Raoult's Law
Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its liquid phase at a given temperature. When you dissolve a non-volatile solute — such as table salt or sugar — into a volatile solvent like water, the vapor pressure of the resulting solution is always lower than that of the pure solvent. This happens because solute particles occupy the liquid surface, reducing the rate at which solvent molecules can escape into the gas phase. François-Marie Raoult quantified this relationship in 1887, producing one of the most elegant and useful laws in solution chemistry. Raoult's Law states that the partial vapor pressure of a solvent above a solution is directly proportional to the mole fraction of the solvent in the solution, multiplied by the vapor pressure of the pure solvent at the same temperature. An ideal solution obeys this law perfectly across all compositions — meaning the solvent–solute intermolecular interactions are identical in strength to the pure solvent's interactions. Real solutions, however, often deviate from ideality because the new solute–solvent interactions differ in energy from the original solvent–solvent interactions, giving rise to positive or negative deviations. Understanding Raoult's Law is essential for predicting boiling point elevation, freezing point depression, and osmotic pressure — the four colligative properties that depend only on the number of dissolved particles, not their identity. It also underpins industrial processes such as fractional distillation and the design of antifreeze mixtures. In this article you will learn how to calculate vapor pressures of solutions, distinguish ideal from non-ideal behavior, and interpret deviations in terms of molecular-level interactions.
- Mole Fraction: The Key Composition Variable
- Applying Raoult's Law to Find Solution Vapor Pressure
- Ideal Solutions: When Is Raoult's Law Obeyed?
- Positive Deviations from Raoult's Law
- Negative Deviations from Raoult's Law
- Multi-Component Volatile Solutions (Dalton's Law Extension)
Mole Fraction: The Key Composition Variable
Raoult's Law uses mole fraction (χ) rather than molarity or mass percent because it captures the proportional representation of each component at the molecular level. The mole fraction of solvent A in a two-component solution is χ_A = n_A / (n_A + n_B), where n_A and n_B are the moles of solvent and solute respectively. Note that χ_A + χ_B = 1 always. For a pure solvent χ_A = 1, and for a pure solute χ_A = 0.
Applying Raoult's Law to Find Solution Vapor Pressure
For an ideal solution, the partial vapor pressure of solvent A is P_A = χ_A × P°_A, where P°_A is the vapor pressure of pure solvent A at the same temperature. Because χ_A < 1 whenever any solute is present, P_A < P°_A — vapor pressure is always lowered. The vapor pressure lowering (ΔP) equals (1 − χ_A) × P°_A = χ_B × P°_A, which shows that ΔP depends only on the mole fraction of solute particles, not their chemical identity.
Ideal Solutions: When Is Raoult's Law Obeyed?
A solution behaves ideally when A–B intermolecular forces are equal in strength to the average of A–A and B–B forces. Under these conditions, mixing is accompanied by zero enthalpy change (ΔH_mix = 0) and zero volume change (ΔV_mix = 0). Classic examples include benzene–toluene mixtures (both nonpolar aromatic hydrocarbons) and hexane–heptane mixtures. A plot of P_A vs χ_A is perfectly linear from (0,0) to (1, P°_A), passing through every experimental data point.
Positive Deviations from Raoult's Law
A positive deviation means the observed vapor pressure is higher than Raoult's Law predicts. This occurs when A–B interactions are weaker than A–A or B–B interactions, so molecules escape the liquid more easily than in the ideal case. ΔH_mix > 0 (endothermic mixing). A classic example is ethanol–water: ethanol disrupts the strong hydrogen-bond network of water, making both components more volatile. On a P vs χ diagram, the experimental curve bows above the ideal straight line. In extreme cases, a positive-deviation system can form a minimum-boiling azeotrope — a mixture that boils at a lower temperature than either pure component (e.g., ethanol–water azeotrope at 95.6% ethanol, boiling at 78.1 °C).
