Osmotic Pressure and Molarity: Worked Examples

📚 Quick Study Guide

• 💧 Osmotic Pressure (\(\Pi\)): The pressure required to prevent the flow of solvent across a semipermeable membrane.
• ⚗️ Formula: $\Pi = iMRT$, where:
  • $\Pi$ = Osmotic pressure (atm)
  • $i$ = van't Hoff factor (number of particles the solute dissociates into)
  • $M$ = Molarity (mol/L)
  • $R$ = Ideal gas constant (0.0821 L·atm/mol·K)
  • $T$ = Temperature (K)
• 🧪 Molarity (M): The number of moles of solute per liter of solution.
  • $\text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Liters of solution}}$
• 🌡️ Temperature Conversion: Always convert Celsius (°C) to Kelvin (K) using: $K = °C + 273.15$
• 💡 van't Hoff factor (i):
  • For non-electrolytes (e.g., glucose), $i = 1$
  • For strong electrolytes (e.g., NaCl), $i$ equals the number of ions formed upon dissociation (e.g., for NaCl, $i = 2$)

Practice Quiz

1. Question 1: What is the osmotic pressure of a solution containing 0.2 moles of glucose in 2 L of water at 27°C? (Glucose does not dissociate, R = 0.0821 L·atm/mol·K)
   1. 0.615 atm
   2. 1.23 atm
   3. 2.46 atm
   4. 3.69 atm
2. Question 2: A solution of NaCl (i=2) has a concentration of 0.15 M at 25°C. Calculate the osmotic pressure.
   1. 3.67 atm
   2. 7.34 atm
   3. 1.84 atm
   4. 0.92 atm
3. Question 3: What is the molarity of a solution if its osmotic pressure is 4.926 atm at 27°C, and the solute is a non-electrolyte?
   1. 0.1 M
   2. 0.2 M
   3. 0.3 M
   4. 0.4 M
4. Question 4: Calculate the osmotic pressure of a 0.1 M solution of $CaCl_2$ at 20°C. (Assume complete dissociation, R = 0.0821 L·atm/mol·K)
   1. 2.44 atm
   2. 4.88 atm
   3. 7.32 atm
   4. 9.76 atm
5. Question 5: A solution contains 10 g of a protein in 1 L of water. The osmotic pressure is measured to be 3.09 atm at 25°C. What is the approximate molar mass of the protein? (Assume i=1, R = 0.0821 L·atm/mol·K)
   1. 60 g/mol
   2. 80 g/mol
   3. 100 g/mol
   4. 40 g/mol
6. Question 6: What is the osmotic pressure difference across a semipermeable membrane separating pure water from a 0.05 M solution of $MgSO_4$ at 37°C (Assume complete dissociation)?
   1. 1.23 atm
   2. 2.56 atm
   3. 3.01 atm
   4. 4.12 atm
7. Question 7: If a solution has an osmotic pressure of 2.463 atm at 300 K, what is its molar concentration, assuming i=1 and R = 0.0821 L·atm/mol·K?
   1. 0.05 M
   2. 0.1 M
   3. 0.15 M
   4. 0.2 M