What would the osmotic pressure be for an aqueous solution that contained the following, .4 M NaCl, .3 M glucose and .2 M CaCl2? Assume temp is 25 C.
Osmotic Pressure in atm. = Molarity ( R ) (Kelvin Temp.)
Do this for all three solutions, then add the pressures.
To find the osmotic pressure of a solution, you can use the van't Hoff equation:
Π = i * M * R * T
Where:
- Π is the osmotic pressure (in atm)
- i is the van't Hoff factor (the number of particles into which each solute molecule dissociates)
- M is the molarity of the solution (in mol/L)
- R is the ideal gas constant (0.0821 L * atm / K * mol)
- T is the temperature in Kelvin (25°C = 298 K)
For each compound, you need to determine the van't Hoff factor (i) and calculate the osmotic pressure, and then sum up the contributions from all solutes.
Let's calculate the osmotic pressure for each solute:
1. Sodium chloride (NaCl):
- The chemistry of NaCl tells us that it dissociates completely into Na⁺ and Cl⁻ ions in water.
- Therefore, the van't Hoff factor (i) for NaCl is 2 (2 particles: Na⁺ and Cl⁻).
- Molarity (M) = 0.4 mol/L
- R = 0.0821 L * atm / K * mol
- T = 298 K
- Π(NaCl) = i * M * R * T = 2 * 0.4 * 0.0821 * 298 = 19.355 atm
2. Glucose (C₆H₁₂O₆):
- Glucose does not dissociate into ions and remains as a single molecule in water.
- Therefore, the van't Hoff factor (i) for glucose is 1.
- Molarity (M) = 0.3 mol/L
- R = 0.0821 L * atm / K * mol
- T = 298 K
- Π(glucose) = i * M * R * T = 1 * 0.3 * 0.0821 * 298 = 7.319 atm
3. Calcium chloride (CaCl₂):
- The chemistry of CaCl₂ tells us that it dissociates into Ca²⁺ and 2 Cl⁻ ions in water.
- Therefore, the van't Hoff factor (i) for CaCl₂ is 3 (3 particles: Ca²⁺ and 2 Cl⁻).
- Molarity (M) = 0.2 mol/L
- R = 0.0821 L * atm / K * mol
- T = 298 K
- Π(CaCl₂) = i * M * R * T = 3 * 0.2 * 0.0821 * 298 = 14.846 atm
Finally, add up the osmotic pressures for all solutes:
Total osmotic pressure (Π) = Π(NaCl) + Π(glucose) + Π(CaCl₂)
Total osmotic pressure = 19.355 + 7.319 + 14.846 = 41.52 atm
So, the osmotic pressure for the given solution is 41.52 atm.