Question

Calculate the osmotic pressure of 5% aqueous urea solution (w/v) at 27$^\circ$C. Molecular weight of urea = 60. (R = 0.0821 L atm K$^{-1}$ mol$^{-1}$)

Hint:

Osmotic pressure depends directly on molarity and temperature (\(\pi \propto C \times T\)).

Answer 1

Step 1: Recall formula.
\[ \pi = C R T \] where \(C\) = molarity, \(R = 0.0821 \ L \ atm \ K^{-1} \ mol^{-1}\), \(T = 27+273 = 300 \ K\). Step 2: Calculate molarity.
5% (w/v) = 5 g urea in 100 mL solution = 50 g in 1 L. Moles of urea = \(\frac{50}{60} = 0.833 \ mol\). Molarity = 0.833 M. Step 3: Substitution.
\[ \pi = 0.833 \times 0.0821 \times 300 \] \[ \pi \approx 20.5 \ atm \] Step 4: Conclusion.
Osmotic pressure = \(20.5 \ atm\).