Question

If a solution is prepared by dissolving solute in 0.3 L of water having osmotic pressure 164.1 atm at 300 K, what will be the number of moles of solute in solution? (R = 0.08205 L atm K\({}^{-1}\)mol\({}^{-1}\))

• A. \(0.5\)
• B. \(1\)
• C. \(1.5\)
• D. \(2.0\)

Hint:

Use the osmotic pressure formula pi equals CRT to find the concentration, then multiply by the volume.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Osmotic pressure is \(\pi=CRT\), where \(C\) is the molarity of the solution.

Step 2: Find the concentration
\(C=\dfrac{\pi}{RT}=\dfrac{164.1}{0.08205\times 300}=\dfrac{164.1}{24.615}=6.667\) mol/L.

Step 3: Calculation
Moles of solute \(=C\times V=6.667\times 0.3=2.0\) mol.

Final Answer:
The solution contains 2.0 mol of solute, which is option (D). \[ \boxed{\text{(D) }2.0} \]