Question

The osmotic pressure of a 0.01 M solution of urea at 300 K is found to be 0.25 atm. Calculate value of gas constant (R).

Answer 1

The value of the gas constant (R) is approximately $0.0833 \text{ atm L mol}^{-1} \text{ K}^{-1}$.

Answer 2

The osmotic pressure ($\Pi$) of a solution is given by the formula $\Pi = iCRT$, where $i$ is the van't Hoff factor, $C$ is the molar concentration, $R$ is the gas constant, and $T$ is the absolute temperature. Given: Osmotic pressure ($\Pi$) = 0.25 atm Molar concentration ($C$) = 0.01 M Temperature ($T$) = 300 K Urea is a non-electrolyte, so its van't Hoff factor ($i$) = 1.

Rearranging the formula to solve for $R$: $R = \frac{\Pi}{iCT}$

Substituting the given values: $R = \frac{0.25 \text{ atm}}{1 \times 0.01 \text{ mol/L} \times 300 \text{ K}}$ $R = \frac{0.25}{3} \text{ atm L mol}^{-1} \text{ K}^{-1}$ $R \approx 0.0833 \text{ atm L mol}^{-1} \text{ K}^{-1}$