What Is The Difference Between Real Gases And Ideal Gases

Real gases and ideal gases represent two distinct categories in the realm of thermodynamics, each with unique properties and behaviors. Ideal gases serve as a theoretical model that simplifies the complex interactions between gas molecules, providing a foundation for understanding gas behavior under certain conditions. In contrast, real gases encompass the behavior of actual gases found in nature, which deviate from ideal gas behavior due to factors such as intermolecular forces and molecular volume. Understanding the differences between real and ideal gases is crucial in various scientific and engineering applications, including chemical engineering, materials science, and environmental science.

Introduction to Ideal Gases

Ideal gases are theoretical gases that obey the ideal gas law, a fundamental equation of state that describes the relationship between pressure, volume, temperature, and the number of moles of gas. The ideal gas law assumes that gas molecules have negligible volume and do not interact with each other, meaning there are no intermolecular forces between them. These assumptions simplify the mathematical treatment of gases, making it easier to predict their behavior under various conditions.

The ideal gas law is expressed as:

PV = nRT

Where:

• P is the pressure of the gas
• V is the volume of the gas
• n is the number of moles of gas
• R is the ideal gas constant
• T is the absolute temperature of the gas

Ideal gases serve as a useful approximation for real gases under certain conditions, such as low pressure and high temperature, where the assumptions of negligible molecular volume and intermolecular forces are more valid. However, as pressure increases and temperature decreases, real gases deviate significantly from ideal gas behavior due to the increasing importance of these factors.

Introduction to Real Gases

Real gases, unlike ideal gases, exhibit behavior that deviates from the ideal gas law due to the presence of intermolecular forces and the finite volume of gas molecules. These factors become more significant at high pressures and low temperatures, where gas molecules are closer together and interact more strongly. Intermolecular forces, such as van der Waals forces, can either attract or repel gas molecules, affecting the pressure and volume of the gas. Additionally, the finite volume of gas molecules reduces the available space for them to move around, leading to deviations from ideal gas behavior.

To account for these deviations, various equations of state have been developed for real gases, such as the van der Waals equation and the Redlich-Kwong equation. These equations incorporate correction terms to account for intermolecular forces and molecular volume, providing a more accurate description of real gas behavior under a wider range of conditions.

Key Differences between Real Gases and Ideal Gases

1. Intermolecular Forces

• Ideal Gases: In the ideal gas model, intermolecular forces are assumed to be negligible. This means that gas molecules do not attract or repel each other, and their motion is solely determined by their kinetic energy.
• Real Gases: Real gases experience intermolecular forces, such as van der Waals forces, which can significantly affect their behavior. These forces arise from the attraction and repulsion between molecules due to their electric charges.

2. Molecular Volume

• Ideal Gases: Ideal gases are assumed to have negligible molecular volume. This means that the space occupied by the gas molecules themselves is insignificant compared to the total volume of the gas.
• Real Gases: Real gases have a finite molecular volume, which reduces the available space for gas molecules to move around. This effect becomes more pronounced at high pressures, where gas molecules are closer together.

3. Compressibility Factor

• Ideal Gases: The compressibility factor (Z) for an ideal gas is always equal to 1. This factor represents the ratio of the actual volume of a gas to the volume predicted by the ideal gas law.
• Real Gases: The compressibility factor for real gases deviates from 1, depending on the pressure and temperature. At high pressures, the compressibility factor is typically greater than 1, indicating that the gas is less compressible than an ideal gas. At low pressures, the compressibility factor can be less than 1, indicating that the gas is more compressible than an ideal gas.

4. Applicability

• Ideal Gases: The ideal gas law is a useful approximation for real gases under certain conditions, such as low pressure and high temperature. Under these conditions, the assumptions of negligible molecular volume and intermolecular forces are more valid.
• Real Gases: Real gas equations of state, such as the van der Waals equation, are more accurate for describing the behavior of real gases under a wider range of conditions, especially at high pressures and low temperatures.

5. Deviation from Ideal Gas Law

• Ideal Gases: Ideal gases perfectly obey the ideal gas law, meaning that their pressure, volume, and temperature are related according to the equation PV = nRT.
• Real Gases: Real gases deviate from the ideal gas law, especially at high pressures and low temperatures. This deviation is due to the effects of intermolecular forces and molecular volume, which are not accounted for in the ideal gas law.

Equations of State for Real Gases

To accurately describe the behavior of real gases, various equations of state have been developed that incorporate correction terms to account for intermolecular forces and molecular volume. Some of the most common equations of state for real gases include:

1. Van der Waals Equation

The van der Waals equation is one of the earliest and most widely used equations of state for real gases. It introduces two correction terms to the ideal gas law:

• a: accounts for the attractive intermolecular forces between gas molecules.
• b: accounts for the volume occupied by the gas molecules themselves.

