Raoult's Law Calculator
Calculate vapor pressure of ideal solutions and mixtures using Raoult's Law for colligative property analysis
💧 Calculate Vapor Pressure
mol
mol (non-volatile)
Enter values to calculate vapor pressure using Raoult's Law for ideal solutions
📐 Raoult's Law Formulas
For Non-Volatile Solute
Where:
- • Psolution = Vapor pressure of the solution
- • χsolvent = Mole fraction of solvent = nsolvent/(nsolvent + nsolute)
- • P°solvent = Vapor pressure of pure solvent at same temperature
Vapor Pressure Lowering
Where:
- • ΔP = Vapor pressure lowering (always positive)
- • χsolute = Mole fraction of solute = nsolute/(nsolvent + nsolute)
- • The decrease is proportional to solute concentration (colligative property)
For Two Volatile Components
Where:
- • PA, PB = Partial pressures of components A and B
- • χA + χB = 1 (mole fractions sum to unity)
- • Uses Dalton's Law of Partial Pressures combined with Raoult's Law
Example: Sugar in Water
Water at 25°C (P° = 23.8 mmHg) with 0.1 mol sugar in 1.0 mol water:
Step 1: Calculate mole fraction of water
χwater = 1.0/(1.0 + 0.1) = 0.909
Step 2: Apply Raoult's Law
Psolution = 0.909 × 23.8 mmHg = 21.6 mmHg
Step 3: Calculate vapor pressure lowering
ΔP = 23.8 - 21.6 = 2.2 mmHg
Interpretation: Adding sugar lowered vapor pressure by 9.2%, making water less likely to evaporate
What is Raoult's Law?
Raoult's Law, formulated by French chemist François-Marie Raoult in 1887, states that the partial vapor pressure of each component in an ideal solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture—this fundamental principle explains how dissolved solutes lower the vapor pressure of solvents, forming the basis for understanding colligative properties including boiling point elevation, freezing point depression, and osmotic pressure.
For non-volatile solutes (substances that do not evaporate), Raoult's Law predicts that vapor pressure decreases proportionally to the mole fraction of solute added—this occurs because solute particles occupy surface positions that would otherwise be occupied by solvent molecules capable of evaporating, physically blocking evaporation and reducing the number of molecules escaping into the gas phase at equilibrium, creating a measurable and predictable decrease in vapor pressure.
Ideal solutions perfectly obey Raoult's Law when solute-solvent interactions equal solute-solute and solvent-solvent interactions—real solutions approximate ideal behavior when components are chemically similar (like benzene-toluene mixtures) or when solutions are very dilute, though most real solutions show small deviations called positive or negative deviations depending on whether intermolecular forces in the mixture are weaker or stronger than in pure components.
📚 Understanding Colligative Properties
What are Colligative Properties?
Colligative properties depend only on the number of solute particles dissolved in solution, not on the identity or chemical nature of the solute—whether dissolved particles are sugar molecules, salt ions, or protein molecules doesn't matter; only the particle count affects vapor pressure, boiling point, freezing point, and osmotic pressure.
Vapor Pressure Lowering
Adding solute decreases vapor pressure because fewer solvent molecules occupy the surface. Direct consequence of Raoult's Law.
Boiling Point Elevation
Lower vapor pressure means higher temperature needed to boil. Solution boils at higher temperature than pure solvent.
Freezing Point Depression
Solute particles interfere with crystal formation. Solution freezes at lower temperature than pure solvent. Used in antifreeze.
Osmotic Pressure
Pressure required to prevent osmosis across semipermeable membrane. Crucial for biological systems and cell function.
🌐 Real-World Applications
De-Icing and Antifreeze
Road salt (calcium chloride, sodium chloride) lowers water's freezing point through freezing point depression predicted by Raoult's Law—automotive antifreeze uses ethylene glycol to prevent engine coolant from freezing in winter and overheating in summer by altering both freezing and boiling points.
Food Science & Preservation
Ice cream makers add salt to ice to lower its temperature below 0°C, making homemade ice cream possible—food preservation through salting or sugar curing works by lowering water's vapor pressure and osmotic effects, preventing bacterial growth and extending shelf life of meats and vegetables.
Distillation & Separation
Fractional distillation of petroleum, alcohol production, and chemical purification all rely on Raoult's Law predictions of vapor-liquid equilibrium—components with different vapor pressures separate at different temperatures, enabling industrial-scale purification and separation of liquid mixtures.
Molecular Weight Determination
Measuring vapor pressure lowering, freezing point depression, or osmotic pressure allows calculation of unknown molecular weights—this cryoscopic method was historically crucial for determining molar masses of organic compounds and biological macromolecules before modern spectroscopic techniques.
Desalination & Water Treatment
Reverse osmosis desalination applies pressure greater than osmotic pressure predicted by colligative properties to purify seawater—understanding vapor pressure relationships helps design efficient multi-stage flash distillation systems for producing freshwater from saline sources in water-scarce regions.
Pharmaceutical Formulation
Drug solubility, stability, and delivery depend on colligative properties—intravenous solutions must be isotonic (same osmotic pressure as blood) to prevent cell damage, requiring precise control of dissolved solute concentrations based on Raoult's Law principles and osmotic pressure calculations.
⚠️ Important Considerations
🎯 Ideal Solution Requirements:
Raoult's Law applies exactly only to ideal solutions where intermolecular forces between unlike molecules equal those between like molecules—most real solutions show small deviations. Ideal behavior is best approximated by chemically similar components (benzene-toluene) or very dilute solutions where solvent-solvent interactions dominate.
⚗️ Non-Volatile Solute Assumption:
For the simple form of Raoult's Law, the solute must be non-volatile (negligible vapor pressure)—if the solute evaporates significantly, both components contribute to vapor pressure and the two-component volatile mixture formula must be used instead, applying Raoult's Law to each component separately and summing partial pressures.
🧂 Ionic Compounds and van't Hoff Factor:
Electrolytes like NaCl dissociate into multiple ions, multiplying the colligative effect—1 mole of NaCl produces approximately 2 moles of particles (Na⁺ and Cl⁻), doubling the vapor pressure lowering compared to 1 mole of non-dissociating sugar. The van't Hoff factor (i) accounts for this: ΔP = i × χsolute × P°.
🌡️ Temperature Dependence:
Pure solvent vapor pressure (P°) varies significantly with temperature according to the Clausius-Clapeyron equation—all Raoult's Law calculations require knowing P° at the specific temperature of interest. Vapor pressure increases exponentially with temperature, doubling approximately every 10°C for water near room temperature.
About the Author
Adam
Co-Founder @RevisionTown
Math Expert specializing in diverse international curricula including IB (International Baccalaureate), AP (Advanced Placement), GCSE, IGCSE, and various other educational programs worldwide.
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