Differentiate Between Real Gas And Ideal Gas

Let's delve into the fascinating world of gases, exploring the subtle yet significant differences between real and ideal gases. While the concept of an ideal gas provides a simplified model for understanding gas behavior, real gases exhibit complexities that arise from intermolecular forces and the finite volume occupied by gas molecules. Understanding these distinctions is crucial in various scientific and engineering applications, allowing for more accurate predictions and designs.

What is an Ideal Gas?

An ideal gas is a theoretical gas that perfectly obeys the ideal gas law, a cornerstone of thermodynamics. This law describes the relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas:

PV = nRT

Where R is the ideal gas constant.

The ideal gas model rests on two fundamental assumptions:

• Gas molecules have no volume: In other words, the space occupied by the molecules themselves is negligible compared to the total volume of the gas.
• There are no intermolecular forces: The molecules are assumed to not attract or repel each other. They only interact through perfectly elastic collisions.

These assumptions simplify calculations and provide a useful approximation for gas behavior under certain conditions, particularly at low pressures and high temperatures. Under these conditions, the space between gas molecules is large, minimizing intermolecular interactions and making the volume of the molecules insignificant relative to the total volume.

What is a Real Gas?

Real gases, on the other hand, are gases found in the real world. They deviate from ideal behavior because the assumptions of the ideal gas model are not entirely valid. Real gas molecules do possess volume, and they do exert intermolecular forces on each other.

These deviations become more pronounced under conditions of high pressure and low temperature. At high pressure, the space between molecules decreases, making the molecular volume a significant factor. At low temperatures, the kinetic energy of the molecules decreases, allowing intermolecular forces to have a greater influence.

Key Differences: Ideal Gas vs. Real Gas

The core differences between ideal and real gases stem from the validity of the ideal gas assumptions:

1. Molecular Volume:

• Ideal Gas: Assumes that gas molecules have negligible volume.
• Real Gas: Accounts for the finite volume occupied by gas molecules. This means that the actual volume available for the gas to move around in is less than the container's volume.

2. Intermolecular Forces:

• Ideal Gas: Assumes no intermolecular forces exist.
• Real Gas: Recognizes the presence of attractive and repulsive forces between molecules. These forces, such as van der Waals forces (Dipole-dipole, London dispersion, and Hydrogen bonding), influence the gas's behavior, especially at high pressures and low temperatures. Attractive forces tend to reduce the volume compared to an ideal gas, while repulsive forces increase it.

3. Compressibility:

• Ideal Gas: The compressibility factor (Z), defined as PV/nRT, is always equal to 1.
• Real Gas: The compressibility factor (Z) can be greater than or less than 1, indicating deviations from ideal behavior. When Z < 1, the gas is more compressible than an ideal gas due to attractive forces dominating. When Z > 1, the gas is less compressible than an ideal gas because repulsive forces and the finite molecular volume become significant.

4. Applicability of the Ideal Gas Law:

• Ideal Gas: The ideal gas law (PV = nRT) is strictly applicable under all conditions.
• Real Gas: The ideal gas law provides a good approximation under conditions of low pressure and high temperature. However, it becomes less accurate under conditions of high pressure and low temperature, requiring the use of more complex equations of state.

5. Equations of State:

• Ideal Gas: Described by the simple ideal gas law (PV = nRT).

• Real Gas: Requires more complex equations of state to accurately model their behavior. Some common equations of state for real gases include:

  • Van der Waals Equation: This equation incorporates corrections for both intermolecular forces and molecular volume:

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

    Where 'a' accounts for the attractive forces between molecules, and 'b' accounts for the volume occupied by the molecules themselves.

  • Redlich-Kwong Equation: This equation is another two-parameter equation of state that provides improved accuracy over the van der Waals equation, particularly at higher pressures.

  • Soave-Redlich-Kwong (SRK) Equation: A modification of the Redlich-Kwong equation that improves the prediction of vapor pressures.

  • Peng-Robinson Equation: Another widely used two-parameter equation of state that often provides better accuracy than the SRK equation, especially for liquids.

The Van der Waals Equation: A Closer Look

The van der Waals equation offers a valuable way to understand how real gases deviate from ideal behavior. Let's break down the equation and its implications:

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

• The term 'a(n/V)^2' represents the correction for intermolecular forces. The constant 'a' is a measure of the strength of attraction between the gas molecules. The term (n/V)^2 represents the square of the molar density, which is proportional to the frequency of intermolecular collisions. The higher the density, the more frequent the collisions, and the greater the influence of attractive forces, thus effectively reducing the measured pressure.

• The term 'nb' represents the correction for the volume occupied by the gas molecules. The constant 'b' is a measure of the volume excluded by one mole of gas. It accounts for the fact that molecules cannot occupy the same space. Therefore, the effective volume available for the molecules to move in is reduced by 'nb'.

