, $C = 0.1 \text{ M}$ is the molar concentration, $R = 0.0821 \text{ atm dm}^3 \text{ K}^{-1} \text{ mol}^{-1}$ is the gas constant, and $T = 300 \text{ K}$ is the temperature.

Substitution yields $\pi = 1.125 \times 0.1 \times 0.0821 \times 300 = 2.770875 \text{ atm}$.

Rounding to two decimal places, $\pi \approx 2.77 \text{ atm}$, which corresponds to option $\boxed{\text{C}}$.