Calculate osmotic pressure and understand colligative properties of solutions
1 for non-electrolytes, 2 for NaCl, 3 for CaCl₂, etc.
298 K = 25°C (room temperature), 310 K = 37°C (body temperature)
π = iMRT
Key Concept: Osmotic pressure is the minimum pressure needed to prevent water from flowing through a semipermeable membrane from a dilute solution to a concentrated one.
Osmotic pressure (π) is the minimum pressure required to prevent the flow of solvent molecules through a semipermeable membrane from a dilute solution into a more concentrated solution. It is one of the four main colligative properties of solutions.
π = iMRT
The Van't Hoff factor represents the number of particles (ions or molecules) that a compound produces when dissolved in solution.
Compounds that do not dissociate in solution.
Examples: glucose (C₆H₁₂O₆), sucrose (C₁₂H₂₂O₁₁), ethanol (C₂H₅OH)
C₆H₁₂O₆(s) → C₆H₁₂O₆(aq) [1 particle]
Ionic compounds that completely dissociate.
• NaCl: Na⁺ + Cl⁻ → i = 2
• CaCl₂: Ca²⁺ + 2Cl⁻ → i = 3
• Al₂(SO₄)₃: 2Al³⁺ + 3SO₄²⁻ → i = 5
• K₃PO₄: 3K⁺ + PO₄³⁻ → i = 4
Partially dissociate, actual i depends on degree of ionization.
Acetic acid (CH₃COOH): Only ~1% ionized
Theoretical i = 2, but actual i ≈ 1.01 in dilute solution
Problem: Calculate the osmotic pressure of a 0.15 M glucose solution at 37°C (body temperature).
Given:
π = iMRT
π = (1)(0.15)(0.08206)(310)
π = 3.82 atm
This is close to normal blood osmotic pressure!
Problem: What molarity of NaCl solution gives the same osmotic pressure as 0.15 M glucose at 310 K?
Given: π = 3.82 atm, i = 2 (NaCl → Na⁺ + Cl⁻), T = 310 K
M = π/(iRT)
M = 3.82/(2 × 0.08206 × 310)
M = 0.075 M
Only half the molarity needed because NaCl produces twice as many particles!
Problem: Seawater has approximately 0.6 M NaCl. What pressure is needed for reverse osmosis desalination at 25°C?
Given: i = 2, M = 0.6 mol/L, T = 298 K
π = iMRT
π = (2)(0.6)(0.08206)(298)
π = 29.3 atm ≈ 30 bar
Reverse osmosis plants must apply >30 atm to push water through membranes!
Osmotic pressure is one of four main colligative properties - properties that depend on the number of solute particles, not their identity.
Adding solute decreases vapor pressure of solvent (Raoult's Law)
Solutions boil at higher temperature than pure solvent (ΔTb = Kbm)
Solutions freeze at lower temperature (ΔTf = Kfm) - salt on icy roads!
Pressure needed to prevent solvent flow through membrane (π = iMRT)
Why Colligative Properties Matter: They all result from the same fundamental principle - adding solute particles disrupts the solvent's normal behavior. The number of particles (not their type) determines the magnitude of the effect.
The spontaneous flow of solvent molecules through a semipermeable membrane from a region of lower solute concentration to higher solute concentration. Osmosis continues until equilibrium or until osmotic pressure is reached.
A barrier that allows solvent molecules (like water) to pass through but blocks solute particles. Examples: cell membranes, dialysis tubing, reverse osmosis membranes. Selectivity based on size, charge, or other properties.
Applying pressure greater than osmotic pressure forces solvent to flow from high concentration to low concentration (opposite of natural osmosis). Used in desalination and water purification. Requires energy input to overcome natural osmotic pressure.
Always use Kelvin (K), never Celsius. Convert: K = °C + 273.15
Common: 25°C = 298 K (room temp), 37°C = 310 K (body temp), 0°C = 273 K
Don't forget i! Non-electrolytes: i = 1. Count all ions for electrolytes: NaCl (i=2), MgCl₂ (i=3), Al₂(SO₄)₃ (i=5). Weak electrolytes have i between 1 and theoretical maximum.
Pressure: 1 atm = 101.325 kPa = 760 mmHg = 14.7 psi
R constant varies: 0.08206 L·atm/(mol·K) or 8.314 J/(mol·K) - use correct one!