Osmotic pressure of 0.02 M urea solution at 27 °C, is (given $R = 0.0821\, atm\, L\, mol^{-1}\, K^{-1}$)

0.4926 atm

The correct answer is Option (1) → 0.4926 atm

Using the van't Hoff equation for osmotic pressure:

$\pi = iCRT$

Identify the variables:

• Concentration ($C$): $0.02\ \text{mol/L}$

• Gas Constant ($R$): $0.0821\ \text{L} \cdot \text{atm} / (\text{mol} \cdot \text{K})$

• Temperature ($T$): Convert from Celsius to Kelvin:

$T = 27\ ^\circ\text{C} + 273 = 300\ \text{K}$

• van't Hoff factor ($i$): For urea, which is a non-electrolyte, $i = 1$.

Substitute the values into the equation:

$\pi = (1) \times (0.02\ \text{mol/L}) \times \left(0.0821\ \frac{\text{L} \cdot \text{atm}}{\text{mol} \cdot \text{K}}\right) \times (300\ \text{K})$

Calculate the result:

$\pi = 0.4926\ \text{atm}$

The calculated osmotic pressure is $\mathbf{0.4926\ \text{atm}}$.