# Ideal Gas vs. Real Gas

## What's the Difference?

Ideal gases and real gases are two different concepts used to describe the behavior of gases. Ideal gases are theoretical gases that follow the ideal gas law, which assumes that gas particles have no volume and do not interact with each other. This means that ideal gases have perfectly elastic collisions and their behavior can be accurately predicted using mathematical equations. On the other hand, real gases are actual gases that exist in the real world and do not strictly follow the assumptions of the ideal gas law. Real gases have volume and experience intermolecular forces, such as van der Waals forces, which affect their behavior. As a result, real gases deviate from ideal gas behavior at high pressures and low temperatures.

## Comparison

Attribute | Ideal Gas | Real Gas |
---|---|---|

Particle Volume | Negligible | Non-negligible |

Particle Interactions | No interactions | Interactions present |

Particle Size | Negligible | Non-negligible |

Pressure-Volume Relationship | Follows ideal gas law | Deviation from ideal gas law |

Temperature-Volume Relationship | Follows ideal gas law | Deviation from ideal gas law |

Compressibility Factor | Always equal to 1 | Varies with conditions |

Boyle's Law | Follows exactly | Deviation from ideal behavior |

Charles's Law | Follows exactly | Deviation from ideal behavior |

Avogadro's Law | Follows exactly | Deviation from ideal behavior |

Real Gas Equation | Not applicable | Van der Waals equation, Peng-Robinson equation, etc. |

## Further Detail

### Introduction

Gases are one of the fundamental states of matter, and their behavior can be described by two main models: ideal gas and real gas. While ideal gases are theoretical and follow certain assumptions, real gases exhibit deviations from these assumptions due to intermolecular forces and other factors. In this article, we will explore the attributes of ideal gas and real gas, highlighting their similarities and differences.

### 1. Molecular Structure

In an ideal gas, molecules are considered to be point masses with no volume or intermolecular forces. This assumption simplifies calculations and allows for easy mathematical treatment. On the other hand, real gases have molecules with finite volumes and experience intermolecular forces such as van der Waals forces, dipole-dipole interactions, and hydrogen bonding. These forces affect the behavior of real gases, especially at high pressures and low temperatures.

### 2. Pressure-Volume Relationship

According to Boyle's Law, the pressure and volume of an ideal gas are inversely proportional at constant temperature. This relationship is expressed by the equation P₁V₁ = P₂V₂, where P represents pressure and V represents volume. However, real gases deviate from this ideal behavior, especially at high pressures and low temperatures. The compressibility factor, Z, is introduced to account for these deviations and correct the ideal gas equation.

### 3. Temperature-Volume Relationship

Charles's Law states that the volume of an ideal gas is directly proportional to its temperature at constant pressure. This relationship is expressed by the equation V₁/T₁ = V₂/T₂, where T represents temperature. While this relationship holds reasonably well for most real gases, deviations can occur at extremely low temperatures or when intermolecular forces become significant.

### 4. Ideal Gas Law

The ideal gas law combines Boyle's Law, Charles's Law, and Avogadro's Law into a single equation: PV = nRT. Here, P represents pressure, V represents volume, n represents the number of moles, R is the ideal gas constant, and T represents temperature. The ideal gas law provides a useful approximation for many gases under normal conditions. However, it fails to account for the deviations observed in real gases.

### 5. Deviations from Ideal Behavior

Real gases deviate from ideal behavior due to intermolecular forces and molecular volume. At high pressures, the volume of gas molecules becomes significant, leading to a decrease in the available volume for gas particles to move. This results in a higher pressure than predicted by the ideal gas law. Additionally, at low temperatures, intermolecular forces become more pronounced, causing the gas particles to attract each other and reducing their kinetic energy. As a result, real gases occupy less volume than predicted by the ideal gas law.

### 6. Van der Waals Equation

To account for the deviations observed in real gases, Johannes van der Waals introduced a modified equation of state known as the van der Waals equation: (P + a(n/V)²)(V - nb) = nRT. Here, a and b are van der Waals constants that vary for different gases. The term a(n/V)² corrects for intermolecular forces, while the term nb corrects for molecular volume. The van der Waals equation provides a more accurate description of real gas behavior, especially at high pressures and low temperatures.

### 7. Critical Point

Every gas has a critical point, which represents the temperature and pressure above which the gas cannot be liquefied, regardless of the applied pressure. At the critical point, the liquid and gas phases become indistinguishable, and the substance exhibits unique properties. The critical point is characterized by the critical temperature (Tc) and critical pressure (Pc). Real gases have critical points that differ from those predicted by the ideal gas law due to intermolecular forces and molecular volume.

### 8. Real Gas Behavior at Low Temperatures

At extremely low temperatures, real gases can exhibit interesting behavior. Some gases, such as helium and hydrogen, undergo a phase transition known as Bose-Einstein condensation, where a significant fraction of the gas particles occupy the lowest energy state. This behavior is not predicted by the ideal gas law and requires quantum mechanical considerations. Additionally, some gases may exhibit solidification or liquefaction at low temperatures, further deviating from ideal gas behavior.

### 9. Real Gas Behavior at High Pressures

At high pressures, real gases can deviate significantly from ideal behavior. The intermolecular forces become more dominant, causing the gas particles to come closer together and occupy less volume. This compression effect leads to a decrease in the compressibility factor, Z, below 1. The van der Waals equation provides a better description of real gas behavior at high pressures, accounting for both molecular volume and intermolecular forces.

### Conclusion

In conclusion, ideal gas and real gas models provide different perspectives on the behavior of gases. Ideal gases are theoretical and assume point masses with no volume or intermolecular forces, allowing for simple mathematical treatment. On the other hand, real gases exhibit deviations from ideal behavior due to intermolecular forces and molecular volume. These deviations become more significant at high pressures and low temperatures. The van der Waals equation offers a more accurate description of real gas behavior, accounting for both intermolecular forces and molecular volume. Understanding the attributes of ideal gas and real gas models is crucial for various scientific and engineering applications.

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