Question

An aqueous solution of volume \( V \) ml contains a non-volatile solute of unknown mass \( W_B \) g and molar mass \( M_B \) g/mol. If the Osmotic pressure of the solution is \( 1.013 \) bar, which one of the following is the mathematical expression to be used to calculate \( W_B \)?

• A. \( W_B = \frac{\pi M_B V}{760RT \times 1000} \)
• B. \( W_B = \frac{\pi M_B V \times 1000}{76RT} \)
• C. \( W_B = \frac{\pi M_B V}{RT} \)
• D. \( W_B = \frac{\pi M_B V}{1000RT} \)

Hint:

Always convert volume to litres when using osmotic pressure formula \( \pi = CRT \).

Answer 1

The Correct Option is D

Step 1: Write osmotic pressure formula.
\[ \pi = \frac{n}{V}RT \]
where \( n \) = number of moles.

Step 2: Express moles in terms of mass.
\[ n = \frac{W_B}{M_B} \]

Step 3: Substitute in formula.
\[ \pi = \frac{W_B}{M_B} \cdot \frac{RT}{V} \]

Step 4: Rearrange for \( W_B \).
\[ W_B = \frac{\pi M_B V}{RT} \]

Step 5: Convert volume units.
Given volume is in ml, so convert to litres:
\[ V(\text{L}) = \frac{V}{1000} \]

Step 6: Substitute corrected volume.
\[ W_B = \frac{\pi M_B \cdot \frac{V}{1000}}{RT} \]
\[ W_B = \frac{\pi M_B V}{1000RT} \]

Step 7: Final conclusion.
\[ \boxed{\frac{\pi M_B V}{1000RT}} \]