Calculate vapor pressure of solutions and understand colligative properties using Raoult's Law
Raoult's Law: Psolvent = χsolvent × P°solvent
For ideal solutions: partial pressure is proportional to mole fraction
mmHg, atm, kPa, or any pressure unit
Between 0 and 1
Between 0 and 1
Raoult's Law states that the partial vapor pressure of a solvent in an ideal solution is equal to the vapor pressure of the pure solvent multiplied by its mole fraction in the solution.
PA = χA × P°A
When a non-volatile solute is added to a solvent, the vapor pressure decreases:
ΔP = P° - Psolution
ΔP = χsolute × P°
The decrease is proportional to the mole fraction of solute, making it a colligative property.
Problem:
A solution contains 0.100 mol of glucose dissolved in 0.900 mol of water at 25°C. What is the vapor pressure of water in the solution? (P° = 23.8 mmHg)
Step 1: Calculate mole fraction of water
χwater = 0.900 / (0.900 + 0.100) = 0.900
Step 2: Apply Raoult's Law
P = 0.900 × 23.8 mmHg = 21.42 mmHg
Step 3: Calculate vapor pressure lowering
ΔP = 23.8 - 21.42 = 2.38 mmHg
Result:
The vapor pressure of water is lowered by 2.38 mmHg due to the dissolved glucose.
| Type | Behavior |
|---|---|
| Ideal | Follows Raoult's Law exactly |
| Positive Deviation | P > predicted (weaker interactions) |
| Negative Deviation | P < predicted (stronger interactions) |
Examples of Ideal Solutions:
Non-Ideal Behavior:
| Solvent | 20°C (mmHg) | 25°C (mmHg) | 30°C (mmHg) |
|---|---|---|---|
| Water | 17.5 | 23.8 | 31.8 |
| Ethanol | 44.6 | 59.0 | 78.8 |
| Benzene | 74.7 | 95.1 | 118.2 |
| Acetone | 184.8 | 229.5 | 282.7 |
| Methanol | 94.0 | 126.8 | 167.0 |
| Diethyl Ether | 440.0 | 534.0 | 647.0 |
ΔTb = Kb × m × i
Solutions boil at higher temperatures than pure solvents
ΔTf = Kf × m × i
Solutions freeze at lower temperatures than pure solvents
Π = MRT
Pressure required to prevent osmosis across a membrane