2.4 Ideal and real gas behavior
3 min read•august 6, 2024
Gas behavior is a crucial concept in thermodynamics. Ideal gases follow simple laws, but real gases deviate due to molecular interactions and . Understanding these differences helps predict how gases behave under various conditions.
equations, like Van der Waals and virial equations, account for these deviations. They introduce factors like and , which are essential for accurately describing gas behavior in real-world applications.
Ideal Gas Behavior
Ideal Gas Law and Its Assumptions
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- relates , volume, , and amount of gas ([PV = nRT](https://www.fiveableKeyTerm:pv_=_nrt))
- Assumes gas molecules have negligible volume compared to the container
- Assumes no intermolecular forces between gas molecules
- Assumes elastic collisions between molecules and container walls
- Assumes average kinetic energy of molecules is proportional to absolute temperature
Deviations from Ideal Behavior
- Real gases deviate from ideal behavior at high pressures and low temperatures
- Deviations occur due to finite volume of gas molecules (affects volume available for motion)
- Deviations also caused by intermolecular forces between gas molecules (affects pressure)
- is the highest temperature and pressure at which a substance can exist as a liquid and gas in equilibrium
- (Z) quantifies the deviation of a real gas from ideal behavior ()
Real Gas Equations of State
Van der Waals Equation
- Modifies law to account for finite molecular volume and intermolecular forces
- Introduces constants a (accounts for intermolecular attraction) and b (accounts for molecular volume)
- :
- Predicts the existence of a critical point and liquid-vapor equilibrium
- Provides a more accurate description of real gas behavior than the ideal gas law
Virial Equation
- Expresses the compressibility factor as a power series in terms of pressure or volume
- :
- B(T) and C(T) are the second and third virial coefficients, which depend on temperature
- Virial coefficients account for the cumulative effect of intermolecular interactions
- Truncated virial equations (e.g., truncated after the second term) are often used for simplicity
Real Gas Properties
Compressibility Factor and Its Applications
- Compressibility factor (Z) is the ratio of the actual volume of a gas to the volume predicted by the ideal gas law at the same pressure and temperature
- Z = 1 for an ideal gas, Z < 1 for a gas with dominant intermolecular attractions, and Z > 1 for a gas with dominant repulsive interactions
- Compressibility factor is used to correct the ideal gas law for real gas behavior ()
- Z can be determined experimentally or estimated using generalized compressibility charts (Nelson-Obert charts)
Reduced Properties and the Corresponding States Principle
- Reduced properties are dimensionless quantities that relate the actual properties of a gas to its critical properties
- Reduced pressure: , reduced temperature: , reduced volume:
- The corresponding states principle states that all gases, when compared at the same reduced conditions, have approximately the same compressibility factor
- This principle allows the estimation of real gas properties using generalized charts or equations with reduced properties
- The law of corresponding states is useful for predicting the behavior of gases when limited experimental data is available
Key Terms to Review (24)
Adiabatic process: An adiabatic process is a thermodynamic process in which no heat is exchanged with the surroundings, meaning that any change in internal energy is solely due to work done on or by the system. This concept is crucial in understanding how different thermodynamic properties and state variables behave when energy transfer occurs without heat exchange.
Attraction Forces: Attraction forces are the interactions that cause particles to draw closer together, influencing the behavior of matter at both microscopic and macroscopic levels. These forces play a vital role in determining the properties of gases, including their compressibility and expansion behavior. In the context of gas behavior, attraction forces can differentiate between ideal gases, which exhibit no intermolecular attractions, and real gases, which experience varying degrees of attraction that affect their physical characteristics.
Boyle's Law: Boyle's Law states that the pressure of a given mass of gas is inversely proportional to its volume when temperature is held constant. This relationship highlights how, for an ideal gas, if you decrease the volume, the pressure increases, and vice versa, showcasing a fundamental principle of gas behavior that connects with the ideal gas equation, the distinction between ideal and real gases, and fundamental property relations.
Charles's Law: Charles's Law states that the volume of a gas is directly proportional to its absolute temperature, provided that the pressure remains constant. This relationship highlights how gases expand when heated and contract when cooled, making it essential for understanding the behavior of gases in various conditions, particularly when examining ideal and real gases, and their fundamental properties.
Compressibility: Compressibility is a measure of how much a substance decreases in volume under pressure, indicating its ability to be compressed. This property is crucial in understanding the behavior of gases and liquids, especially under varying temperatures and pressures, as it helps differentiate between ideal and real gas behavior, influences equations of state, and affects fluid dynamics near critical points.
Compressibility Factor: The compressibility factor, denoted as Z, is a dimensionless quantity that describes how much a real gas deviates from ideal gas behavior. It relates the molar volume of a real gas to the molar volume predicted by the ideal gas law under the same temperature and pressure conditions, highlighting the limitations of the ideal gas equation and the nature of real gases.
Critical Point: The critical point is a specific set of conditions at which the properties of a substance change drastically, marking the end of distinct liquid and gas phases. At this point, both the liquid and gas phases become indistinguishable, leading to a state known as a supercritical fluid, where unique properties arise that are different from those of gases and liquids.
