Raoult's Law vs Henry's Law: Vapor Pressure and Gas Solubility Explained

Raoult's Law vs Henry's Law: Vapor Pressure and Gas Solubility Explained

2025-12-16

In physical chemistry and chemical engineering, understanding solution behavior is essential for vapor–liquid equilibrium (VLE) analysis, separation processes, and material loss estimation. Two fundamental laws are widely used:

  • Raoult’s Law – relates vapor pressure to liquid-phase composition
  • Henry’s Law – relates gas solubility to gas-phase partial pressure

Although they apply to different components, both laws exhibit linear behavior in ideal solutions. This article explains their definitions, similarities, deviations in real systems, and practical engineering applications.

1. Raoult’s Law and Henry’s Law

1.1 Raoult’s Law

Raoult’s Law describes the partial vapor pressure of a component in an ideal liquid mixture. It is accurate for solvents and volatile components when intermolecular interactions between unlike molecules are negligible.

Mathematical expression:

$$ P_i = x_i \cdot P_i^0 $$
Symbol Meaning
(P_i) partial vapor pressure of component (i) in the vapor phase
(x_i) mole fraction of component (i) in the liquid phase
(P_i^0) saturated vapor pressure of pure component (i) at the same temperature

Example

A liquid mixture contains 50 mol% ethanol.
The saturated vapor pressure of pure ethanol at 25 °C is 0.08 atm.

$$ x_{\text{ethanol}} = 0.5 $$ $$ P_{\text{ethanol}}^0 = 0.08\ \text{atm} $$ $$ P_{\text{ethanol}} = x_{\text{ethanol}} \cdot P_{\text{ethanol}}^0 = 0.5 \times 0.08 = 0.04\ \text{atm} $$

1.2 Henry’s Law

Henry’s Law describes the solubility of a gas in a liquid at equilibrium. It is applicable to dilute gas components dissolved in liquids.

Mathematical expression:

$$ C = k_H \cdot P $$

Where:

  • (C) — concentration of dissolved gas in the liquid
  • (P) — partial pressure of the gas in the vapor phase
  • (k_H) — Henry’s constant (depends on solvent and temperature)

Typical applications include:

  • Gas absorption and stripping operations
  • Carbonated beverage production
  • Environmental engineering (air–water equilibrium systems)

2. Relationship in Ideal Solutions

In ideal solutions, solute–solvent interactions are negligible, and both laws exhibit linear proportionality.

Linear behavior

  • Raoult’s Law (liquid → vapor):
$$ P_i = x_i \cdot P_i^0 $$
  • Henry’s Law (gas → liquid):
$$ C = k_H \cdot P $$

Henry’s Law can be rearranged to express partial pressure:

$$ P = \frac{C}{k_H} $$

At gas saturation, when the dissolved concentration reaches (C_{\text{sat}}), the corresponding partial pressure equals the saturated vapor pressure (P_{\text{sat}}):

$$ P_{\text{sat}} = \frac{C_{\text{sat}}}{k_H} \quad \Rightarrow \quad \frac{1}{k_H} = P_{\text{sat}} $$

Conceptual comparison

Law Primary focus Mathematical form
Raoult’s Law Vapor pressure (P_i = x_i P_i^0)
Henry’s Law Gas solubility (C = k_H P)
  • Raoult’s Law focuses on vapor pressure changes caused by liquid composition
  • Henry’s Law focuses on dissolved gas concentration governed by gas pressure

In ideal systems, both laws describe the same linear thermodynamic behavior from different perspectives.

3. Deviations in Real Solutions

Real solutions deviate from ideality due to intermolecular forces, such as hydrogen bonding, polarity differences, and van der Waals forces.

3.1 Raoult’s Law deviations

  • Vapor pressure no longer varies linearly with mole fraction
  • Positive deviation: weaker intermolecular interactions → higher vapor pressure
  • Negative deviation: stronger interactions → lower vapor pressure

3.2 Henry’s Law deviations

  • Gas solubility deviates from linearity at elevated pressures
  • Strongly influenced by solvent composition and temperature

Practical validity in real systems

  • Raoult’s Law remains valid for the solvent in dilute solutions
  • Henry’s Law remains valid for trace gas solutes

Example: Nitrogen dissolved in liquid propylene

  • Liquid phase: predominantly propylene with trace nitrogen
  • Propylene vapor pressure:
$$ P_{\text{propylene}} \approx X_{\text{propylene}} \cdot P_{\text{propylene}}^0 $$
  • Nitrogen solubility:
$$ C_{\text{N}_2} \approx k_H \cdot P_{\text{N}_2} $$

These approximations are widely used for engineering calculations.

4. Applications in Chemical Engineering

In industrial storage and transfer systems, non-condensable gas (NCG) purging is commonly required. During purging, volatile liquids may evaporate into the gas phase, resulting in material losses.

Step 1: Vapor pressure of liquid component

$$ P_{\text{material}} = X_{\text{material}} \cdot P_{\text{material}}^0 $$

Step 2: Gas-phase volume fraction

$$ y_{\text{material}} = \frac{P_{\text{material}}}{P_{\text{total}}} $$

Loss reduction strategies

  • Increasing system pressure reduces vapor-phase concentration
  • Lowering temperature reduces saturated vapor pressure

Example: Propylene tank purged with nitrogen

Operating conditions: 20 °C, total pressure = 15 atm

Parameter Value
Mole fraction \(X_{\text{C}_3\text{H}_6}\) 1
Saturated vapor pressure \(P_{\text{C}_3\text{H}_6}^0\) 10 atm
System pressure \(P_{\text{total}}\) 15 atm

Vapor-phase mole fraction:

$$ y_{\text{C}_3\text{H}_6} = \frac{10}{15} \approx 0.667 $$

Lowering the temperature to 0 °C:

$$ P_{\text{C}_3\text{H}_6}^0 \approx 5.7\ \text{atm} \quad \Rightarrow \quad y_{\text{C}_3\text{H}_6} \approx 0.38 $$

Increasing total pressure while keeping temperature at 20 °C:

$$ y_{\text{C}_3\text{H}_6} = \frac{10}{30} \approx 0.333 $$

Result: Both lowering temperature and increasing total pressure reduce propylene loss. Combined, the effect is even more significant.

5. Summary

  1. Raoult’s Law and Henry’s Law show similar linear behavior in ideal solutions.
  2. In real systems, deviations occur, but Raoult’s Law remains applicable to solvents and Henry’s Law to trace gases.
  3. These principles are powerful tools for pressure control, temperature optimization, and material loss reduction in chemical engineering practice.