Question

What is the osmotic pressure of a semi-molar solution at 27°C? (\( R = 0.0821 \, \text{atm L mol}^{-1} \text{K}^{-1} \))

• A. 4.96 atm
• B. 2.46 atm
• C. 20.5 atm
• D. 12.3 atm

Hint:

Osmotic pressure depends on the molarity of the solution, the temperature, and the gas constant.

Answer 1

The Correct Option is D

Step 1: Formula for osmotic pressure.
The osmotic pressure (\( \pi \)) is given by the formula: \[ \pi = \frac{nRT}{V} \] Where: - \( n = 0.5 \, \text{mol} \) is the amount of solute (semi-molar solution), - \( R = 0.0821 \, \text{atm L mol}^{-1} \text{K}^{-1} \) is the ideal gas constant, - \( T = 27°C = 300 \, \text{K} \) is the temperature in Kelvin.

Step 2: Calculation.
Substitute the values into the formula: \[ \pi = (0.5 \times 0.0821 \times 300) = 12.3 \, \text{atm} \]
Step 3: Conclusion.
The osmotic pressure is 12.3 atm, so the correct answer is (D) 12.3 atm.