What Is Difference Between Ideal Gas And Real Gas

In the realm of thermodynamics and chemistry, the concept of gases plays a pivotal role in understanding the behavior of matter. While the ideal gas model provides a simplified, yet powerful, framework for describing gases, real gases exhibit deviations from this idealized behavior. This article delves into the fundamental differences between ideal and real gases, exploring the underlying assumptions, equations, and factors that contribute to their distinct characteristics.

Unveiling the Ideal Gas Model

The ideal gas model, a cornerstone of thermodynamics, postulates that gases consist of particles that:

• Exhibit negligible intermolecular forces: The attractive or repulsive forces between gas molecules are considered insignificant.
• Occupy negligible volume: The volume occupied by the gas molecules themselves is negligible compared to the total volume of the gas.
• Undergo perfectly elastic collisions: Collisions between gas molecules and the container walls are perfectly elastic, meaning no energy is lost during the collisions.

Based on these assumptions, the ideal gas law emerges as a fundamental equation:

PV = nRT

Where:

• P = Pressure of the gas
• V = Volume of the gas
• n = Number of moles of the gas
• R = Ideal gas constant (8.314 J/(mol·K) or 0.0821 L·atm/(mol·K))
• T = Temperature of the gas in Kelvin

The ideal gas law provides a simple and accurate representation of gas behavior under certain conditions, particularly at low pressures and high temperatures.

The Reality of Real Gases

In contrast to the idealized world of ideal gases, real gases deviate from the ideal gas law due to the following factors:

• Intermolecular forces: Real gas molecules do experience attractive and repulsive forces, especially at high pressures and low temperatures. These forces can significantly affect the gas's behavior.
• Non-negligible volume: The volume occupied by real gas molecules is not always negligible, especially at high pressures where the molecules are more closely packed.
• Inelastic collisions: Collisions between real gas molecules and the container walls are not perfectly elastic, resulting in some energy loss.

These deviations from the ideal gas model necessitate the use of more complex equations of state to accurately describe the behavior of real gases.

Delving into the Key Differences

The differences between ideal and real gases stem from the underlying assumptions made in the ideal gas model. Let's explore these differences in detail:

1. Intermolecular Forces: A Critical Distinction

The ideal gas model assumes that intermolecular forces are negligible. However, real gas molecules exhibit attractive forces (van der Waals forces) and repulsive forces. These forces become more significant at high pressures, where the molecules are closer together, and at low temperatures, where the molecules have less kinetic energy to overcome the attractive forces.

Van der Waals forces include:

• Dipole-dipole interactions: These occur between polar molecules with permanent dipoles.
• London dispersion forces: These are temporary, weak attractive forces that arise from temporary fluctuations in electron distribution within molecules.

The presence of intermolecular forces in real gases leads to:

• Lower pressure than predicted by the ideal gas law: Attractive forces between molecules reduce the force with which they collide with the container walls, resulting in lower pressure.
• Lower volume than predicted by the ideal gas law: Attractive forces pull the molecules closer together, reducing the overall volume of the gas.

2. Molecular Volume: A Matter of Space

The ideal gas model assumes that the volume occupied by gas molecules is negligible compared to the total volume of the gas. This assumption holds true at low pressures where the molecules are far apart. However, at high pressures, the volume occupied by the molecules becomes a significant fraction of the total volume, invalidating the ideal gas law.

The non-negligible volume of real gas molecules leads to:

• Higher pressure than predicted by the ideal gas law: The actual volume available for the molecules to move around in is smaller than the total volume, leading to more frequent collisions with the container walls and higher pressure.

3. Compressibility Factor: Quantifying Deviations

The compressibility factor (Z) is a dimensionless quantity that quantifies the deviation of a real gas from ideal gas behavior. It is defined as:

Z = PV / nRT

For an ideal gas, Z = 1 under all conditions. For real gases, Z can be greater than or less than 1, depending on the pressure, temperature, and nature of the gas.

• Z < 1: Indicates that the gas is more compressible than an ideal gas, which typically occurs at moderate pressures where attractive forces dominate.
• Z > 1: Indicates that the gas is less compressible than an ideal gas, which typically occurs at high pressures where the volume of the molecules becomes significant.

4. Equations of State for Real Gases: Accounting for Deviations

To accurately describe the behavior of real gases, scientists have developed various equations of state that take into account intermolecular forces and molecular volume. Some of the most commonly used equations of state include:

• Van der Waals equation: This equation introduces two correction factors to the ideal gas law:

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

Where:

• a = Accounts for the attractive forces between molecules.

• b = Accounts for the volume occupied by the molecules.

• Redlich-Kwong equation: This equation is more accurate than the van der Waals equation, especially at high pressures.

• Soave-Redlich-Kwong (SRK) equation: This is a modification of the Redlich-Kwong equation that provides even better accuracy.

• Peng-Robinson equation: This equation is widely used in the petroleum industry due to its accuracy in predicting the behavior of hydrocarbons.

