Question

Calculate the osmotic pressure of 0.5 M aqueous solution of nonvolatile solute at 300 K .
\(\left[ \text{R} = 0.0821 \text{ atm dm}^3 \text{ K}^{-1} \text{ mol}^{-1} \right]\)

• A. 9.51 atm
• B. 12.32 atm
• C. 15.60 atm
• D. 6.75 atm

Hint:

For nonelectrolytes in dilute solution, osmotic pressure is directly calculated by: \[ \pi = CRT \] Just be careful to use temperature in kelvin.

Answer 1

The Correct Option is B

Concept:
Osmotic pressure of a dilute solution is given by: \[ \pi = CRT \] where:
• \(C\) = molarity of solution
• \(R\) = gas constant
• \(T\) = temperature in kelvin

Step 1: Write the given values.
\[ C = 0.5\ \text{mol dm}^{-3} \] \[ R = 0.0821\ \text{atm dm}^3 \text{K}^{-1}\text{mol}^{-1} \] \[ T = 300\ \text{K} \]

Step 2: Substitute into the osmotic pressure formula.
\[ \pi = CRT \] \[ \pi = 0.5 \times 0.0821 \times 300 \]

Step 3: Calculate the value.
\[ \pi = 12.315 \approx 12.32\ \text{atm} \] Hence, the correct answer is:
\[ \boxed{(B)\ 12.32\ \text{atm}} \]