Name: how real gases deviate from ideal behavior
Uploaded: 2025-05-22T09:05:49.000Z
Duration: 1 min 10 s
Channel: JoVE

The ideal gas equation has two significant drawbacks: first, it does not consider the volume of gas molecules, and second, it does not account for attractive intermolecular forces between the gas molecules. 
If the gas contains n number of moles and each one of them occupies volume b, then the total volume occupied by the gas molecules is nb. Thus, the volume available for gas molecules to move will be total volume minus nb.
The attractive intermolecular forces reduce the pressure proportional to the square of the molar density. In the absence of attractive intermolecular forces, higher pressure is required to reach the same nRT.
This is the van der Waals equation of state that tries to address the drawbacks of the ideal gas equation. Here, a and b are empirical constants that are dependent on the type of gas under study.
The van der Waals equation predicts the behavior of real gas adequately, such as liquid to vapor transition and the Joule-Thomson effect.

van der waals equation

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837&#8722;1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume of the molecules is represented by a positive constant b, which can be thought of as the volume of a mole of molecules. This is subtracted from the total volume to give the remaining volume that the molecules can move in. The constants a and b are determined experimentally for each gas. The resulting equation is
<img alt="Van der Waals equation, \( (p + a(n/V)^2)(V-nb) = nRT \), diagram, real gas behavior study." src="/files/ftp_upload/13668/13668_Equation_1.svg" style="text-align: center; height: 30px;" data-altupdatedat="1754904545000" data-alt="Van der Waals equation; p+a(n/V)&#178;(V-nb)=nRT; gas behavior; thermodynamics formula." />
For carbon dioxide gas with the van der Waals equation, constant a is 0.364 J&#183;m3/mol2 and constant b is 4.27 x 10&#8722;5 m3/mol. If 1 mole of this gas is confined in a volume of 300 cm3 at 300 K, then the pressure of the gas can be calculated using the van der Waals equation. Rearranging the van der Waals equation for pressure,
<img alt="Van der Waals equation, gas behavior, formula illustrating non-ideal gas properties, physics study." src="/files/ftp_upload/13668/13668_Equation_2.svg" style="text-align: center; height: 30px;" data-altupdatedat="1754904545000" data-alt="Van der Waals equation, thermodynamic formula, gas behavior, pressure calculation." />
and substituting the known quantities in it,
<img alt="Van der Waals equation showing pressure calculation; ideal vs. real gas relation; thermodynamics." src="/files/ftp_upload/13668/13668_Equation_3.svg" style="text-align: center; height: 32px;" data-altupdatedat="1754904545000" data-alt="Van der Waals equation; equation; calculates real gas pressure; thermodynamics; volume correction." />
gives the pressure of carbon dioxide gas
<img alt='Pressure equation, "p = 9.69 &#215; 10^6 Pa," static equilibrium, scientific formula.' src="/files/ftp_upload/13668/13668_Equation_4.svg" style="text-align: center; height: 16px;" data-altupdatedat="1754904545000" data-alt="Pressure equation \(p = 9.69 \times 10^6 \, \text{Pa}\), formula image for scientific calculations." />
In the low-density limit (small n), the a and b terms are negligible, and the van der Waals equation reduces to the ideal gas law. On the other hand, if the second term from the van der Waals equation is small, meaning that the molecules are very close together, then the pressure must be higher to give the same nRT, as expected in the situation of a highly compressed gas. However, the increase in pressure is less than that argument would suggest because, at high densities, the pressure correction term from the van der Waals equation is significant. Since the pressure correction term is positive, it requires a lower pressure to give the same nRT. The van der Waals equation of state works well for most gases under various conditions, such as for predicting liquid-gas phase transitions.

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch ...

Education

JoVE Core

Physics

Unit 1

The Kinetic Theory of Gases

KEY TERMS AND CONCEPTS

how real gases deviate from ideal behavior

Real gases often deviate from the ideal gas law, especially at low temperatures and high pressures. The van der Waals equation improves the ideal gas model by adding two corrections that account for these real-world effects.

One correction accounts for attractive forces between molecules. These forces become stronger at higher densities and lower the measured pressure, so the equation adds a pressure term based on the square of the molar density and a positive constant a.

The second correction accounts for the space occupied by the molecules themselves. A positive constant b represents the volume of the molecules, or the volume of a mole of molecules, and this amount is subtracted from the total volume to leave the space the gas can actually move in. The values of a and b are found experimentally for each gas.

For carbon dioxide, the van der Waals constants are a = 0.364 J·m3/mol2 and b = 4.27 x 10−5 m3/mol. If 1 mole of carbon dioxide is confined to 300 cm3 at 300 K, the pressure can be calculated by rearranging the van der Waals equation for pressure and substituting the known values.

At low density, the a and b terms are small, so the van der Waals equation reduces to the ideal gas law. At very high density, the molecules are close together, so a higher pressure is needed to reach the same nRT. Even then, the pressure increase is smaller than a simple compression argument suggests because the pressure correction term becomes significant. This makes the van der Waals equation useful for many gases, including cases that involve liquid-gas phase transitions.

How Real Gases Deviate from Ideal Behavior

how-real-gases-deviate-from-ideal-behavior

equation of state

Gas Behavior in the Equation of State

The equation of state describes how a gas’s pressure, volume, temperature, and number of moles are related. These macroscopic properties help define the condition, or state, of the matter in a thermodynamics system. The relationship between these quantities can be written as a simple mathematical expression. In some cases, it is too complex to express in a formula. Even then, the link between the quantities still exists. When an equation of state cannot be written mathematically, scientists...

ideal gas equation

Gas Laws Behind the Ideal Equation

The ideal gas equation links pressure, volume, temperature, and amount of gas. It describes a hypothetical gas and is built from four empirical gas laws: Boyle’s law, Charles’s law, Avogadro’s law, and Gay-Lussac’s law. When these proportionalities are combined, they give one constant called the universal gas constant. This gas constant has the same value for all real gases under certain conditions. In chemical calculations, that constant is used in the ideal gas equation. The equation works...

