Question

One liter of an aqueous urea solution contains 6 g of urea. The osmotic pressure of the solution at 300 K (assuming an ideal behavior) is ................ kPa. (Round off to one decimal place) 
[Given: Molecular weight of urea = 60, gas constant (R) = 8.3 J K\(^{-1}\) mol\(^{-1}\)]
 

Hint:

The osmotic pressure can be calculated using the formula \(\Pi = \frac{nRT}{V}\), where \(n\) is the number of moles of solute, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin.

Answer 1

Correct Answer: 247

Step 1: Formula for osmotic pressure.
The osmotic pressure \(\Pi\) for a solution is given by the formula: \[ \Pi = \frac{nRT}{V} \] where \(n\) is the number of moles of solute, \(R\) is the gas constant, \(T\) is the temperature, and \(V\) is the volume of the solution. Step 2: Calculate the number of moles of urea.
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molecular weight}} = \frac{6}{60} = 0.1 \, \text{mol} \] Step 3: Substitute the values into the osmotic pressure formula.
For 1 liter of solution, \(V = 1 \, \text{L}\), and \(T = 300 \, \text{K}\): \[ \Pi = \frac{0.1 \times 8.3 \times 300}{1} = 249 \, \text{Pa} = 0.25 \, \text{kPa} \] Step 4: Conclusion.
Thus, the osmotic pressure of the solution is 1.5 kPa.