Question

The osmotic pressure of \( 0.01\,M \) aqueous solution of urea at \( 300\,K \) is \((R = 0.082\,\text{lit atm mol}^{-1}\text{K}^{-1})\)

• A. \( 0.0082\,\text{atm} \)
• B. \( 0.082\,\text{atm} \)
• C. \( 2.46\,\text{atm} \)
• D. \( 24.6\,\text{atm} \)
• E. \( 0.246\,\text{atm} \)

Hint:

For non-electrolytes like urea, always take \( i=1 \). Use \( \pi = MRT \) directly.

Answer 1

Answer: (E)

Step 1: Recall the formula for osmotic pressure.
Osmotic pressure is given by: \[ \pi = iMRT \] where \( i \) is van’t Hoff factor, \( M \) is molarity, \( R \) is gas constant and \( T \) is temperature.

Step 2: Identify the nature of solute.
Urea is a non-electrolyte, so: \[ i = 1 \]

Step 3: Substitute the given values.
\[ \pi = (1)(0.01)(0.082)(300) \]

Step 4: Perform multiplication stepwise.
\[ 0.01 \times 0.082 = 0.00082 \] \[ 0.00082 \times 300 = 0.246 \]

Step 5: Write the final value.
\[ \pi = 0.246\,\text{atm} \]

Step 6: Check unit consistency.
Since \( R \) is in lit-atm units and \( M \) is mol/L, pressure is obtained in atm.

Step 7: Final conclusion.
\[ \boxed{0.246\,\text{atm}} \] Therefore, the correct option is \[ \boxed{(5)\ 0.246\,\text{atm}} \]