9.6 Non-Ideal Gas Behavior
3 min read•june 25, 2024
Gas behavior isn't always straightforward. At high pressures or low temps, gases start acting weird. The volume of particles and forces between them become important, making gases deviate from ideal behavior.
Enter the . It fixes the ideal gas law by considering particle size and interactions. The helps us spot non-ideal behavior. Knowing when to use ideal vs. non-ideal equations is key for accurate predictions.
Factors and Equations Related to Non-Ideal Gas Behavior
Factors in gas behavior deviation
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- Volume of gas particles becomes significant relative to total volume at high pressures (CO2 at 100 atm)
- Leads to less available volume for gas particles to occupy and increases frequency of particle collisions
- between gas particles become more significant at high pressures and low temperatures (H2 at 10 K)
- Attractive forces () cause gas particles to collide less frequently with container walls, reducing pressure
- Repulsive forces at very short distances prevent gas particles from occupying the same space
Van der Waals equation interpretation
- van der Waals equation: corrects for non-ideal behavior by considering volume of gas particles and
- : correction factor for intermolecular forces (0.55 L2⋅atm/mol2 for CO2)
- : correction factor for volume of gas particles (0.03 L/mol for CO2)
- Pressure correction term: accounts for reduction in pressure due to attractive intermolecular forces
- Becomes more significant at high pressures and low volumes (compressed gas cylinders)
- Volume correction term: accounts for reduction in available volume due to volume of gas particles
- Subtracts from total volume, where is number of moles and is volume correction factor (0.5 L for 1 mol of CO2 at 100 atm)
Compressibility and Comparison of Ideal and Non-Ideal Gas Behavior
Compressibility as non-ideal indicator
- : is the ratio of actual volume to volume predicted by ideal gas law
- Deviations from Z = 1 indicate non-ideal behavior (Z = 0.8 for N2 at 200 atm and 300 K)
- Z > 1: gas is less compressible than an ideal gas, occurs at high pressures when intermolecular repulsive forces dominate (He at 1000 atm)
- Volume is greater than predicted by ideal gas law
- Z < 1: gas is more compressible than an ideal gas, occurs at low pressures when intermolecular attractive forces dominate (Cl2 at 1 atm)
- Volume is less than predicted by ideal gas law
Ideal vs van der Waals calculations
- Ideal gas law: assumes gas particles have negligible volume and no intermolecular forces
- Suitable for low pressures and high temperatures (N2 at 1 atm and 298 K)
- van der Waals equation: accounts for volume of gas particles and intermolecular forces
- Provides more accurate results at high pressures and low temperatures (CO2 at 50 atm and 250 K)
- Comparing calculations:
- At low pressures and high temperatures, both equations yield similar results (< 5% difference for O2 at 1 atm and 500 K)
- At high pressures and low temperatures, van der Waals equation provides more accurate predictions of gas properties, such as pressure, volume, and factor (20% difference for NH3 at 100 atm and 200 K)
Advanced Concepts in Non-Ideal Gas Behavior
- : the temperature and pressure at which the liquid and gas phases of a substance become indistinguishable
- : the temperature at which a behaves most like an ideal gas over a wide range of pressures
- : a measure of the tendency of a substance to escape from a phase, replacing pressure in thermodynamic equations for non-ideal gases
- : an expansion series that describes the pressure of a gas as a function of its molar volume, providing a more accurate description of than the van der Waals equation
Key Terms to Review (17)
Boyle Temperature: The Boyle temperature, also known as the critical temperature, is a key concept in the study of non-ideal gas behavior. It represents the temperature at which a gas's compressibility factor deviates significantly from the ideal gas law, indicating the onset of non-ideal behavior.
The Boyle temperature is a crucial parameter in understanding the phase transitions and thermodynamic properties of real gases, as it marks the point where the gas can no longer be accurately described by the simple assumptions of the ideal gas model.
Compressibility: Compressibility is a measure of how much a substance can be reduced in volume by the application of pressure. It is a fundamental property of gases, liquids, and solids that describes their ability to be compressed or squeezed into a smaller space without changing their chemical composition.
