Question

Write the definition of osmotic pressure. Calculate the osmotic pressure of 2% aqueous solution of urea at 27$^\circ$C. Solution constant $R = 0.082\ \text{L atm K^{-1}\ \text{mol}^{-1}$.}

Hint:

For dilute, non-electrolyte solutions use \(\pi=MRT\).
"2% (w/v)" means \(2\ \text{g}\) solute per \(100\ \text{mL}\) solution; convert to \(\text{mol L}^{-1}\) before using \(RT\).

Answer 1

Definition:
Osmotic pressure \((\pi)\) is the excess pressure that must be applied to a solution separated from its pure solvent by a semipermeable membrane to prevent the net flow of solvent into the solution.
Formula (for a non-electrolyte):
\[ \pi = iMRT (i=1\ \text{for urea}) \]
Given/Assumption:
2% (w/v) solution \(\Rightarrow\) \(2\ \text{g urea in }100\ \text{mL solution}\).
Molar mass of urea \(=60\ \text{g mol}^{-1}\). Temperature \(T=27^\circ\text{C}=300\ \text{K}\).

Step 1: Molarity \(M\).
Mass per litre \(= 20\ \text{g L}^{-1}\) \(\Rightarrow\) \(M=\dfrac{20}{60}=0.333\ \text{mol L}^{-1}\).

Step 2: Osmotic pressure.
\[ \pi = (0.333)\times(0.082)\times(300) = 8.19\ \text{atm} \approx 8.2\ \text{atm} \]
\[ \boxed{\pi \approx 8.2\ \text{atm (at 27$^\circ$C)}} \]