Question

Calculate the mass of solute dissolved in \(1 \text{ dm}^3\) water has osmotic pressure \(3.0 \text{ atm}\) at \(300 \text{ K}\)
\([ \text{Molar mass of solute} = 41 \text{ g mol}^{-1}, \text{R} = 0.082 \text{ dm}^3 \text{ atm K}^{-1} \text{ mol}^{-1} ]\)

• A. 4.00 g
• B. 5.00 g
• C. 6.20 g
• D. 7.25 g

Hint:

Osmotic pressure: \(\pi = CRT\)

Answer 1

The Correct Option is B

Concept:
\[ \pi = \frac{n}{V}RT \]

Step 1: Rearrange formula. \[ n = \frac{\pi V}{RT} \]

Step 2: Substitute values. \[ n = \frac{3.0 \times 1}{0.082 \times 300} \] \[ n = \frac{3}{24.6} \approx 0.122 \text{ mol} \]

Step 3: Find mass. \[ \text{Mass} = n \times M = 0.122 \times 41 \approx 5.0 \text{ g} \] Conclusion: \[ \text{Mass = 5.00 g} \]