Raoult's Law vs Henry's Law — Reducing Material Loss from NCG Emissions

2025-12-16

Engineering Problem: Material Loss Caused by NCG Emissions

In many chemical engineering systems—such as storage tanks, reactors, absorbers, and transfer lines—non-condensable gases (NCGs) are inevitably present.
Typical NCGs include nitrogen, hydrogen, methane, or purge gases used for safety and process control.

During venting or purging operations, NCGs carry volatile liquid components into the vapor phase, leading to:

Loss of valuable raw materials
Increased emissions and environmental impact
Higher operating and recovery costs

A key engineering question therefore arises:

How can material loss caused by non-condensable gas emissions be quantitatively estimated and effectively reduced?

The answer lies in understanding vapor–liquid equilibrium (VLE) behavior, which is fundamentally governed by Raoult’s Law and Henry’s Law.
This article explains how these two laws describe the same thermodynamic reality from different perspectives and how they can be used to minimize material loss in real engineering systems.

1. Raoult’s Law and Henry’s Law

1.1 Raoult’s Law

Raoult’s Law describes the vapor pressure contribution of a volatile component in an ideal liquid mixture.
It is most accurate for solvents or major components when intermolecular interactions are similar.

Mathematical expression:

$$ P_i = x_i \cdot P_i^0 $$

Symbol definitions (engineering notation):

P_i: partial vapor pressure of component i
x_i: mole fraction of component i in the liquid phase
P_i⁰: saturated vapor pressure of pure component i at system temperature

Example

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

$$ P_{\text{ethanol}} = 0.5 \times 0.08 = 0.04\ \text{atm} $$

This means ethanol contributes 0.04 atm to the total vapor pressure.

1.2 Henry’s Law

Henry’s Law describes the equilibrium solubility of a dilute gas in a liquid.
It is applicable to trace gas components, such as nitrogen dissolved in hydrocarbons.

Mathematical expression:

$$ C = k_H \cdot P $$

Symbol definitions:

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 engineering applications:

Gas absorption and stripping
Purge gas design
Environmental air–water equilibrium calculations

2. Relationship Between Raoult’s Law and Henry’s Law

Although Raoult’s Law and Henry’s Law are often taught separately, they describe linear equilibrium behavior in ideal systems.

Linear equilibrium forms

Liquid → vapor (Raoult’s Law)

$$ P_i = x_i \cdot P_i^0 $$

Gas → liquid (Henry’s Law)

$$ C = k_H \cdot P $$

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

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

At gas saturation, the dissolved concentration reaches C_sat, and the corresponding vapor pressure equals the saturated vapor pressure P_sat:

$$ P_{\text{sat}} = \frac{C_{\text{sat}}}{k_H} $$

Conceptual comparison

Raoult’s Law
Engineering focus: Vapor pressure of volatile liquids
Mathematical form: P_i = x_i P_i⁰
Henry’s Law
Engineering focus: Solubility of trace gases
Mathematical form: C = k_H P
Key insight:
In ideal systems, both laws describe the same linear thermodynamic behavior, but from opposite phase perspectives.

3. Deviations in Real Solutions

Real industrial systems deviate from ideality due to intermolecular forces.

3.1 Raoult’s Law deviations

Vapor pressure no longer scales linearly with composition
Positive deviation: weaker interactions → higher vapor pressure
Negative deviation: stronger interactions → lower vapor pressure

3.2 Henry’s Law deviations

Valid mainly at low gas concentrations
Strong dependence on temperature and solvent composition

Practical engineering validity

Raoult’s Law remains valid for major liquid components
Henry’s Law remains valid for trace non-condensable gases

Example: Nitrogen dissolved in liquid propylene

Liquid phase: mostly propylene
Gas phase: nitrogen-rich purge gas

$$ P_{\text{propylene}} \approx x_{\text{propylene}} \cdot P_{\text{propylene}}^0 $$

$$ C_{\text{N}_2} \approx k_H \cdot P_{\text{N}_2} $$

These approximations are widely used in purge and vent loss calculations.

4. Engineering Application: Reducing Material Loss from NCG Emissions

During NCG purging, volatile liquids evaporate into the gas phase and are discharged.

Step 1: Vapor pressure of the liquid component

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

Step 2: Gas-phase mole fraction

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

Loss reduction strategies

Increase total system pressure
Reduce operating temperature

Example: Propylene tank purged with nitrogen

At 20 °C and a total pressure of 15 atm, the saturated vapor pressure of propylene is 10 atm, and the liquid phase consists almost entirely of propylene (mole fraction ≈ 1). Under these conditions, the mole fraction of propylene in the vapor phase can be calculated as follows:

$$ y_{\text{C3H6}} = \frac{P_{\text{C3H6}}}{P_{\text{total}}} = \frac{10}{15} \approx 0.667 $$

The relationship between the volume of non-condensable gas (NCG) purged and the propylene lost is given by:

$$ V_{\text{C3H6,loss}} = \frac{y_{\text{C3H6}}}{1 - y_{\text{C3H6}}} \cdot V_{\text{NCG}} $$

For example, if 100 L of NCG is purged at this condition:

$$ V_{\text{C3H6,loss}} \approx \frac{0.667}{1 - 0.667} \cdot 100 \approx 200\ \text{L} $$

If the temperature is lowered to 0 °C, the saturated vapor pressure of propylene decreases to approximately 5.7 atm. The vapor-phase mole fraction becomes:

$$ y_{\text{C3H6}} = \frac{5.7}{15} \approx 0.38 $$

Purging 100 L of NCG under this condition results in:

$$ V_{\text{C3H6,loss}} \approx \frac{0.38}{1 - 0.38} \cdot 100 \approx 61\ \text{L} $$

If the total system pressure is increased to 30 atm at 20 °C (with saturated vapor pressure still 10 atm):

$$ y_{\text{C3H6}} = \frac{10}{30} \approx 0.333 $$ $$ V_{\text{C3H6,loss}} \approx \frac{0.333}{1 - 0.333} \cdot 100 \approx 50\ \text{L} $$

Conclusion: Lowering temperature or increasing total pressure both significantly reduce propylene loss during NCG purging.

5. Summary

Material loss from non-condensable gas emissions originates from vapor–liquid equilibrium behavior.
Raoult’s Law governs volatile liquid evaporation, while Henry’s Law governs trace gas solubility.
Applying these principles enables effective pressure control, temperature optimization, and loss reduction in chemical engineering systems.

Recommended Engineering Tool

To make calculations easier, We developed an app that can calculate the saturated vapor pressure for hundreds of chemical substances. You can download it here: Vapor Pressure Calculator App

Author: Hadel
Published: 2025-12-16
Source: chem.zhanghd.fun