These equations of state provide a more realistic representation of real gas behavior by incorporating the effects of intermolecular forces and molecular volume.

Factors Influencing Real Gas Behavior

Several factors influence the extent to which a real gas deviates from ideal gas behavior:

• Pressure: At high pressures, the molecules are closer together, increasing the significance of intermolecular forces and molecular volume. This leads to greater deviations from the ideal gas law.
• Temperature: At low temperatures, the molecules have less kinetic energy to overcome attractive forces, leading to greater deviations from the ideal gas law.
• Nature of the gas: Gases with strong intermolecular forces, such as polar molecules or large molecules, exhibit greater deviations from the ideal gas law compared to gases with weak intermolecular forces, such as nonpolar molecules or small molecules.

When Does the Ideal Gas Law Suffice?

Despite the limitations of the ideal gas law, it provides a good approximation of gas behavior under certain conditions:

• Low pressures: At low pressures, the molecules are far apart, minimizing intermolecular forces and making the molecular volume negligible.
• High temperatures: At high temperatures, the molecules have sufficient kinetic energy to overcome attractive forces, reducing their significance.
• Gases with weak intermolecular forces: Gases with weak intermolecular forces, such as helium and neon, tend to behave more ideally than gases with strong intermolecular forces.

Under these conditions, the ideal gas law can be used to accurately predict gas behavior without significant error.

Applications of Ideal and Real Gas Concepts

The concepts of ideal and real gases have numerous applications in various fields:

• Chemical engineering: Understanding gas behavior is crucial in designing and operating chemical reactors, distillation columns, and other chemical processes.
• Thermodynamics: Ideal and real gas models are used to analyze thermodynamic cycles, such as the Carnot cycle and the Rankine cycle.
• Meteorology: The ideal gas law is used to model atmospheric processes, such as the formation of clouds and the movement of air masses.
• Aerospace engineering: Understanding gas behavior is essential in designing aircraft and spacecraft, as well as in analyzing the performance of engines and propulsion systems.

Examples to Illustrate the Differences

Let's consider a few examples to illustrate the differences between ideal and real gases:

Example 1: Comparing Ideal and Real Gas Behavior of Nitrogen at High Pressure

Nitrogen gas is compressed to a high pressure of 500 atm at a temperature of 300 K. The molar volume of nitrogen is measured to be 0.04 L/mol.

• Ideal Gas Law Prediction:

Using the ideal gas law, we can calculate the predicted molar volume:

V = nRT / P = (1 mol)(0.0821 L·atm/(mol·K))(300 K) / (500 atm) = 0.0493 L/mol

• Deviation from Ideal Behavior:

The measured molar volume (0.04 L/mol) is significantly lower than the value predicted by the ideal gas law (0.0493 L/mol). This indicates that nitrogen gas deviates from ideal behavior at high pressure due to intermolecular forces and the non-negligible volume of the molecules.

Example 2: Comparing Ideal and Real Gas Behavior of Water Vapor at High Temperature

Water vapor is heated to a high temperature of 500 K at a pressure of 1 atm.

• Ideal Gas Law Prediction:

Using the ideal gas law, we can calculate the predicted molar volume:

V = nRT / P = (1 mol)(0.0821 L·atm/(mol·K))(500 K) / (1 atm) = 41.05 L/mol

• Deviation from Ideal Behavior:

At this high temperature, the kinetic energy of the water vapor molecules is high enough to overcome the intermolecular forces to a large extent. Therefore, the measured molar volume is close to the value predicted by the ideal gas law, indicating that water vapor behaves more ideally at high temperatures.

The Critical Point: A Transition Zone

The critical point of a substance represents the temperature and pressure above which distinct liquid and gas phases do not exist. At the critical point, the properties of the liquid and gas phases become identical, and the substance exists as a supercritical fluid.

• Critical Temperature (Tc): The temperature above which a gas cannot be liquefied, no matter how much pressure is applied.
• Critical Pressure (Pc): The pressure required to liquefy a gas at its critical temperature.
• Critical Volume (Vc): The volume occupied by one mole of a substance at its critical temperature and pressure.

Near the critical point, real gas behavior deviates significantly from ideal gas behavior due to strong intermolecular forces and high density.

Conclusion: A Tale of Two Gases

In summary, the ideal gas model provides a simplified representation of gas behavior, assuming negligible intermolecular forces and molecular volume. While this model is useful under certain conditions, real gases deviate from ideal behavior due to the presence of intermolecular forces and the non-negligible volume of the molecules. These deviations become more significant at high pressures, low temperatures, and for gases with strong intermolecular forces. To accurately describe the behavior of real gases, more complex equations of state are required. Understanding the differences between ideal and real gases is crucial in various fields, including chemical engineering, thermodynamics, meteorology, and aerospace engineering. By considering the limitations of the ideal gas model and employing appropriate equations of state for real gases, scientists and engineers can accurately predict and control the behavior of gases in a wide range of applications.