ChemistryPhysical ChemistryA-Level

CCEAAPIBAbiturBachilleratoCAPSCBSECESS

Raoult's law

Partial vapour pressure of a component in an ideal solution.

Understand the formulaSee the free derivationOpen the full walkthrough

P_{i} = x_{i} P_{i}^{*}

Open Full Walkthrough Try Calculator

This public page keeps the free explanation visible and leaves premium worked solving, advanced walkthroughs, and saved study tools inside the app.

Core idea

Overview

Raoult's law states that the partial vapor pressure of a component in an ideal solution is equal to the product of its mole fraction in the liquid phase and the vapor pressure of the pure component. This principle assumes that the intermolecular forces between unlike molecules are equal to those between like molecules in the pure substances.

When to use: Apply this equation when analyzing ideal mixtures where components have similar chemical structures and molecular sizes. It is most accurate for dilute solutions or mixtures of non-polar liquids like benzene and toluene at low to moderate pressures.

Why it matters: This law provides the theoretical basis for colligative properties such as vapor pressure lowering and boiling point elevation. It is a critical tool for chemical engineers designing distillation processes to separate chemical mixtures based on volatility.

Symbols

Variables

x_i = Mole Fraction, P_i^* = Pure Vapour Pressure, P_i = Partial Pressure

x_{i}

Mole Fraction

V a r iab l e

P_{i}^{*}

Pure Vapour Pressure

k P a

P_{i}

Partial Pressure

k P a

Walkthrough

Derivation

Formula: Raoult's Law

In an ideal solution, the partial vapour pressure of a component equals its mole fraction times the vapour pressure of the pure component.

Solution is ideal: intermolecular forces A–A, B–B, and A–B are similar.
Temperature is constant.

State the Law:

Partial pressure equals mole fraction times the pure-component vapour pressure.

p_{A} = x_{A} p_{A}^{⋆}

Result

p_{A} = x_{A} p_{A}^{⋆}

Source: Standard curriculum — A-Level Chemistry (Raoult’s law)

Free formulas

Rearrangements

Solve for $P_{i}$

Make Pi the subject

P_{i} = x_{i} P_{i}^{*}

Pi is already the subject of the formula.

Difficulty: 1/5

Solve for $x_{i}$

Raoult's Law (Solve for Mole Fraction)

x_{i} = \frac{P _{i}}{P _{i}^{*}}

Rearrange Raoult's Law, $P_{i} = x_{i} P_{i}^{*}$ , to solve for the mole fraction ( $x_{i}$ ) of a component in a solution, given its partial pressure ( $P_{i}$ ) and the vapor pressure of the pure component ( $P_{i}^{*}$ ).

Difficulty: 2/5

Solve for $P_{i}^{*}$

Make Pi^* the subject

P_{i}^{*} = \frac{P _{i}}{x _{i}}

Rearrange Raoult's law to solve for the pure vapor pressure.

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph is a straight line passing through the origin with a slope equal to the pure component vapour pressure. This linear relationship means that doubling the mole fraction results in a proportional increase in partial pressure. For a chemistry student, this shape indicates that the partial pressure is directly dependent on the concentration of the component, where small mole fractions lead to low vapour pressure and large mole fractions approach the pure component pressure. The most important feature is the co

Graph type: linear

Why it behaves this way

Intuition

Imagine the surface of a liquid mixture where molecules of different components are randomly distributed; the partial pressure of a component above the liquid is proportional to its fraction at the surface and its

P_{i}

The pressure exerted by the vapor of component i above the liquid solution.

Represents how much component i contributes to the total gas pressure; directly proportional to how many i molecules escape the liquid surface.

x_{i}

The ratio of moles of component i to the total moles of all components in the liquid solution.

Indicates the proportion of component i molecules available at the liquid surface to potentially vaporize.

P_{i}^{*}

The vapor pressure of pure component i at the same temperature as the solution.

This is the maximum vapor pressure component i can exert, reflecting its intrinsic tendency to vaporize when unmixed.

Free study cues

Insight

Canonical usage

Ensure consistent pressure units for all pressure terms and that mole fraction is dimensionless.

Common confusion

A common mistake is using different units for $P_{i}$ and $P_{i}$ ^*, leading to incorrect calculations. Another is confusing mole fraction with mole percentage without proper conversion.

Dimension note

The mole fraction ( $x_{i}$ ) is a dimensionless quantity, representing the ratio of moles of a component to the total moles in the mixture.

Unit systems

$P_{i}$ Any consistent unit of pressure (e.g., Pa, atm, bar, mmHg) · Must be in the same unit as P_i^*.

$x_{i}$ Dimensionless · Expressed as a fraction, not a percentage, unless explicitly converted.

$P_{i}^{*}$ Any consistent unit of pressure (e.g., Pa, atm, bar, mmHg) · Must be in the same unit as P_i.

One free problem

Practice Problem

A chemical solution contains a component with a mole fraction of 0.60. If the vapor pressure of the pure component at this temperature is 120.0 mmHg, calculate the partial vapor pressure exerted by this component in the mixture.

Mole Fraction0.6

Pure Vapour Pressure120 kPa

Solve for: $P i$

Hint: Multiply the given mole fraction by the vapor pressure of the pure substance.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

Predicting vapor pressure above a water-ethanol mixture.

Study smarter

Tips

Ensure the mole fraction (xi) refers specifically to the liquid phase of the mixture.
The vapor pressure of the pure substance (Pist) must be determined at the exact same temperature as the solution.
In non-ideal solutions, deviations occur if the attractive forces between different molecules are significantly stronger or weaker than those in the pure states.

Avoid these traps

Common Mistakes

Applying to non-ideal solutions without correction.
Confusing partial and total pressure.

Common questions

Frequently Asked Questions

In an ideal solution, the partial vapour pressure of a component equals its mole fraction times the vapour pressure of the pure component.

Apply this equation when analyzing ideal mixtures where components have similar chemical structures and molecular sizes. It is most accurate for dilute solutions or mixtures of non-polar liquids like benzene and toluene at low to moderate pressures.

This law provides the theoretical basis for colligative properties such as vapor pressure lowering and boiling point elevation. It is a critical tool for chemical engineers designing distillation processes to separate chemical mixtures based on volatility.

Applying to non-ideal solutions without correction. Confusing partial and total pressure.