The van der Waals equation is expressed as:

(P + a(n/V)^2)(V - nb) = nRT

Where:

• P is the pressure of the gas
• V is the volume of the gas
• n is the number of moles of gas
• R is the ideal gas constant
• T is the absolute temperature of the gas
• a is the van der Waals constant for attraction
• b is the van der Waals constant for volume

The van der Waals equation provides a more accurate description of real gas behavior than the ideal gas law, especially at moderate pressures and temperatures. However, it can still deviate from experimental data under extreme conditions.

2. Redlich-Kwong Equation

The Redlich-Kwong equation is another popular equation of state for real gases that is more accurate than the van der Waals equation, especially at high pressures. It introduces temperature-dependent correction terms to account for intermolecular forces.

The Redlich-Kwong equation is expressed as:

P = (RT)/(V_m - b) - a/(T^(1/2)V_m(V_m + b))

Where:

• P is the pressure of the gas
• V_m is the molar volume of the gas
• R is the ideal gas constant
• T is the absolute temperature of the gas
• a is a constant that depends on the gas
• b is a constant that depends on the gas

The Redlich-Kwong equation is widely used in chemical engineering and other fields for modeling the behavior of real gases.

3. Soave-Redlich-Kwong (SRK) Equation

The Soave-Redlich-Kwong (SRK) equation is a modification of the Redlich-Kwong equation that provides improved accuracy for predicting the vapor pressure of pure substances. It introduces a temperature-dependent parameter to account for the effects of molecular shape and polarity.

The SRK equation is expressed as:

P = (RT)/(V_m - b) - (αa)/(V_m(V_m + b))

Where:

• P is the pressure of the gas
• V_m is the molar volume of the gas
• R is the ideal gas constant
• T is the absolute temperature of the gas
• a is a constant that depends on the gas
• b is a constant that depends on the gas
• α is a temperature-dependent parameter

The SRK equation is widely used in process simulation and design for predicting the behavior of real gases in chemical processes.

4. Peng-Robinson Equation

The Peng-Robinson equation is another widely used equation of state for real gases that is known for its accuracy in predicting the volumetric behavior of hydrocarbons. It is similar to the SRK equation but uses a different temperature-dependent parameter.

The Peng-Robinson equation is expressed as:

P = (RT)/(V_m - b) - (aα)/(V_m^2 + 2bV_m - b^2)

Where:

• P is the pressure of the gas
• V_m is the molar volume of the gas
• R is the ideal gas constant
• T is the absolute temperature of the gas
• a is a constant that depends on the gas
• b is a constant that depends on the gas
• α is a temperature-dependent parameter

The Peng-Robinson equation is widely used in the petroleum industry for modeling the behavior of crude oil and natural gas.

When to Use Ideal Gas Law vs. Real Gas Equations

The choice between using the ideal gas law and real gas equations depends on the specific conditions and the desired accuracy.

Use Ideal Gas Law When:

• The pressure is low (typically below a few atmospheres).
• The temperature is high (well above the boiling point of the gas).
• The gas is non-polar and has a simple molecular structure.
• High accuracy is not required.

Use Real Gas Equations When:

• The pressure is high (several atmospheres or more).
• The temperature is low (near or below the boiling point of the gas).
• The gas is polar or has a complex molecular structure.
• High accuracy is required.

In general, it is always best to use real gas equations when dealing with real gases, especially under conditions where the ideal gas law is likely to deviate significantly. However, the ideal gas law can be a useful approximation for quick calculations and estimations when high accuracy is not required.

Impact of the Differences

The differences between real and ideal gases have significant implications in various fields, including:

• Chemical Engineering: In chemical engineering, accurate modeling of gas behavior is essential for designing and optimizing chemical processes. Real gas equations of state are used to predict the behavior of gases in reactors, distillation columns, and other process equipment.
• Materials Science: In materials science, the properties of gases are important in various applications, such as the synthesis of thin films and the processing of materials. Real gas behavior must be considered when designing and controlling these processes.
• Environmental Science: In environmental science, understanding the behavior of gases is crucial for studying air pollution, climate change, and other environmental issues. Real gas behavior is considered when modeling the transport and fate of pollutants in the atmosphere.
• Thermodynamics: In thermodynamics, the differences between real and ideal gases are fundamental to understanding the behavior of thermodynamic systems. Real gas equations of state are used to calculate thermodynamic properties such as enthalpy, entropy, and Gibbs free energy.

Conclusion

In conclusion, real gases and ideal gases represent two distinct categories of gases with unique properties and behaviors. Ideal gases are theoretical gases that obey the ideal gas law, while real gases exhibit deviations from ideal gas behavior due to intermolecular forces and molecular volume. The choice between using the ideal gas law and real gas equations depends on the specific conditions and the desired accuracy. Real gas equations of state, such as the van der Waals equation and the Redlich-Kwong equation, provide a more accurate description of real gas behavior under a wider range of conditions. Understanding the differences between real and ideal gases is crucial in various scientific and engineering applications, including chemical engineering, materials science, and environmental science.