Raoult's Law Calculator
Enter the pure-component vapor pressures and liquid-phase mole fractions for a binary mixture and this calculator returns the partial pressures of each component, the total vapor pressure, and the vapor-phase mole fractions (y values) from Dalton's Law. Switch to Nonvolatile Solute mode to find the vapor pressure lowering caused by a dissolved solid. All results update as you type, with a full worked solution shown beneath.
What is Raoult's Law?
Raoult's Law (1887) states that the partial vapor pressure of each volatile component in an ideal liquid mixture is equal to the vapor pressure of the pure component multiplied by its mole fraction in the liquid phase. Mathematically, Pi = xi x P°i, where Pi is the partial pressure of component i, xi is its liquid-phase mole fraction, and P°i is its pure-component vapor pressure at the same temperature. The total vapor pressure over the mixture is the sum of all partial pressures, consistent with Dalton's Law of partial pressures: Ptotal = PA + PB + ... Adding a nonvolatile solute (one that has no vapor pressure of its own) reduces the number of solvent molecules at the liquid surface, which lowers the vapor pressure below the pure-solvent value. This vapor pressure lowering is one of the four colligative properties of solutions, alongside boiling point elevation, freezing point depression, and osmotic pressure.
How to use this calculator
Select Binary ideal mixture to model a two-component system where both components are volatile (common examples: benzene-toluene, hexane-heptane, ethanol-water at low concentrations). Enter the pure vapor pressures of each component in any supported pressure unit (mmHg, atm, kPa, Pa, bar), then enter the mole fraction of component A in the liquid phase. Component B's mole fraction is automatically set to 1 minus xA. The calculator returns the partial pressures PA and PB, the total vapor pressure Ptotal, and the vapor-phase mole fractions yA and yB. Select Nonvolatile solute to model a dissolved solid (e.g. glucose, NaCl, urea) that lowers the solvent's vapor pressure. Enter the pure solvent vapor pressure and the moles of solvent and solute. The calculator returns the solvent mole fraction, the solution vapor pressure, and the vapor pressure lowering. For electrolytes, multiply the moles of solute by the Van't Hoff factor (e.g. 2 for NaCl, 3 for CaCl2) before entering.
Binary mixture: P-x-y diagram and vapor enrichment
For a binary ideal mixture, a P-x-y diagram plots total pressure against the liquid mole fraction (liquid line, straight) and the vapor mole fraction (vapor line, curved). The area between the two lines is the two-phase region where liquid and vapor coexist at equilibrium. The vapor phase is always richer in the more volatile component (the one with the higher pure vapor pressure) than the liquid. The vapor mole fraction is calculated from Dalton's Law: yA = PA / Ptotal. This enrichment is the basis of fractional distillation: repeated vaporization and condensation progressively concentrates the more volatile component in the vapor. The calculator uses the classic benzene-toluene pair as its default example, where benzene (P° = 96 mmHg) is more volatile than toluene (P° = 29.1 mmHg) and is therefore enriched in the vapor.
Limitations and non-ideal behavior
Raoult's Law holds exactly only for ideal solutions, where the intermolecular forces between unlike molecules are the same as those between like molecules. Real mixtures deviate in two directions. Positive deviations (e.g. ethanol-water) occur when unlike molecules attract each other less strongly than like molecules: total pressure is higher than ideal and the mixture may form a maximum-boiling azeotrope. Negative deviations (e.g. acetone-chloroform) occur when unlike molecules attract more strongly: total pressure is lower than ideal and a minimum-boiling azeotrope can form. At azeotrope compositions, the vapor and liquid have the same composition and ordinary distillation cannot separate the mixture. For non-ideal systems, Raoult's Law is modified by activity coefficients (gamma_i): Pi = xi x gamma_i x P°i. Ideal-solution behavior is a reasonable first approximation for mixtures of chemically similar compounds such as benzene-toluene or hexane-heptane.
Common pure-component vapor pressures at 25 °C
| Substance | Vapor pressure (mmHg) | Vapor pressure (kPa) | Notes |
|---|---|---|---|
| Water | 23.8 | 3.17 | Very common solvent |
| Ethanol | 59.3 | 7.91 | Volatile alcohol |
| Acetone | 231 | 30.8 | Common lab solvent |
| Benzene | 96 | 12.8 | Classic Raoult example |
| Toluene | 29.1 | 3.88 | Paired with benzene |
| Hexane | 151 | 20.2 | Nonpolar solvent |
| Heptane | 45.9 | 6.12 | Paired with hexane |
| Methanol | 127 | 16.9 | Volatile alcohol |
| Chloroform | 199 | 26.5 | Heavy volatile solvent |
| Diethyl ether | 534 | 71.2 | Highly volatile |
Reference values for entering into the calculator. All values at 25 °C; use the Antoine equation for other temperatures.
Frequently asked questions
What is the formula for Raoult's Law?
Raoult's Law is Pi = xi x P°i, where Pi is the partial vapor pressure of component i, xi is the mole fraction of component i in the liquid phase, and P°i is the vapor pressure of the pure component at the same temperature. For a binary mixture, the total vapor pressure is Ptotal = xA x P°A + xB x P°B.
How do I find the vapor-phase mole fraction (y value)?
Once you have the partial pressures from Raoult's Law, apply Dalton's Law: yA = PA / Ptotal and yB = PB / Ptotal. These always sum to 1. The vapor is richer in the more volatile component (higher P°) than the liquid.
What is vapor pressure lowering and how is it calculated?
Vapor pressure lowering is the reduction in vapor pressure when a nonvolatile solute is dissolved in a solvent. By Raoult's Law, P = x_solvent x P°, so delta P = P° - P = x_solute x P°. It depends only on the mole fraction of solute particles, not on the identity of the solute, making it a colligative property.
When does Raoult's Law fail?
Raoult's Law is only exact for ideal solutions. Real mixtures deviate when unlike molecules interact differently from like molecules. Strong positive deviations occur in systems like ethanol-water; strong negative deviations occur in systems like acetone-chloroform. The law also fails for electrolytes unless a Van't Hoff factor is applied to account for dissociation.
What pressure units can I use?
This calculator accepts mmHg (torr), atm, kPa, Pa, and bar. All inputs must be in the same unit. Reference tables commonly list vapor pressures in mmHg or kPa; conversions are 1 atm = 760 mmHg = 101.325 kPa = 1.01325 bar.
How do I handle electrolyte solutes like NaCl?
Electrolytes dissociate in solution, increasing the effective number of solute particles. For NaCl (i = 2) dissolving 1 mol gives 2 mol of particles. Multiply moles of solute by the Van't Hoff factor (i) before entering the moles of solute field. For NaCl, enter 2 x n_NaCl; for CaCl2 (i = 3), enter 3 x n_CaCl2.
Why is the benzene-toluene system used as the classic example?
Benzene and toluene are chemically very similar (both aromatic hydrocarbons) and their mixture behaves nearly ideally, meaning measured pressures agree closely with the values predicted by Raoults Law. That makes the pair ideal for demonstrating the law without the complication of activity coefficients.