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What is Raoult's law?

Class 12 ChemistryNCERT chapter: Solutionsइसे हिंदी में पढ़ें

Exam-ready answer

Raoult's law states that for a solution of volatile liquids, the partial vapour pressure of each component of the solution is directly proportional to its mole fraction present in the solution. So p₁ = p₁°x₁ and p₂ = p₂°x₂, where p° is the vapour pressure of the pure component. The total vapour pressure is p_total = p₁ + p₂. Solutions obeying it over the whole concentration range are ideal solutions.

Explanation

Consider a closed vessel with two volatile liquids, 1 and 2, mixed together. Both evaporate, and at equilibrium the vapour above the solution exerts partial pressures p₁ and p₂. In the mixture, molecules of each liquid make up only a fraction of the surface, so fewer of them escape than from the pure liquid. Raoult's law gives p₁ = p₁°x₁ and p₂ = p₂°x₂, where x₁ and x₂ are mole fractions in the solution.

By Dalton's law of partial pressures, p_total = p₁ + p₂ = p₁°x₁ + p₂°x₂. Since x₁ = 1 − x₂, this becomes p_total = p₁° + (p₂° − p₁°)x₂. So the total vapour pressure varies linearly with the mole fraction of either component. A plot of p₁, p₂ and p_total against mole fraction gives three straight lines. Mixtures such as n-hexane and n-heptane, or benzene and toluene, behave nearly like this.

If the solute is non-volatile, such as glucose or sugar in water, only the solvent contributes to vapour pressure: p₁ = p₁°x₁. Then (p₁° − p₁)/p₁° = x₂, the relative lowering of vapour pressure equals the mole fraction of the solute. Solutions that obey Raoult's law at all concentrations are ideal, with ΔmixH = 0 and ΔmixV = 0. Non-ideal solutions show positive deviation (ethanol + acetone) or negative deviation (chloroform + acetone).

Points to remember

  1. Raoult's law: partial vapour pressure of each volatile component is directly proportional to its mole fraction in solution.
  2. p₁ = p₁°x₁, p₂ = p₂°x₂; p_total = p₁° + (p₂° − p₁°)x₂.
  3. With a non-volatile solute: (p₁° − p₁)/p₁° = x₂ (relative lowering of vapour pressure).
  4. Ideal solutions obey Raoult's law over the entire range; ΔmixH = 0 and ΔmixV = 0 (e.g., n-hexane + n-heptane, benzene + toluene).
  5. Positive deviation: p higher than predicted (ethanol + acetone); negative deviation: p lower than predicted (chloroform + acetone).

Exam tip

Write the statement, then both equations p₁ = p₁°x₁ and p_total = p₁° + (p₂° − p₁°)x₂, and sketch the vapour pressure versus mole fraction graph with three straight lines. Label axes x₁ = 1 to x₂ = 1 clearly; the graph often carries a mark by itself.

Questions students also ask

What is the difference between ideal and non-ideal solutions?
An ideal solution obeys Raoult's law at all concentrations, with no heat change and no volume change on mixing, because A–B attractions equal A–A and B–B attractions. Non-ideal solutions do not obey the law; their vapour pressure is higher or lower than predicted, showing positive or negative deviation.
How is Raoult's law a special case of Henry's law?
Henry's law says the partial pressure of a gas over a solution is p = K_H x. Raoult's law says p = p°x for a volatile component. Both state that partial pressure is proportional to mole fraction; Raoult's law is the case in which the constant K_H equals the pure component's vapour pressure p°.
Why does a chloroform and acetone mixture show negative deviation?
Chloroform's hydrogen forms a hydrogen bond with the oxygen of acetone. These new attractions are stronger than those in the pure liquids, so molecules escape less easily into the vapour. The vapour pressure becomes lower than Raoult's law predicts, which is a negative deviation.

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