Question

Calculate the mass of nonvolatile solute dissolved in \(0.3\) dm\(^3\) water having osmotic pressure \(0.1\) atm at \(300\)K.
[Molar mass of solute = \(328\) g mol\(^{-1}\), R = \(0.082\) dm\(^3\)atm K\(^{-1}\)mol\(^{-1}\)]

• A. \(0.4\) g
• B. \(0.6\) g
• C. \(0.8\) g
• D. \(1.0\) g

Hint:

Use pi = CRT with C in mol per dm3, then multiply moles by molar mass.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Osmotic pressure is given by the van't Hoff equation, similar in form to the ideal gas law.

Step 2: Key Formula:
\[ \pi = CRT = \frac{n}{V}RT \quad\Rightarrow\quad n = \frac{\pi V}{RT} \]

Step 3: Detailed Explanation:
\[ n = \frac{0.1 \times 0.3}{0.082 \times 300} = \frac{0.03}{24.6} = 1.22 \times 10^{-3} \text{ mol} \]
Mass \(= n \times M = 1.22 \times 10^{-3} \times 328 = 0.4 \text{ g}\).

Step 4: Why the other options are wrong.
0.6 g, 0.8 g and 1.0 g would need moles of \(1.83\times10^{-3}\), \(2.44\times10^{-3}\) and \(3.05\times10^{-3}\), requiring osmotic pressures of 0.15, 0.2 and 0.25 atm for this volume.

Final Answer:
The mass of solute is \(0.4\) g, option (A). \[ \boxed{0.4 \text{ g}} \]