10.3 Real gas behavior and equations of state
2 min read•july 23, 2024
Real gases don't always play by the rules of ideal gas behavior. As rises and drops, come into play, causing deviations from the ideal gas law.
To accurately model real gases, we need more complex equations. The van der Waals and virial equations account for molecular interactions and size, giving us a better picture of how gases behave in extreme conditions.
Real Gas Behavior
Ideal vs real gas behavior
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- Ideal gas behavior assumes no intermolecular forces between gas molecules (helium at room temperature) and follows the ideal gas law: , which is accurate at low pressures (< 1 atm) and high temperatures (> 300 K)
- Real gas behavior considers intermolecular forces between gas molecules (nitrogen at high pressure), deviates from the ideal gas law, especially at high pressures (> 10 atm) and low temperatures (< 100 K), and requires more complex equations of state to accurately model behavior ()
Intermolecular forces in gases
- Intermolecular forces include attractive and between gas molecules, such as dipole-dipole interactions (HCl), London dispersion forces (CH4), and hydrogen bonding (H2O)
- Strength of intermolecular forces depends on molecular size (larger molecules have stronger forces) and polarity (polar molecules have stronger forces)
- Effects on real gas behavior include causing gas molecules to occupy a non-zero , reducing the pressure exerted by the gas compared to ideal gas predictions, and leading to condensation and liquefaction at high pressures and low temperatures (propane in a tank)
Equations of State for Real Gases
Van der Waals equation of state
- van der Waals equation of state modifies the ideal gas law to account for intermolecular forces and molecular size using the equation:
- Parameters (attraction) and (repulsion) are specific to each gas and determined experimentally (a = 1.39 L2atm/mol2 and b = 0.0391 L/mol for CO2)
- Improvements over the ideal gas law include predicting the existence of a and phase transitions and being more accurate at high pressures and low temperatures (predicting liquid-vapor equilibrium)
Virial equation for gases
- of state expresses the () as a power series in pressure () or density ()
- Virial coefficients (second) and (third) account for two-molecule and three-molecule interactions, respectively, and are determined experimentally or theoretically for each gas (B(300 K) = -123.2 cm3/mol for N2)
- Application involves truncating the virial equation to the desired level of accuracy, using experimental data to determine virial coefficients, and calculating the compressibility factor and other properties using the virial equation (predicting the behavior of natural gas in pipelines)
Key Terms to Review (20)
Adiabatic process: An adiabatic process is a thermodynamic process in which no heat is exchanged between the system and its surroundings. This means that any change in the internal energy of the system is entirely due to work done on or by the system, making it a critical concept in understanding various thermodynamic cycles and processes.
Anders Jonas Ångström: Anders Jonas Ångström was a Swedish physicist known for his significant contributions to the field of spectroscopy and the study of light. He is particularly recognized for developing the Ångström unit, which measures wavelengths of light and is crucial for understanding real gas behavior and equations of state. His work laid the foundation for analyzing how gases absorb and emit light, thereby influencing the equations that describe real gas behavior under various conditions.
Attractive forces: Attractive forces are the interactions between particles that pull them together, influencing the physical properties and behavior of substances. These forces play a crucial role in understanding how real gases deviate from ideal behavior, as they can cause variations in pressure and volume when particles attract each other more strongly than predicted by ideal gas laws. Recognizing these forces helps in refining equations of state for real gases.
Compressibility Factor: The compressibility factor (Z) is a dimensionless quantity that describes how much a real gas deviates from ideal gas behavior. It is defined as the ratio of the molar volume of a real gas to the molar volume of an ideal gas at the same temperature and pressure, expressed as Z = PV/RT. Understanding the compressibility factor is essential for analyzing real gas behavior and establishing equations of state, which describe the relationship between pressure, volume, and temperature in gases.
Critical Point: The critical point is the end point of a phase equilibrium curve, where distinct liquid and gas phases cease to exist, and the properties of the substance become indistinguishable. At this point, both the temperature and pressure are at their critical values, leading to a supercritical fluid state that exhibits unique behaviors, connecting various aspects of thermodynamic systems and phase equilibria.
Ideal gas limit: The ideal gas limit refers to the condition under which real gases behave like ideal gases, typically occurring at high temperatures and low pressures. In this limit, the interactions between gas molecules become negligible, and the volume occupied by the gas particles themselves is also minimal compared to the volume of the container. Understanding the ideal gas limit helps in applying the ideal gas law and evaluating deviations from ideal behavior in real gases.
