Raoult’s Law

For an ideal liquid mixture, Raoult’s law relates a component’s partial pressure to its liquid mole fraction. The relation Raoult’s Law answers a specific question about Vapour–liquid equilibrium and introductory distillation calculations for ideal mixtures. At a fixed temperature, x_A=0.40 and p_A°=50.0 kPa give p_A=20.0 kPa. If x_B=0.60 and p_B°=30.0 kPa, p_total=20.0+18.0=38.0 kPa. Check: the mole fractions sum to one and each partial pressure is below its pure-component vapour pressure. Its check verifies the calculation and the expected balance or sign. Map each symbol to the actual sample before substituting values. A plausible number alone does not prove that the model assumptions are satisfied in an experiment.

The quantities mean: p_i: Partial pressure of component i above the liquid (Pa); x_i: Liquid-phase mole fraction of component i (dimensionless); p_i^0: Vapour pressure of pure component i at the same temperature (Pa). The unit rule is p_i and p_i° in the same pressure unit · x_i dimensionless. Numerator and denominator must describe the same sample and compatible measurement scales. For solutions, distinguish final volume from solvent mass; for gases, pressure and volume units must match the gas constant. Check units after full substitution. This exposes a missing conversion factor before it disappears inside a rounded result. Keep each symbol tied to its definition.

Applies approximately to ideal liquid mixtures at one temperature; nonideality requires activities. For an ideal solution, p_i=x_i p_i°. Dalton’s law then gives the total pressure as the sum of component partial pressures. Nonideal liquid mixtures require activities or activity coefficients rather than mole fraction alone. The pure-component vapour pressure must refer to the same temperature. A nonvolatile solute lowers the solvent vapour pressure in the ideal dilute limit. Check this scope before calculating: temperature, composition, phase and concentration scale can affect the result. If the sample violates an assumption, extra decimal places will not fix the model. State the mismatch or choose a better description, such as activities for nonideal solutions or a real-gas model at high pressure.

Recheck the example independently: At a fixed temperature, x_A=0.40 and p_A°=50.0 kPa give p_A=20.0 kPa. If x_B=0.60 and p_B°=30.0 kPa, p_total=20.0+18.0=38.0 kPa. Check: the mole fractions sum to one and each partial pressure is below its pure-component vapour pressure. Then verify the unit (p_i and p_i° in the same pressure unit · x_i dimensionless) and substitute the result back into the relation. A material balance must remain consistent; a pressure or temperature relation must change in the physically expected direction. A failed check often points to mixed reference quantities, an unconverted unit, or an assumption that does not fit the sample.

Raoult’s Law sits beside Mole Fraction and Dalton's Law of Partial Pressures but serves a distinct purpose: Vapour–liquid equilibrium and introductory distillation calculations for ideal mixtures. Linked relations may supply inputs, but they do not replace this equation. Check standard state, ideal-mixture assumptions and reaction step separately for each relation. In a multistep problem, first establish the balance or measured quantity, then apply the equilibrium model, and finally verify units. Distinguish them by naming the quantity each predicts and the measurement each requires.