Real gases often deviate from the ideal gas law, especially at low temperatures and high pressures. The van der Waals equation improves the ideal gas model by adding two corrections that account for these real-world effects. One correction accounts for attractive forces between molecules. These forces become stronger at higher densities and lower the measured pressure, so the equation adds a pressure term based on the square of the molar density and a positive constant a. The second...

pv-diagrams

Liquid-Gas Changes on pV Curves

pV curves show how gas pressure changes with volume. A pV diagram is a graph of pressure versus volume for the gas being studied. It helps describe how the substance behaves. When the gas acts like an ideal gas, the ideal gas equation gives the link between pressure and volume. A common pV curve is an isotherm, which is a line drawn at fixed temperature and fixed number of molecules. For an ideal gas, pressure times volume stays constant. That means volume goes down as pressure goes up. The...

kinetic theory of an ideal gas

Avogadro's Number and Gas Particle Motion

Avogadro's number and gas particle motion help explain how gases behave at the particle level. A mole is the amount of a substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. This idea came from Amedeo Avogadro, who proposed that equal volumes of gas at the same pressure and temperature contain equal numbers of molecules, no matter what the gas is. Avogadro's number is the number of molecules in one mole. Its value is 6.02 × 10^23 mol−1. This number...

molecular kinetic energy

Gas Pressure and Molecular Motion

Gas pressure comes from the motion of molecules in a container. The word gas came from a Flemish word meaning “chaos,” and J. B. van Helmont first used it to describe vapors. In a gas, molecules move in a continuous and random way. When a molecule hits a container wall, its velocity changes. The part of the velocity parallel to the wall stays the same. The part perpendicular to the wall reverses direction, but its size does not change. If the molecule’s velocity changes in the x-direction, its...

distribution of molecular speeds

Molecular Speed Curves and Vapor Pressure

Molecular speed curves show how the speeds of gas particles are spread out at a given temperature. For a gas with many molecules, this spread is predictable even though each molecule moves randomly in direction and speed. The pattern is called the Maxwell-Boltzmann distribution. Liquids have a similar speed distribution, but it is not exactly the same as in gases. This difference helps explain boiling and vapor pressure. A molecule must reach at least a certain speed, v a, to escape from the...

maxwell-boltzmann distribution: problem solving

maxwell-boltzmann-distribution-problem-solving

Maxwell-Boltzmann Gas Speed Ratio

The Maxwell-Boltzmann distribution describes how molecular speeds are spread in a gas. Even though individual molecules move in random directions, the whole gas has a predictable speed pattern. This distribution is written as f(v), where v is molecular speed. The distribution function is used to find the expected number of particles with speeds between v1 and v2. Because N is dimensionless, f(v) has units of seconds per meter. The relationship can also be written in differential form for speed...

phase diagram

Water Phase Changes on a Pressure Chart

Water phase changes can be mapped on a pressure and temperature chart called a phase diagram. These plots show which phase a substance is in at different conditions. They also reveal where phase transitions happen, because the boundary lines mark the temperatures and pressures where two phases coexist. The water phase diagram shows how pressure affects boiling. As pressure rises, the boiling temperature increases gradually until it reaches 374 °C at 218 atm. A pressure cooker works this way.

mean free path and mean free time

Gas collisions: path length and time

Gas collisions in a cylinder help explain the mean free path and mean free time. Gas molecules move in random motion. They collide with each other and change speed and direction. The mean free path is the average path length between collisions. The mean free path depends on how many molecules are packed into a volume. It varies inversely with density. When more molecules are present, collisions happen more often, so the mean free path becomes shorter. It also depends on molecule size. Larger...

heat capacity: problem-solving

Heat Capacity of Gases by Degrees of Freedom

Heat capacity of gases depends on the gas type and the motion of its molecules. It is the amount of heat energy needed to raise the temperature of a unit mass of gas by one degree Celsius. This thermodynamic property is important in science and industry. To solve heat capacity problems, first identify the gas. A gas's molecular structure affects its heat capacity because the molecules have different degrees of freedom. These values can be found from tables or from empirical equations. Next,...

dalton's law of partial pressure

Gas Mixtures and Their Partial Pressures

Gas mixtures have a total pressure that comes from the partial pressures of each gas. A partial pressure is the pressure one gas would make if it filled the whole container by itself. This idea helps explain how gases behave when they are mixed together. When two or more gases share a container, their molecules move randomly and collide with one another. If the gases are at the same temperature, they reach thermal equilibrium. Their molecules then have the same average kinetic energy. In that...

escape velocities of gases

Why Lighter Gases Escape Earth First

Earth’s escape velocity is the speed an object needs to leave gravity behind. Near the top of the atmosphere, about 100 km above Earth, that speed is 11.1 km/s. Gas molecules can escape only if their speeds become high enough to reach that limit. The chance of escape depends on gas temperature and molecular speed. According to kinetic theory, the average kinetic energy of gas molecules is proportional to temperature. As temperature rises, the rms speed, or root-mean-square speed, also rises.

key terms and concepts

See how the van der Waals equation corrects the ideal gas law for molecular attraction and finite molecular volume, with a carbon dioxide example.

How Real Gases Deviate from Ideal Behavior | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

How Real Gases Deviate from Ideal Behavior

Description

Transcript

Tags