An ideal gas is a gas that behaves according to the ideal gas, while a non-ideal or real gas is a gas that deviates from the ideal gas law. Another way to look at it is that an ideal gas is a theoretical gas, while a real gas is an actual gas. Here is a look at the properties of ideal gases and real gases, when it’s appropriate to apply the ideal gas law, and what to do when dealing with real gases.
The Ideal Gas Law
An ideal gas law follows the ideal gas law:
PV = nRT
P is pressure, V is volume, n is the number of moles of the gas, R is the gas constant, and T is the absolute temperature.
The ideal gas law works for all ideal gases, regardless of their chemical identity. But, it is an equation of state that applies only under certain conditions. It assumes particles participate in perfectly elastic collisions, have no volume, and don’t interact with each other except to collide. In other words, the gas behaves according to the kinetic molecular theory of gases.
Similarities Between Real and Ideal Gases
Real and ideal gases share certain properties of gases:
- Mass: Both real and ideal gas particles have mass.
- Low density: Gases are much less dense than liquids or solids. For the most part, gas particles are far apart from one another both in an ideal gas and a real gas.
- Low particle volume: Because gases are not dense, the size or volume of gas particles is very small compared to the distance between particles.
- Motion: Both ideal and real gas particles have kinetic energy. Gas particles move randomly, pretty much in a straight line between collisions.
The ideal gas law is so useful because many real gases behave like ideal gases under two conditions:
- Low pressure: Many gases we encounter in daily life are at relatively low pressure. Pressure becomes a factor when it’s high enough to force particles into close proximity.
- High temperature: In the context of gases, a high temperature is any temperature well above the vaporization temperature. So, even room temperature is hot enough to give real gas particles enough kinetic energy for them to act like an ideal gas.
Real Gas vs Ideal Gas
Under ordinary conditions, many real gases do behave like ideal gases. For example: air, nitrogen, oxygen, carbon dioxide, and the noble gases pretty much follow the ideal gas law near room temperature and atmospheric pressure. However, there are several conditions where real gases deviate from ideal gas behavior:
- High pressure: High pressure forces gas particles close enough to interact with one another. Also, the particle volume is more important because the distance between molecules is smaller.
- Low temperature: At low temperatures, gas atoms and molecules have less kinetic energy. They move slowly enough that interactions between particles and energy lost during collisions is important. An ideal gas never changes into a liquid or a solid, while a real gas does.
- Heavy gases: In gases with a high density, particles interact with one another. Intermolecular forces are more apparent. For example, many refrigerants don’t behave like ideal gases.
- Gases with intermolecular forces: Particles in some gases readily interact with one another. For example, hydrogen bonding occurs in water vapor.
Real gases are subject to:
- Van der Waals forces
- Compressibility effects
- Variable specific heat capacity
- Variable composition
- Non-equilibrium thermodynamic effects
- Chemical reactions
Summary of Differences Between Real Gases and Ideal Gases
| Difference | Real Gas | Ideal Gas |
|---|---|---|
| Particle Volume | Definite volume | No or negligible volume |
| Collisions (with container and each other) | Non-elastic | Elastic |
| Intermolecular forces | Yes | No |
| Interactions | Particles interact and may react | No interactions aside from collision |
| Phase transition | Yes, according to a phase diagram | No |
| Gas law | van der Waals Equation | Ideal Gas Law |
| Exists in the real world | Yes | No |
Ideal Gas Law vs van der Waals Equation
If the ideal gas law doesn’t work with real gases, how do you perform calculations? You use the van der Waals equation. The van der Waals equation is like the ideal gas law, but it includes two correction factors. One factor adds a constant (a) and amends the pressure value to allow for the small attractive force between gas molecules. The other factor (b) accounts for the effect of particle volume, changing the V in the ideal gas law into V – nb.
[P + an2/V2](V – nb) = nRT
You need to know the values of a and b to use the van der Waals equation. These values are specific to each gas. For real gases that approximate ideal gases, a and b are very close to zero, turning the van der Waals equation into the ideal gas law. For example, for helium: a is 0.03412 L2-atm/mol2 and b is 0.02370 L/mol. In contrast, for ammonia (NH3): a is 4.170 L2-atm/mol2 and b is 0.03707 L/mol.
Gases with large values for a have high boiling points, while those with low values for a liquefy close to absolute zero. The value for b indicates the relative size of a gas particle, so it’s useful for estimating the radius of monatomic gases, such as noble gas atoms.
References
- Cengel, Yunus A. and Michael A. Boles (2010). Thermodynamics: An Engineering Approach (7th Ed.). McGraw-Hill. ISBN 007-352932-X.
- Tschoegl, N. W. (2000). Fundamentals of Equilibrium and Steady-State Thermodynamics. Amsterdam: Elsevier. ISBN 0-444-50426-5.
- Tuckerman, Mark E. (2010). Statistical Mechanics: Theory and Molecular Simulation (1st ed.). ISBN 978-0-19-852526-4.
- Xiang, H. W. (2005). The Corresponding-States Principle and its Practice: Thermodynamic, Transport and Surface Properties of Fluids. Elsevier. ISBN 978-0-08-045904-2.