Question

At 10°C, a urea solution has the osmotic pressure 500 mm of Hg. Now, if the solution is being diluted and the temperature is increased to 25°C, then osmotic pressure becomes 105.3 mm of Hg. Predict the degree of dilution of the urea solution.

• A. 0.2 times
• B. 4.5 times
• C. 5 times
• D. 1.6 times

Hint:

The osmotic pressure is directly proportional to the temperature, so temperature changes cause proportional changes in osmotic pressure.

Answer 1

The Correct Option is B

Step 1: Use the formula for osmotic pressure.
Osmotic pressure (\( \Pi \)) is given by the equation:
\[ \Pi = \frac{nRT}{V} \] Where: \( n \) is the number of moles of solute, \( R \) is the gas constant, \( T \) is the temperature in Kelvin, \( V \) is the volume of the solution. 
Step 2: Relate the osmotic pressures.
Since the number of moles of solute and the volume remain constant, the osmotic pressure is directly proportional to the temperature. Hence, we can use the relation: \[ \frac{\Pi_2}{\Pi_1} = \frac{T_2}{T_1} \] Where:
\( \Pi_1 = 500 \, \text{mm of Hg} \), \( \Pi_2 = 105.3 \, \text{mm of Hg} \), \( T_1 = 10°C = 273 + 10 = 283 \, \text{K} \), \( T_2 = 25°C = 273 + 25 = 298 \, \text{K} \).
Step 3: Calculate the ratio of osmotic pressures.
Now, applying the formula: \[ \frac{105.3}{500} = \frac{298}{283} \] Simplifying: \[ \frac{105.3}{500} \approx 0.2106, \quad \frac{298}{283} \approx 1.053. \] So the degree of dilution is: \[ \text{Degree of dilution} = \frac{1}{4.5} = 4.5 \text{ times}. \]