Compressibility Factor: The compressibility factor, also known as the compression factor or the gas deviation factor, is a dimensionless quantity that describes the deviation of a real gas from the behavior of an ideal gas. It is used to account for the non-ideal behavior of gases, which arises due to the finite size and intermolecular interactions of gas molecules.
Compressibility factor (Z): The compressibility factor (Z) is a measure of how much the behavior of a real gas deviates from an ideal gas. It is defined as the ratio $Z = \frac{PV}{nRT}$.
Critical point: The critical point is the end point of a phase equilibrium curve, where the properties of gas and liquid phases become indistinguishable. It represents the highest temperature and pressure at which a substance can exist as a liquid and gas in equilibrium.
Critical Point: The critical point is a unique point on a phase diagram where the distinct liquid and gas phases of a substance merge into a single, homogeneous supercritical fluid phase. At the critical point, the properties of the liquid and gas phases become indistinguishable, marking the end of the phase transition between the two states.
Fugacity: Fugacity is a measure that describes the 'escaping tendency' of a substance from a phase, particularly in the context of gases. It relates closely to the chemical potential and accounts for deviations from ideal gas behavior, reflecting how real gases behave under different conditions. Understanding fugacity is essential for analyzing non-ideal gas interactions, particularly under high pressures or low temperatures, where these deviations become significant.
Intermolecular forces: Intermolecular forces are the forces of attraction and repulsion between molecules that influence the physical properties of substances. These forces are weaker than intramolecular forces, which hold atoms together within a molecule.
Intermolecular Forces: Intermolecular forces are the attractive or repulsive forces that exist between molecules, as opposed to the intramolecular forces that hold atoms together within a molecule. These forces play a crucial role in determining the physical properties and behavior of substances across various topics in chemistry, including non-ideal gas behavior, the properties of liquids, phase transitions, and the dissolution process.
Joule-Thomson Effect: The Joule-Thomson effect is a thermodynamic phenomenon that describes the temperature change of a gas or fluid when it is forced to expand through a valve or porous plug without doing work and without a change in its kinetic energy. This effect is crucial in understanding the behavior of non-ideal gases.
Non-Ideal Gas Behavior: Non-ideal gas behavior refers to the deviation of real gases from the ideal gas law, which assumes that gases behave as perfectly elastic, point-like particles with no intermolecular interactions. Real gases exhibit non-ideal behavior due to the finite size of gas molecules and the presence of intermolecular forces, such as van der Waals forces and dipole-dipole interactions.
Real Gas: A real gas is a gas that does not behave exactly as predicted by the ideal gas law. Unlike an ideal gas, a real gas exhibits intermolecular interactions and deviations from the assumptions of the ideal gas model, such as non-negligible molecular volume and attractive/repulsive forces between molecules.
Van der Waals Constants: van der Waals constants are a set of parameters used to describe the behavior of real gases, which deviate from the ideal gas law due to the finite size of gas molecules and the attractive forces between them. These constants help account for the non-ideal behavior of gases under certain conditions of temperature and pressure.
Van der Waals equation: The van der Waals equation is a mathematical model that describes the behavior of real gases by accounting for the finite size of molecules and intermolecular forces. It modifies the Ideal Gas Law to better predict gas behavior under high pressure and low temperature conditions.
Van der Waals forces: Van der Waals forces are weak intermolecular forces that arise from the interactions between induced or permanent dipoles in molecules. They play a crucial role in determining the physical properties of liquids and solids.
Van der Waals Forces: van der Waals forces are a type of weak intermolecular attractive forces that arise between neutral atoms or molecules. These forces are responsible for the non-ideal behavior of gases, the properties of liquids and solids, and the structure and general properties of nonmetals and noble gases.
Virial Equation: The virial equation is a mathematical expression that describes the relationship between the pressure, volume, and temperature of a real gas. It is used to model the non-ideal behavior of gases, which deviates from the ideal gas law due to intermolecular interactions and the finite size of gas molecules.