Properties of Real Gases

Introduction

Real gases deviate from ideal behavior under certain conditions, especially at high pressures and low temperatures. Understanding these deviations is crucial for accurately describing and predicting the behavior of gases in physical and chemical processes.

Ideal vs. Real Gases

Comparison of Ideal and Real Gases

Ideal gases are a theoretical construct that simplifies the study of gases by assuming certain properties. Real gases, however, exhibit behaviors that require more complex models.

• Ideal Gases:

  • Assume negligible volume of gas particles compared to the container.

  • Particles do not interact (no attractive or repulsive forces).

  • Do not condense under any temperature or pressure.

  • Accurately modeled by the ideal gas law: .

• Real Gases:

  • Have non-negligible volume (especially for larger molecules).

  • Experience both attractive and repulsive intermolecular forces.

  • Can condense at low temperatures.

  • Require more complex equations of state (E.O.S.) for accurate modeling.

Key Point: Gases behave ideally at low pressure and high temperature. All gases deviate from ideal behavior at high pressure and low temperature.

Critical Phenomena

Phase Behavior and the Critical Point

The critical point is a unique state where the distinction between liquid and gas phases disappears. Any successful real gas equation of state must account for the fact that gases can condense at low temperatures and high pressures.

• Critical Point: The temperature and pressure at which the liquid and gas phases of a substance become indistinguishable.

• Supercritical Fluid: A phase above the critical temperature and pressure where the substance exhibits properties of both liquids and gases.

Example: The phase diagram of water shows the critical point at 647 K and 22.1 MPa, beyond which water becomes a supercritical fluid.

Equations of State (E.O.S.) for Real Gases

Need for Modified Equations

The ideal gas law does not account for the volume of gas particles or intermolecular forces. To describe real gases, we use modified equations of state that incorporate these factors.

van der Waals Equation

The van der Waals equation introduces corrections for particle volume and intermolecular forces:

• Correction for Volume: Gas particles occupy space, so the available volume is less than the container volume.

• Correction for Intermolecular Forces: Attractive forces between particles reduce the pressure exerted on the container walls.

van der Waals Equation:

• a: Empirical constant accounting for attractive forces.

• b: Empirical constant accounting for particle volume.

Application: The van der Waals equation is widely used for modeling real gases and is especially successful in describing critical phenomena.

Virial Equation of State

The virial equation expresses the pressure as a power series in terms of the inverse molar volume:

• B(T), C(T), ...: Virial coefficients, which depend on temperature and molecular interactions.

• The accuracy of the fit improves as more terms are added, but each successive term contributes less.

Application: The virial equation provides an excellent fit to experimental data, especially when several coefficients are included.

Compression Factor (Z)

Definition and Interpretation

The compression factor, Z, quantifies the deviation of a real gas from ideal behavior:

• Z = 1: Ideal gas behavior.

• Z < 1: Attractive forces dominate (lower pressure than ideal).

• Z > 1: Repulsive forces dominate (higher pressure than ideal).

Graphical Interpretation: Plots of Z versus pressure or temperature reveal regions where real gases deviate from ideality due to intermolecular forces.

Law of Corresponding States (LOC)

Unifying Principle for Real Gases

The Law of Corresponding States states that all gases obey the same equation of state when expressed in terms of reduced variables (relative to their critical properties). This principle allows for the comparison of different gases on a common scale.

• Reduced Variables:

  • Reduced pressure:

  • Reduced temperature:

  • Reduced volume:

• At the critical point, the properties of all gases converge, allowing for universal behavior to be described.

Application: The LOC is most accurate for gases that are approximately spherical in shape and is commonly used in engineering and physical chemistry.

Summary Table: Ideal vs. Real Gases

Additional info: The notes are based on CHEM 331, but the physical principles and equations discussed are foundational in college-level physics and physical chemistry courses.