What Is The Difference Between Ideal Gas And Real Gas

Ideal and real gases represent two distinct concepts in the realm of thermodynamics, each with its own set of assumptions and behaviors. While the ideal gas model provides a simplified framework for understanding gas behavior, real gases exhibit more complex characteristics due to intermolecular forces and molecular volume. Understanding the differences between these two models is crucial for accurate predictions and calculations in various scientific and engineering applications.

Ideal Gas: A Simplified Model

An ideal gas is a theoretical gas that adheres to specific assumptions, simplifying the mathematical treatment of its behavior. These assumptions are:

• Negligible Molecular Volume: The volume occupied by the gas molecules themselves is considered negligible compared to the total volume of the container.
• No Intermolecular Forces: There are no attractive or repulsive forces between gas molecules.
• Perfectly Elastic Collisions: Collisions between gas molecules and the container walls are perfectly elastic, meaning no energy is lost during collisions.

Based on these assumptions, the behavior of an ideal gas can be described by the ideal gas law:

PV = nRT

Where:

• P = Pressure
• V = Volume
• n = Number of moles
• R = Ideal gas constant (8.314 J/mol·K)
• T = Temperature

The ideal gas law provides a simple and accurate approximation of gas behavior under certain conditions, particularly at low pressures and high temperatures. Under these conditions, the assumptions of negligible molecular volume and intermolecular forces hold reasonably well.

Real Gas: Accounting for Complexities

Real gases, on the other hand, deviate from the ideal gas model due to the presence of intermolecular forces and finite molecular volume. These factors become significant under high pressures and low temperatures, where the assumptions of the ideal gas model no longer hold true.

• Intermolecular Forces: Real gas molecules experience attractive and repulsive forces, such as van der Waals forces. These forces affect the gas's pressure and volume. Attractive forces reduce the pressure exerted by the gas, while repulsive forces increase it.
• Finite Molecular Volume: Real gas molecules occupy a finite volume, which reduces the available volume for the gas to move around in. This effect becomes more pronounced at high pressures, where the molecules are packed closer together.

Key Differences Summarized

Why Real Gases Deviate from Ideal Behavior

The deviation of real gases from ideal behavior can be explained by considering the effects of intermolecular forces and finite molecular volume:

Intermolecular Forces Impact

• Attractive Forces: Attractive forces between gas molecules reduce the pressure exerted by the gas on the container walls. This is because the molecules are pulled inward by their neighbors, reducing the force with which they collide with the walls. As a result, the actual pressure of a real gas is lower than that predicted by the ideal gas law.
• Repulsive Forces: At very short distances, repulsive forces between gas molecules become significant. These forces increase the pressure exerted by the gas, as the molecules resist being compressed into a smaller volume. This effect is more pronounced at high pressures, where the molecules are packed closely together.

Finite Molecular Volume Impact

The finite volume of gas molecules reduces the available volume for the gas to move around in. The ideal gas law assumes that the entire volume of the container is available for the gas molecules to occupy. However, in real gases, the volume occupied by the molecules themselves must be subtracted from the total volume to obtain the effective volume available for the gas to move around in. This effect becomes more pronounced at high pressures, where the molecules occupy a significant portion of the total volume.

Equations of State for Real Gases

To account for the non-ideal behavior of real gases, various equations of state have been developed. These equations incorporate correction factors to account for intermolecular forces and finite molecular volume. Some of the most commonly used equations of state for real gases include:

Van der Waals Equation

The van der Waals equation is one of the most well-known and widely used equations of state for real gases. It 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 gas molecules.
• b = accounts for the finite volume of gas molecules.

The van der Waals equation provides a more accurate description of real gas behavior than the ideal gas law, particularly at moderate pressures and temperatures.

Redlich-Kwong Equation

The Redlich-Kwong equation is another popular equation of state for real gases. It is given by:

P = (RT)/(V_m - b) - a/(T^(0.5)V_m(V_m + b))

Where:

• a and b are empirical constants that depend on the specific gas.
• Vm is the molar volume.

The Redlich-Kwong equation is generally more accurate than the van der Waals equation, especially at higher pressures.

Peng-Robinson Equation

The Peng-Robinson equation is a more complex equation of state that is widely used in the petroleum industry. It is given by:

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

Where:

• a, b, and α are empirical constants that depend on the specific gas and temperature.