Negative Deviations from Raoult's Law
A negative deviation means the observed vapor pressure is lower than predicted. This occurs when A–B interactions are stronger than the pure component interactions, holding molecules in the liquid more tightly. ΔH_mix < 0 (exothermic mixing). An example is acetone–chloroform: the carbonyl oxygen of acetone forms a strong hydrogen bond with the C–H of chloroform (\ce{(CH3)2CO···HCCl3}), creating stronger attractions than in either pure liquid. The vapor pressure curve dips below the ideal line. Extreme negative deviations produce maximum-boiling azeotropes, such as hydrochloric acid–water (boiling at 108.6 °C at 20.2% HCl).
Multi-Component Volatile Solutions (Dalton's Law Extension)
When both components are volatile (e.g., benzene–toluene), each exerts its own partial pressure: P_A = χ_A P°_A and P_B = χ_B P°_B. By Dalton's Law, the total vapor pressure is P_total = P_A + P_B = χ_A P°_A + χ_B P°_B. This combined relationship is the foundation of distillation: the vapor above the mixture is richer in the more volatile component (higher P°), allowing separation by repeated vaporization and condensation steps.
The Key Equation
- P_A — Partial vapor pressure of solvent A (kPa or mmHg): The contribution of component A to the total pressure above the solution surface.
- \chi_A — Mole fraction of A (dimensionless (0 to 1)): Ratio of moles of A to total moles of all components: χ_A = n_A / (n_A + n_B + ...).
- P^\circ_A — Vapor pressure of pure solvent A (kPa or mmHg): The equilibrium vapor pressure of the pure liquid solvent at the same temperature as the solution.
Worked Example
Problem. A student dissolves 36.0 g of glucose (\ce{C6H12O6}, M = 180.2 g/mol) in 180.0 g of water (\ce{H2O}, M = 18.02 g/mol) at 25 °C. The vapor pressure of pure water at 25 °C is 3.167 kPa. Assuming an ideal solution, calculate: (a) the mole fraction of water, and (b) the vapor pressure of the solution.
Answer. Mole fraction of water = 0.9804; vapor pressure of solution = 3.105 kPa (lowering of 0.062 kPa).
Origins · 1 minFrançois-Marie Raoult and how this was discovered
Raoult formulated his vapor pressure law in 1887 after years of meticulous measurements on hundreds of solutions. He demonstrated that vapor pressure lowering depends only on the ratio of solute to solvent particles — an early insight into what we now call colligative properties. His work also established the basis for cryoscopy (freezing point depression measurements), which became a standard technique for determining molecular masses of dissolved substances in the late 19th century. Raoult conducted most of his landmark experiments in Grenoble, France, using primitive thermometers and hand-blown glass apparatus. Despite his foundational contributions to physical chemistry, he was largely self-funded and worked without the large research groups common among his contemporaries.
Related Concepts
- Boiling Point Elevation — Boiling point elevation is a direct consequence of vapor pressure lowering described by Raoult's Law — a solution must be heated to a higher temperature before its vapor pressure equals atmospheric pressure.
- Freezing Point Depression — Like boiling point elevation, freezing point depression is a colligative property rooted in the same vapor pressure lowering principle, with the solution's vapor pressure curve intersecting the solid phase line at a lower temperature.
- Mole Fraction and Molality — Raoult's Law is expressed in terms of mole fraction; understanding how to convert between concentration units (molarity, molality, mole fraction) is essential for applying the law correctly.
- Enthalpy of Mixing — The sign of ΔH_mix directly explains whether a real solution shows positive (endothermic) or negative (exothermic) deviations from Raoult's Law, linking thermodynamics to vapor pressure behavior.
- Fractional Distillation and Azeotropes — Raoult's Law for volatile mixtures (P_total = χ_A P°_A + χ_B P°_B) is the theoretical foundation of fractional distillation; azeotropes arise at extremes of positive or negative deviation.