In chemical plants, gases are everywhere in reactors, compressors, and storage systems. To design these processes safely and accurately, engineers need to understand how gases behave under different pressures and temperatures. The Ideal Gas Law works well for simple conditions, but in real operations, gases often behave differently. That’s when Real Gas Equations, like the Van der Waals Equation, become important.
In this article, we will learn these laws in detail and explore the differences between Ideal Gases and Real Gases, their assumptions, and industrial applications
Table of Contents
What is Ideal gas law?
The Ideal Gas Law is a fundamental equation that relates the pressure, volume, temperature, and number of moles of an ideal gas.
PV=nRT
- P = Pressure of the gas
- V = Volume of the gas
- n = Number of moles
- R = Universal gas constant
- T = Absolute temperature (in Kelvin)
You can use the Ideal Gas Law Calculator by us to quickly find any variable if you know the other three.
Assumptions of the Ideal Gas Law
Negligible molecular volume: Gas molecules are extremely small compared to the container, so their own volume can be ignored.
No intermolecular forces: Molecules do not attract or repel each other and move independently.
Constant random motion: Gas particles move freely in all directions and collide with each other or the container walls.
Perfectly elastic collisions: No energy is lost during molecular collisions.
Kinetic energy depends only on temperature: The average kinetic energy of gas molecules is directly proportional to the absolute temperature.
Because of these assumptions, the Ideal Gas Law works well under low-pressure and high-temperature conditions
However, in industrial equipment such as compressors and reactors, gases are often subjected to high pressures or low temperatures, leading molecules to come closer and interact, causing the gas to deviate from ideal behavior.
To predict this behavior more accurately, Real Gas Equations, such as the Van der Waals Equation, are used to correct the limitations of the Ideal Gas Law.
What Is a Real Gas?
Real gases, also known as non-ideal gases, are gases that deviate from the Ideal Gas Law. Their molecules occupy a finite volume and experience intermolecular forces such as attraction and repulsion.
They behave differently under high pressure or low temperature, where molecular attractions and repulsions become more noticeable.
Dutch scientist Johannes Van der Waals proposed a modified version of the Ideal Gas Law known as the Van der Waals Equation
![\[\left( P + \frac{a n^2}{V^2} \right) (V - n b) = n R T\]](http://chemicaltweak.b-cdn.net/wp-content/ql-cache/quicklatex.com-c1c2ecc0de93c9b26e15fd686ce61f91_l3.png "Rendered by QuickLaTeX.com")
P = Pressure of the gas
V = Volume of the gas
n = Number of moles
R = Universal gas constant
T = Absolute temperature (K)
a = measure of intermolecular attraction (Pa·m⁶·mol⁻²)
b = measure of finite molecular volume (m³·mol⁻¹)
You can use our Van der Waals Equation Calculator to calculate real gas properties for different substances.
Why Do Gases Deviate from Ideal Behavior?
Gases deviate from ideal behavior due to molecular interactions and finite volume. The main reasons are listed below
1. Attractive Forces
At moderate pressures and low temperatures, gas molecules move closer together. Attractive forces reduce the force of collisions with the container walls, leading to lower pressure than predicted by the Ideal Gas Law.
2. Repulsive Forces
At very high pressures, gas molecules are forced closer, and repulsive forces dominate. This makes the measured pressure higher than the ideal prediction.
3. Finite Molecular Volume
Gas molecules occupy space. The actual free volume available for motion is less than the total volume of the container, which the Ideal Gas Law does not consider.
Example: CO₂ Gas Behavior: Ideal vs Real Gas Comparison
Let’s consider CO₂ gas at 300 K and compare the pressure calculated using both equations.
| Condition | Ideal Gas Pressure (atm) | Van der Waals Pressure (atm) |
|---|---|---|
| 1 mol CO₂, 1 L volume | 24.6 | 22.9 |
The Van der Waals Equation gives a more accurate result as it accounts for molecular attractions and volume effects that are ignored in the Ideal Gas Law.
Ideal Gas vs Real Gas
This table provides a clear summary of the differences between Ideal Gas and Real Gas and explains why they matter in chemical industries.
| Property | Ideal Gas | Real Gas |
|---|---|---|
| Molecular volume | Negligible | Considered (volume b) |
| Intermolecular forces | None | Present (a accounts for attractions) |
| Governing Equation | PV = nRT | (P + a(n/V)²) (V - nb) = nRT |
| Behavior at high pressure | Obeys the Law | Deviates; repulsive forces dominate (higher pressure) |
| Behavior at low temperature | Obeys the Law | Deviates; attractive forces dominate (lower pressure) |
| Example gases | Hydrogen, Helium (at STP) | Carbon dioxide CO₂, ammonia NH₃, SO₂ |
Industrial Application
Understanding real gas behavior is essential in chemical and process engineering and these equations are use to design and optimize systems such as:
- Compressors and gas storage tanks
- Reactors operating under high pressure
- Cryogenic systems handling gases at low temperatures
- Vapor–liquid equilibrium (VLE) models in distillation or absorption
Conclusion
This was a detailed article on ideal gas vs real gas. The Ideal Gas Law explains gas behavior under simple conditions, but it loses accuracy at high pressure or low temperature. In those situations, real gas models such as the Van der Waals equation give better predictions.
Knowing when to apply each concept helps engineers make accurate calculations and design safer, more efficient systems.
