Determine the osmotic pressure at 22.5 °C of a 2.5 L aqueous solution that contains 50.0 g of sucrose (molar mass = 342.3).

• A. 0.108 atm
• B. 0.146 atm
• C. 0.270 atm
• D. 1.42 atm
• E. 3.54 atm

Answer: (D)

Verified step by step guidance

1. First, calculate the number of moles of sucrose using the formula: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \). Here, the mass of sucrose is 50.0 g and the molar mass is 342.3 g/mol.
2. Next, determine the molarity of the solution. Molarity (M) is defined as the number of moles of solute divided by the volume of the solution in liters. Use the formula: \( M = \frac{\text{moles of sucrose}}{2.5 \text{ L}} \).
3. Convert the temperature from Celsius to Kelvin, as the osmotic pressure formula requires temperature in Kelvin. Use the conversion: \( T(K) = T(°C) + 273.15 \). For 22.5 °C, calculate the temperature in Kelvin.
4. Use the formula for osmotic pressure: \( \Pi = MRT \), where \( \Pi \) is the osmotic pressure, \( M \) is the molarity, \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin.
5. Substitute the values of molarity, the ideal gas constant, and temperature in Kelvin into the osmotic pressure formula to calculate the osmotic pressure of the solution.