By incorporating these corrections, the van der Waals equation provides a more accurate description of real gas behavior than the ideal gas law, particularly under conditions where the ideal gas assumptions are not valid.

Why Do Gases Deviate from Ideal Behavior?

The deviations from ideal gas behavior arise from the inherent properties of real gas molecules:

• Finite Molecular Size: Real gas molecules occupy a finite volume. This volume becomes significant at high pressures when the molecules are packed closely together. The ideal gas law assumes that the molecules are point masses with no volume, which is not true in reality.
• Intermolecular Forces: Real gas molecules experience attractive and repulsive forces. These forces, collectively known as van der Waals forces, arise from temporary fluctuations in electron distribution within the molecules (London dispersion forces), dipole-dipole interactions between polar molecules, and hydrogen bonding. These forces are negligible at low pressures and high temperatures because the molecules are far apart and moving rapidly, but they become important at high pressures and low temperatures when the molecules are close together and moving slowly.

When is the Ideal Gas Law a Good Approximation?

Despite the deviations of real gases, the ideal gas law can still provide a good approximation under certain conditions:

• Low Pressure: At low pressures, the gas molecules are far apart, making the molecular volume negligible compared to the total volume of the gas. Also, the intermolecular forces become less significant as the distance between molecules increases.

• High Temperature: At high temperatures, the kinetic energy of the gas molecules is high, overcoming the effects of intermolecular forces. The molecules move rapidly and collide frequently, minimizing the influence of attractive forces.

In general, the ideal gas law is a reasonable approximation for gases at pressures close to atmospheric pressure and temperatures above room temperature. However, for highly accurate calculations, especially at high pressures or low temperatures, it's essential to use equations of state that account for the non-ideal behavior of real gases.

Applications of Real Gas Equations of State

The equations of state for real gases are crucial in various engineering and scientific applications where accurate modeling of gas behavior is essential:

• Chemical Engineering: In chemical reactors and separation processes, accurate prediction of gas properties is crucial for optimizing process conditions and equipment design. Real gas equations of state are used to calculate the thermodynamic properties of gases, such as enthalpy, entropy, and fugacity.

• Petroleum Engineering: In the extraction, processing, and transportation of natural gas and crude oil, the behavior of gases under high pressures and temperatures is critical. Real gas equations of state are used to model the phase behavior of hydrocarbon mixtures and to design pipelines and storage facilities.

• Aerospace Engineering: In the design of aircraft and spacecraft, accurate prediction of the properties of air and other gases at extreme conditions is essential. Real gas equations of state are used to model the flow of gases through nozzles and around airfoils.

• Thermodynamics: Real gas equations of state are fundamental to understanding the behavior of thermodynamic systems and to developing accurate thermodynamic models.

Examples Illustrating the Differences

Let's look at some examples to illustrate the differences between ideal and real gases:

• Scenario 1: Compression of a Gas

  Imagine compressing a gas at constant temperature.

  • Ideal Gas: According to the ideal gas law, the pressure increases linearly with decreasing volume (Boyle's Law).

  • Real Gas: Initially, as the volume decreases, the pressure increases, but not linearly. Attractive forces may cause the pressure to be lower than predicted by the ideal gas law (Z < 1). As the compression continues and the molecules get closer, repulsive forces become more significant, causing the pressure to increase more rapidly than predicted by the ideal gas law (Z > 1).

• Scenario 2: Liquefaction of Gases

  • Ideal Gas: An ideal gas cannot be liquefied because there are no intermolecular forces to hold the molecules together in the liquid phase.

  • Real Gas: Real gases can be liquefied by cooling them to low temperatures and/or compressing them to high pressures. These conditions promote the formation of intermolecular bonds, leading to the transition from the gaseous to the liquid phase.

Factors Affecting Deviation from Ideal Behavior

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

• Pressure: Higher pressures lead to greater deviations because the molecules are closer together, increasing the influence of intermolecular forces and making the molecular volume more significant.

• Temperature: Lower temperatures lead to greater deviations because the kinetic energy of the molecules is reduced, allowing intermolecular forces to have a greater impact.

• Nature of the Gas: Gases with strong intermolecular forces (e.g., polar molecules) tend to deviate more from ideal behavior than gases with weak intermolecular forces (e.g., nonpolar molecules).

• Molecular Weight and Complexity: Gases with larger and more complex molecules tend to deviate more from ideal behavior due to their larger size and greater potential for intermolecular interactions.

Conclusion: Choosing the Right Model

In summary, while the ideal gas law provides a useful simplification for understanding gas behavior, it's essential to recognize its limitations and to use more sophisticated equations of state when dealing with real gases under conditions where the ideal gas assumptions are not valid. The choice between using the ideal gas law or a real gas equation of state depends on the specific application and the desired level of accuracy. Understanding the differences between ideal and real gases is crucial for accurate predictions and designs in various scientific and engineering fields.