Ideal Gas: An ideal gas is a theoretical gas that perfectly follows the ideal gas law, which states that the pressure, volume, and temperature of a gas are related through the equation $$PV = nRT$$. In this model, gases are assumed to have no intermolecular forces and occupy no volume, allowing for simplified calculations of their behavior under various conditions. This concept helps in understanding how real gases behave under certain conditions and is fundamental in exploring thermodynamic processes.
Ideal Gas Law: The ideal gas law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and amount of an ideal gas through the equation PV = nRT. This law connects various thermodynamic properties and state variables, illustrating how changes in one property can affect others, while also serving as a foundational concept for understanding both ideal and real gas behaviors.
Isothermal process: An isothermal process is a thermodynamic process in which the temperature of the system remains constant throughout the entire process. This means that any heat added to the system is used to do work, and vice versa, maintaining equilibrium between heat transfer and work done.
Mean Free Path: The mean free path is the average distance a particle travels between collisions with other particles in a gas. This concept is crucial in understanding gas behavior, as it highlights how the size and density of particles affect their movement and interactions, providing insight into the differences between ideal and real gases.
Phase Equilibrium: Phase equilibrium refers to the condition in which multiple phases of a substance coexist at equilibrium, where the macroscopic properties remain constant over time. In this state, the rates of phase transitions, such as evaporation and condensation or melting and freezing, are equal, leading to a stable distribution of the phases.
Pressure: Pressure is defined as the force exerted per unit area on a surface in a direction perpendicular to that surface. It plays a crucial role in understanding how fluids behave under different conditions, influencing various thermodynamic properties, systems, and processes.
Pv = nrt: The equation $$pv = nRT$$ describes the behavior of an ideal gas, linking pressure (p), volume (v), number of moles (n), and temperature (T). This relationship illustrates how gases behave under varying conditions, emphasizing that when one property changes, others must adjust to maintain the equation's balance. It serves as a foundational concept for understanding both ideal and real gas behavior, as it allows for predictions of how gases will react to changes in their environment.
Real gas: A real gas is a substance that does not behave ideally due to interactions between its molecules and the volume occupied by the gas itself. Unlike an ideal gas, which follows the ideal gas law strictly under all conditions, real gases exhibit deviations from this behavior at high pressures and low temperatures, where intermolecular forces become significant. Understanding real gas behavior is crucial for accurate calculations in thermodynamics and chemical engineering.
Reduced Properties: Reduced properties are dimensionless quantities used to describe the behavior of substances in thermodynamics. They are calculated by normalizing the properties of a substance against its critical properties, making it easier to compare different substances and predict their behavior under varying conditions, especially when dealing with real gas behavior and phase transitions.
Root Mean Square Speed: Root mean square speed is a statistical measure of the average speed of particles in a gas, calculated as the square root of the average of the squares of the individual speeds. This concept is crucial for understanding the kinetic theory of gases, as it relates directly to temperature, pressure, and molecular motion, highlighting how gas behavior can be predicted under ideal conditions versus real conditions.
Sublimation: Sublimation is the process where a solid changes directly into a gas without passing through the liquid state. This phase transition is crucial in understanding how substances behave under different temperature and pressure conditions, as well as how they are represented in phase diagrams. The phenomenon also plays a key role in the behavior of gases, whether ideal or real, and is tied to concepts like the phase rule, which describes the relationships between phases in a system.
Temperature: Temperature is a measure of the average kinetic energy of the particles in a substance, reflecting how hot or cold the substance is. It plays a crucial role in determining the state of a substance and influences various thermodynamic properties, making it essential in understanding systems, processes, and behaviors of fluids.
Van der Waals equation: The van der Waals equation is a modified ideal gas equation that accounts for the finite size of particles and the interactions between them. It provides a more accurate representation of real gas behavior, particularly under high pressure and low temperature conditions, connecting closely to various thermodynamic properties and state variables.
Virial Equation: The virial equation is a mathematical expression that relates the pressure, volume, and temperature of a gas, allowing for deviations from ideal gas behavior by incorporating interaction between particles. It expands upon the ideal gas law by including terms that account for intermolecular forces and the size of the molecules, making it useful for both ideal and real gases. This equation is especially significant when studying gases under high pressure or low temperature conditions, where real gas behavior becomes pronounced.
Viscosity: Viscosity is a measure of a fluid's resistance to flow, reflecting how easily it deforms under shear stress. It plays a crucial role in understanding fluid dynamics, as it affects how fluids behave under different conditions, including their flow characteristics and energy transfer. Viscosity is influenced by temperature, pressure, and the nature of the fluid, which can be classified as either ideal or real, impacting applications in various fields, especially when dealing with supercritical fluids.
Volume: Volume is the measure of the space that a substance (solid, liquid, or gas) occupies. It plays a critical role in understanding thermodynamic properties, influencing the behavior of systems and substances during processes such as expansion and compression, as well as determining state variables like pressure and temperature.
Z factor: The z factor, also known as the compressibility factor, is a dimensionless quantity that describes how much a real gas deviates from ideal gas behavior under varying conditions of temperature and pressure. This factor is critical in understanding the interactions between gas molecules and helps correct the ideal gas law, which assumes that gases behave ideally at all times. When z is equal to 1, the gas behaves ideally; when z is less than 1, the gas is more compressible than predicted by the ideal gas law, and when z is greater than 1, it is less compressible.