Osmotic Pressure
NaCl, KCl: i≈2 | CaCl₂: i≈3 | Sugar: i≈1
Standard temperature: 298 K (25°C)
What is Osmotic Pressure?
Osmotic pressure is the pressure needed to prevent osmosis (water movement) across a semipermeable membrane.
van 't Hoff Equation:
π = i·c·R·T
Also used for colligative properties
π = i·c·R·T
Also used for colligative properties
Constants:
| R | 0.08206 L·atm/(mol·K) |
| R | 8.314 J/(mol·K) |
| Std. Temp. | 298 K (25°C) |
Important: Temperature must be entered in Kelvin!
Formulas
Osmotic Pressure:
π = i·c·R·T
π = i·c·R·T
Concentration:
c = π / (i·R·T)
c = π / (i·R·T)
Temperature:
T = π / (i·c·R)
T = π / (i·c·R)
Pressure Unit Conversion:
1 atm = 101325 Pa = 1.01325 bar
1 atm = 101325 Pa = 1.01325 bar
van 't Hoff Factor i: Indicates the number of particles formed by one molecule in solution. Ideal: i=1 (sugar), i=2 (NaCl). Actual i is often slightly smaller due to ion association.
Practical Examples
Example 1: Osmotic Pressure of NaCl Solution
0.1 mol/L NaCl at 25°C (298 K)
i = 2 (NaCl dissociates into Na⁺ and Cl⁻)
R = 0.08206 L·atm/(mol·K)
π = 2 × 0.1 × 0.08206 × 298 ≈ 4.88 atm
0.1 mol/L NaCl at 25°C (298 K)
i = 2 (NaCl dissociates into Na⁺ and Cl⁻)
R = 0.08206 L·atm/(mol·K)
π = 2 × 0.1 × 0.08206 × 298 ≈ 4.88 atm
Example 2: Blood Plasma (Isotonic)
Human blood plasma has about 0.3 mol/L solutes
i ≈ 1.5 (due to various ions and proteins)
π ≈ 1.5 × 0.3 × 0.08206 × 298 ≈ 11 atm
This is why saline solution must be isotonic (0.9%)
Human blood plasma has about 0.3 mol/L solutes
i ≈ 1.5 (due to various ions and proteins)
π ≈ 1.5 × 0.3 × 0.08206 × 298 ≈ 11 atm
This is why saline solution must be isotonic (0.9%)
Example 3: Calculate Concentration
A pressure of 2.4 atm is observed with a sugar solution (i=1) at 298 K.
c = 2.4 / (1 × 0.08206 × 298) ≈ 0.098 mol/L
A pressure of 2.4 atm is observed with a sugar solution (i=1) at 298 K.
c = 2.4 / (1 × 0.08206 × 298) ≈ 0.098 mol/L
Technical Background
Biological Significance:
- Cell Tonicity: Isotonic solutions cause no changes; hypertonic solutions lead to plasmolysis; hypotonic solutions cause hemolysis
- Kidney Function: Osmotic gradient in Henle's loop is essential
- Plant Cells: Turgor pressure arises from osmosis
- Medicine: Saline and dextrose solutions must be isotonic
van 't Hoff Factors (Typical Values):
| Sugar (C₆H₁₂O₆) | i = 1.0 |
| NaCl | i ≈ 1.9 (ideal: 2) |
| CaCl₂ | i ≈ 2.7 (ideal: 3) |
| Blood Plasma | i ≈ 1.5–1.8 |
Colligative Properties:
- Osmotic pressure, boiling point elevation, freezing point depression, vapor pressure lowering
- All depend on the number of dissolved particles, not their identity
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