The Peng-Robinson equation is known for its accuracy in predicting the behavior of both liquid and vapor phases of real gases.

Beattie-Bridgeman Equation

The Beattie-Bridgeman equation is an equation of state based on five experimentally determined constants. It is expressed as:

P = (RT/V^2)(1 - e)(V + B) - (A/V^2)

Where:

A = A_0(1 - a/V)
B = B_0(1 - b/V)
e = c/(VT^3)

And A₀, B₀, a, b, and c are constants determined experimentally. This equation is quite accurate when dealing with high-pressure gases.

Compressibility Factor

The compressibility factor (Z) is a dimensionless quantity that represents the deviation of a real gas from ideal 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 and temperature.

• Z < 1: The gas is more compressible than an ideal gas. This typically occurs at moderate pressures, where attractive forces between gas molecules dominate.
• Z > 1: The gas is less compressible than an ideal gas. This typically occurs at high pressures, where repulsive forces and the finite volume of gas molecules become significant.

The compressibility factor provides a convenient way to assess the deviation of a real gas from ideal behavior and to use the ideal gas law with appropriate corrections.

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:

• Ideal Gas Law: The ideal gas law is a good approximation at low pressures and high temperatures, where intermolecular forces and molecular volume are negligible. It is also suitable for quick estimations and qualitative analysis.
• Real Gas Equations: Real gas equations should be used when:
  • High pressures or low temperatures are involved.
  • High accuracy is required.
  • The gas is close to its condensation point.
  • Intermolecular forces are significant (e.g., polar gases).

In general, it is always a good practice to check the compressibility factor to assess the deviation from ideal behavior. If the compressibility factor is significantly different from 1, then real gas equations should be used for accurate calculations.

Examples of Ideal vs. Real Gas Behavior

Example 1: Inflating a Balloon

When inflating a balloon at room temperature and atmospheric pressure, the ideal gas law provides a reasonable approximation of the relationship between pressure, volume, and the amount of gas in the balloon. However, if the balloon is inflated to a very high pressure or if the temperature is significantly lowered, the ideal gas law may not be accurate, and real gas equations may be needed.

Example 2: Industrial Processes

In industrial processes involving high pressures and low temperatures, such as the production of ammonia or the liquefaction of natural gas, real gas equations are essential for accurate design and operation of equipment. The deviations from ideal behavior can be significant under these conditions, and using the ideal gas law could lead to significant errors.

Example 3: Atmospheric Science

In atmospheric science, the ideal gas law is often used to model the behavior of air. However, at high altitudes, where the pressure is very low, the ideal gas law may not be accurate, and real gas equations may be needed. Additionally, the presence of water vapor in the air can also affect its behavior, and real gas equations that account for the properties of water vapor may be required.

Applications and Significance

The understanding of ideal and real gases is fundamental in various fields:

• Chemical Engineering: Design of chemical reactors, distillation columns, and other equipment.
• Mechanical Engineering: Design of engines, turbines, and compressors.
• Aerospace Engineering: Design of aircraft and spacecraft propulsion systems.
• Atmospheric Science: Modeling atmospheric phenomena and predicting weather patterns.
• Thermodynamics: Understanding and predicting the behavior of thermodynamic systems.

Factors Affecting Gas Behavior

Several factors influence how closely a real gas approximates ideal gas behavior:

• Pressure: Higher pressures increase deviations from ideal behavior due to increased intermolecular interactions and reduced available volume.
• Temperature: Lower temperatures also increase deviations as kinetic energy decreases, allowing intermolecular forces to become more significant.
• Nature of Gas: Gases with strong intermolecular forces (e.g., polar molecules) deviate more from ideal behavior.
• Molecular Size: Larger molecules have greater volume, thus deviating more from ideal gas assumptions.

Conclusion

In summary, while the ideal gas law provides a simplified and useful model for understanding gas behavior under certain conditions, real gases exhibit more complex behavior due to intermolecular forces and finite molecular volume. To accurately predict and calculate the behavior of real gases, particularly at high pressures and low temperatures, it is necessary to use more sophisticated equations of state that account for these factors. The choice between using the ideal gas law and real gas equations depends on the specific conditions and the desired accuracy. Understanding the differences between ideal and real gases is crucial for various scientific and engineering applications, enabling accurate design, operation, and analysis of systems involving gases.