Raoult's Law: Ideal Solution Vapor Pressure
Raoult's Law states P = x·P°: the partial vapor pressure of a component equals its mole fraction times its pure vapor pressure. Ideal solutions (e.g., benzene-toluene) obey this; non-ideal solutions show positive or negative deviations. Foundation for distillation and colligative properties.
Why This Chemistry Calculation Matters
Why: Raoult's Law underpins vapor-liquid equilibrium, distillation design, and solution thermodynamics. Essential for chemical engineering separations and understanding colligative properties.
How: Enter mole fractions (summing to 1) and pure vapor pressures. For ideal solutions, P = x·P°. For non-ideal, use activity coefficients: P = γ·x·P°. Vapor composition follows Dalton's Law: y = P/Ptotal.
- ●Ideal solutions: benzene-toluene, hexane-heptane; similar molecules.
- ●Positive deviation (water-ethanol): weaker interactions than pure components.
- ●Negative deviation (chloroform-acetone): stronger interactions (e.g., H-bonding).
Solution Examples
💧 Water-Ethanol Ideal Solution
Equal mole fractions - ideal behavior
🧪 Benzene-Toluene Mixture
Classic ideal solution example
📈 Water-Ethanol Positive Deviation
Non-ideal solution with positive deviation
📉 Chloroform-Acetone Negative Deviation
Non-ideal solution with negative deviation
🌊 Pure Water
Single component - pure water vapor pressure
🍺 Methanol-Water Mixture
Alcohol-water binary system
⛽ Hexane-Heptane Ideal
Alkane mixture - nearly ideal
💨 Calculate Vapor Composition
Find vapor mole fractions using Dalton's Law
Calculate Vapor Pressure
⚠️For educational and informational purposes only. Verify with a qualified professional.
🔬 Chemistry Facts
Raoult's Law: Pi = xi × P°i for ideal solutions.
— IUPAC
Non-ideal: Pi = γi × xi × P°i; γ > 1 positive, γ < 1 negative deviation.
— IUPAC
Vapor enriched in more volatile component (higher P°).
— NIST
Benzene-toluene is classic ideal solution; water-ethanol shows positive deviation.
— NIST
What is Raoult's Law?
Raoult's Law describes the vapor pressure of ideal solutions. It states that the partial vapor pressure of each component in a solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution.
Pᵢ = partial vapor pressure, P°ᵢ = pure component vapor pressure, xᵢ = mole fraction
How Does Raoult's Law Work?
Raoult's Law is based on the principle that in an ideal solution, the escaping tendency of molecules is proportional to their concentration. Pᵢ = P°ᵢ × xᵢ; P_total = P₁ + P₂.
When to Use Raoult's Law
Use for vapor-liquid equilibrium, distillation design, chemical engineering separation processes, and solution thermodynamics. Essential for binary mixtures and phase behavior.
Types and Key Concepts
Ideal solutions (benzene-toluene, hexane-heptane). Non-ideal: positive deviation (water-ethanol) or negative deviation (chloroform-acetone). Activity coefficients: Pᵢ = γᵢ × P°ᵢ × xᵢ.
Key Formulas
| Raoult's Law | Pᵢ = P°ᵢ × xᵢ |
| Non-Ideal | Pᵢ = γᵢ × P°ᵢ × xᵢ |
| Total Pressure | P_total = P₁ + P₂ |
| Vapor Composition | yᵢ = Pᵢ / P_total |
Practical Examples and Reference Data
| Component | Formula | P° (25°C, mmHg) | Boiling Point (°C) | Category |
|---|---|---|---|---|
| Water | H_{2}O | 23.8 | 100 | Common |
| Ethanol | C_{2}H₅ ext{OH} | 59 | 78.4 | Alcohols |
| Methanol | CH_{3} ext{OH} | 127 | 64.7 | Alcohols |
| Benzene | C₆H₆ | 95.1 | 80.1 | Aromatics |
| Toluene | C₇H₈ | 28.4 | 110.6 | Aromatics |
| Acetone | C_{3}H₆O | 230 | 56.1 | Ketones |
| Chloroform | CHCl_{3} | 199 | 61.2 | Halocarbons |
| Carbon Tetrachloride | ext{CCl}₄ | 114 | 76.7 | Halocarbons |
| Diethyl Ether | C₄H_{1}_{0}O | 537 | 34.6 | Ethers |
| Hexane | C₆H_{1}₄ | 151 | 68.7 | Alkanes |
| Heptane | C₇H_{1}₆ | 45.8 | 98.4 | Alkanes |
| Octane | C₈H_{1}₈ | 14.1 | 125.7 | Alkanes |
| Acetic Acid | CH_{3} ext{COOH} | 15.7 | 118.1 | Acids |
| Formic Acid | ext{HCOOH} | 42 | 100.8 | Acids |
| Pyridine | C₅H₅N | 20 | 115.2 | Heterocycles |
| Cyclohexane | C₆H_{1}_{2} | 97.6 | 80.7 | Cycloalkanes |
| Tetrahydrofuran | C₄H₈O | 145 | 66 | Ethers |
| Dichloromethane | CH_{2}Cl_{2} | 435 | 39.8 | Halocarbons |
| Ethyl Acetate | C₄H₈O_{2} | 95 | 77.1 | Esters |
| Isopropanol | C_{3}H₇ ext{OH} | 44 | 82.6 | Alcohols |
Practical Examples
Example: Benzene-Toluene Ideal Solution
Given:
- Benzene: P° = 95.1 mmHg, x = 0.6
- Toluene: P° = 28.4 mmHg, x = 0.4
- Temperature: 25°C
Solution:
P_benzene = 95.1 × 0.6 = 57.1 mmHg
P_toluene = 28.4 × 0.4 = 11.4 mmHg
P_total = 57.1 + 11.4 = 68.5 mmHg
y_benzene = 57.1/68.5 = 0.833
Example: Water-Ethanol Positive Deviation
Given:
- Water: P° = 23.8 mmHg, x = 0.5
- Ethanol: P° = 59.0 mmHg, x = 0.5
- γ_water = 1.2, γ_ethanol = 1.3
Solution:
P_water = 1.2 × 23.8 × 0.5 = 14.3 mmHg
P_ethanol = 1.3 × 59.0 × 0.5 = 38.4 mmHg
P_total = 52.7 mmHg
Higher than ideal (41.4 mmHg)
Limitations of Raoult's Law
- Does not apply to solutions with very different molecular sizes, strong H-bonding, electrolytes, or high pressure
- Assumes chemically similar components, random mixing, and constant temperature
📚 Official Data Sources
⚠️ Disclaimer: This calculator uses IUPAC definitions for Raoult's law and solution thermodynamics. Vapor pressure data is approximate; for precise work consult IUPAC Gold Book, NIST Chemistry WebBook, and Atkins Physical Chemistry.