3.1 Ideal gas equation and its limitations
3 min read•august 6, 2024
The ideal gas equation is a cornerstone of thermodynamics, relating , , , and amount of gas. It's crucial for understanding gas behavior, but it's not perfect. Real gases deviate from ideal behavior, especially at high pressures and low temperatures.
To account for these deviations, we use the . This helps modify the for real gases, considering intermolecular forces and finite molecular volume. Understanding these limitations is key to accurately predicting and analyzing gas behavior in various conditions.
Ideal Gas Law and its Variables
Equation and Components
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- Ideal gas law relates pressure, volume, temperature, and amount of gas
- Pressure force per unit area exerted by gas molecules colliding with container walls measured in pascals (Pa) or atmospheres (atm)
- Volume space occupied by the gas typically measured in cubic meters or liters
- Temperature average kinetic energy of gas molecules must be expressed in Kelvin for ideal gas law calculations
- Gas constant proportionality constant specific to the gas being studied has a value of for ideal gases
Relationships and Applications
- Directly proportional relationships between pressure and temperature as well as moles and volume and when other variables held constant
- Inversely proportional relationship between pressure and volume when temperature and moles held constant ()
- Can be used to calculate changes in gas properties during processes like isothermal compression or isobaric expansion
- Enables determination of molar mass and density of gases by measuring , , , and mass of a gas sample
Deviations from Ideal Gas Behavior
Compressibility Factor
- Compressibility factor ratio of actual molar volume of a gas to the molar volume predicted by the ideal gas law at the same temperature and pressure
- Quantifies the extent of deviation from ideal gas behavior for an ideal gas and for a real gas
- Depends on the specific gas, temperature, and pressure with greater deviations occurring at high pressures and low temperatures
- Can be used to modify the ideal gas law for real gases to account for non-ideal behavior
Real Gas Behavior and Intermolecular Forces
- Real gases exhibit non-ideal behavior due to the presence of intermolecular forces and finite molecular volume which are neglected in the ideal gas model
- Attractive forces (van der Waals forces) between molecules cause real gases to have lower pressure and molar volume than predicted by the ideal gas law
- Repulsive forces between molecules at high pressures cause real gases to have higher pressure and molar volume than predicted by the ideal gas law
- The degree of deviation depends on the strength of intermolecular forces specific to each gas with larger, more polarizable molecules (CO2) exhibiting greater deviations than smaller, non-polar molecules (He)
Limitations of the Ideal Gas Law
High Pressure Limitations
- Ideal gas law assumes molecules have negligible volume and do not interact with each other which breaks down at high pressures
- At high pressures, the finite volume of molecules becomes significant relative to the container volume leading to lower molar volumes than predicted
- Repulsive intermolecular forces at high pressures cause the pressure to be higher than predicted by the ideal gas law
- The compressibility factor of real gases deviates significantly from unity at high pressures indicating non-ideal behavior
Low Temperature Limitations
- At low temperatures, the attractive intermolecular forces between gas molecules become more significant causing deviations from ideal behavior
- Real gases have lower pressure and molar volume than predicted by the ideal gas law at low temperatures due to the increased influence of attractive forces
- The compressibility factor of real gases is typically less than unity at low temperatures indicating non-ideal behavior
- As temperature decreases, real gases may condense into liquids or solids, a behavior not accounted for by the ideal gas law which assumes gases remain in the gaseous state at all temperatures
Key Terms to Review (19)
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.
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.
Calculating Molar Mass: Calculating molar mass involves determining the mass of one mole of a substance, which is the sum of the atomic masses of all the elements present in its molecular formula. This concept is crucial for understanding the behavior of gases, especially when applying the ideal gas equation, where molar mass helps relate the mass of a gas to its volume and number of moles. Knowing the molar mass also aids in recognizing limitations of the ideal gas law in various conditions, such as high pressure and low temperature.
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 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.
Gas Stoichiometry: Gas stoichiometry refers to the quantitative relationship between the amounts of reactants and products in a chemical reaction involving gases. This concept is essential in determining how much of each gas will react or be produced based on the balanced chemical equation, particularly when applying the ideal gas law to calculate volumes, moles, or masses of gaseous substances under specified conditions.
High Pressure: High pressure refers to a condition where the force exerted by a gas or fluid is greater than the surrounding atmospheric pressure. In the context of the ideal gas equation, high pressure can lead to significant deviations from the ideal behavior of gases, as real gases experience intermolecular forces and occupy physical space that the ideal gas law does not account for.
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.
Ideal vs. Real Gas Behavior: Ideal vs. real gas behavior refers to the differences between the theoretical predictions of gas behavior described by the ideal gas law and the actual behavior of real gases, especially under high pressure and low temperature conditions. The ideal gas law assumes no interactions between gas particles and that they occupy no volume, which simplifies calculations but does not account for real-world complexities. Understanding these differences helps in predicting how gases will behave under various conditions and when deviations from the ideal gas law become significant.
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.
Low Temperature: Low temperature refers to conditions where the thermal energy of a system is significantly below that of its surroundings, often measured in relation to the properties of gases. In the context of fluids and thermodynamics, low temperatures can influence gas behavior, specifically causing deviations from ideal gas behavior and affecting phase changes. Understanding low temperature is essential for analyzing how substances behave under various thermal conditions and the limitations of theoretical models like the ideal gas equation.
Negligible intermolecular forces: Negligible intermolecular forces refer to the weak attractions or repulsions between molecules that are so minor they can be ignored in certain contexts, particularly when analyzing the behavior of gases. This concept is crucial for understanding ideal gases, where it's assumed that these forces do not affect the gas's pressure, volume, or temperature. Recognizing when intermolecular forces can be neglected helps in simplifying the equations used to describe gas behavior and leads to a clearer understanding of thermodynamic principles.
Phase Transitions: Phase transitions refer to the changes between different states of matter, such as solid, liquid, and gas, that occur due to variations in temperature or pressure. These transitions are crucial for understanding material behavior and can involve latent heat, which is energy absorbed or released during the process. Recognizing phase transitions is essential for analyzing systems under varying conditions and helps explain phenomena like vaporization, melting, and sublimation.
Point Particles: Point particles are theoretical entities used in physics to simplify the modeling of particles by treating them as having no spatial extent, meaning they occupy a single point in space. This abstraction allows for the simplification of complex interactions and behaviors of particles, making it easier to apply equations like the ideal gas equation, which describes the behavior of gases under various conditions.
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.
Real gas effects: Real gas effects refer to the deviations from ideal gas behavior that occur when gases are subjected to high pressures and low temperatures. Unlike ideal gases, which follow the ideal gas law without any exceptions, real gases exhibit interactions between molecules and occupy a finite volume, leading to discrepancies in pressure, volume, and temperature relationships.
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.
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.