Multiple Choice
Which of the following factors is responsible for the osmotic pressure of a solution?
14. Solutions
Osmotic Pressure
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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
Verified step by step guidance1
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.
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: \( M = \frac{\text{moles of sucrose}}{2.5 \text{ L}} \).
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.
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.
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.
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