Intermolecular forces: Intermolecular forces are the attractive forces that exist between molecules, influencing their physical properties and behaviors. These forces play a crucial role in determining the state of matter, phase transitions, and the behavior of real gases compared to ideal gases. Understanding intermolecular forces helps explain why real gases deviate from ideal gas behavior under certain conditions, such as high pressure and low temperature.
Isothermal process: An isothermal process is a thermodynamic process in which the temperature of the system remains constant while heat is exchanged with the surroundings. This constant temperature implies that any internal energy changes in the system are fully compensated by heat transfer, making it an essential concept in understanding how systems behave under thermal equilibrium and the laws governing energy conservation.
Johannes Diderik van der Waals: Johannes Diderik van der Waals was a Dutch physicist known for his work in the field of thermodynamics, particularly for developing an equation of state that describes the behavior of real gases. His contributions significantly improved the understanding of how real gases deviate from ideal gas behavior due to intermolecular forces and the finite volume of gas molecules. Van der Waals' equation accounts for these factors and provides a more accurate model for predicting the properties of gases under various conditions.
Non-ideality: Non-ideality refers to the deviations in behavior observed in real gases when compared to the ideal gas law. These deviations occur due to interactions between gas particles and the volume occupied by the particles themselves, which becomes significant under high pressure or low temperature conditions. Understanding non-ideality is crucial for accurately predicting the behavior of gases in various thermodynamic processes.
Phase Equilibrium: Phase equilibrium refers to a condition in which distinct phases of a substance coexist in a stable manner, with no net change in their respective quantities over time. This balance occurs when the rates of transition between phases, such as solid, liquid, and gas, are equal, leading to an overall stability in the system. Understanding phase equilibrium is essential for analyzing latent heat during phase transitions, chemical potential in thermodynamic systems, the construction of phase diagrams, and the behavior of gases under varying conditions.
Pressure: Pressure is defined as the force exerted per unit area on a surface, which plays a crucial role in various thermodynamic processes and systems. It is a key state variable that influences how substances behave under different conditions, affecting phase changes, equilibria, and the behavior of gases. Understanding pressure is essential for analyzing the relationships between temperature, volume, and the state of matter in both microscopic and macroscopic contexts.
Repulsive forces: Repulsive forces are interactions between particles that cause them to push away from each other. In the context of real gas behavior and equations of state, these forces play a significant role in determining how gases deviate from ideal behavior, particularly at high pressures and low temperatures. Understanding repulsive forces is essential to grasp the complexities of real gas interactions, as they influence properties such as volume, pressure, and temperature relationships.
Specific Volume: Specific volume is defined as the volume occupied by a unit mass of a substance, commonly expressed in cubic meters per kilogram (m³/kg). This property is crucial in understanding the behavior of substances during phase changes and in describing the characteristics of gases under different conditions, linking it to equations like the Clausius-Clapeyron equation and models for real gas behavior.
Supercritical fluid: A supercritical fluid is a state of matter that occurs when a substance is subjected to temperature and pressure above its critical point, resulting in a phase that exhibits properties of both liquids and gases. In this state, the fluid can diffuse through solids like a gas while dissolving materials like a liquid, making it unique and useful in various applications such as extraction and chemical reactions.
Temperature: Temperature is a measure of the average kinetic energy of the particles in a substance, reflecting how hot or cold that substance is. It plays a crucial role in various physical processes and influences the behavior of materials and systems in both macroscopic and microscopic contexts.
Van der Waals equation: The van der Waals equation is an adjustment of the ideal gas law that accounts for the volume occupied by gas molecules and the attractive forces between them, providing a more accurate description of real gas behavior. This equation is crucial for understanding the state variables of a system and how they relate to thermodynamic properties, as it offers insights into the deviations from ideal behavior observed in real gases under various conditions.
Vapor pressure: Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid form at a given temperature. This concept is crucial in understanding how real gases behave, as it helps explain the conditions under which a substance can exist in multiple phases, such as liquid and gas. Additionally, vapor pressure plays a significant role in thermodynamics of solutions and mixtures, influencing properties like boiling point and solubility.
Virial equation: The virial equation is an equation of state for real gases that expresses the relationship between pressure, volume, and temperature through a power series expansion in terms of density. This equation allows for a better understanding of how real gases deviate from ideal gas behavior by including correction terms, known as virial coefficients, which account for molecular interactions and finite size effects. By analyzing the virial equation, we can gain insight into the complex behavior of gases under varying conditions.
Volume: Volume is a measure of the three-dimensional space occupied by a substance or object, often expressed in units such as liters or cubic meters. It plays a crucial role in understanding how substances interact, especially under varying temperature and pressure conditions, linking it to essential properties like state variables and equations of state.