Ideal Gas
Gases, unlike solids and liquids have indefinite shape and indefinite volume. As a result, they are subject to pressure changes, volume changes and temperature changes. Real gas behavior is actually complex. For now, let's look at ideal Gases, since their behavior is simpler. By understanding ideal gas behavior, real gas behavior becomes more tangible.
How do we describe an ideal gas? An ideal gas has the following properties:
1. An ideal gas is considered to be a "point mass". A point mass is a particle so small, its mass is very nearly zero. This means an ideal gas particle has virtually no volume.
2. Collisions between ideal Gases are "elastic". This means that no attractive or repulsive forces are involved during collisions. Also, the kinetic energy of the gas molecules remains constant since theses interparticle forces are lacking.
Volume and temperature are by now familiar concepts. Pressure, however, may need some explanation. Pressure is defined as a force per area. When gas molecules collide with the sides of a container, they are exerting a force over that area of the container. This gives rise to the pressure inside the container.
For a gas, pressure, volume, temperature and the moles of gas are all related by the following equation:
PV = nRT
where P = pressure in atmospheres
V = volume in liters
n = moles of gas
R = ideal gas law constant (a proportionality constant)
T = temperature in Kelvin
The ideal gas law constant, R, dictates the units of pressure, volume and temperature. The most common used value for R when dealing with gases is 0.0821 L. atm/mol. K. This unit requires that volume to be expressed in liters, pressure to be expressed in atmospheres, and temperature to be expressed in Kelvin. One thing to keep in mind is that temperature will always be expressed in the Kelvin scale when dealing with any of the gas laws.
Real Gases
So far we have only considered the behavior of "ideal" Gases. How does a real gas differ from an ideal gas? Recall that an ideal gas is considered to be a point mass -- a particle so small that the volume of that particle is negligible. A real gas particle does have real volume. For an ideal gas, the collisions between gas particles was said to be "elastic" -- no attractive or repulsive forces exist, and thus, no energy is exchanged during collisions. For a real gas, collisions are non-elastic. There are a number of real gas laws. We will look at only one here, the van der Waal's equation:
Notice how "corrections" are being made to the pressure term and the volume term. Since collisions of real Gases are non-elastic, the term n2a/V2 is correcting for the interactions of these particles. The value of a is a constant, and must be experimentally determined for each gas. Since real gas particles have real volume, the nb term is correcting for the excluded volume. The value of b is a constant, and must be determined experimentally for each gas. The van der Waals constants, a and b for many gases have been tabulated in the CRC Handbook of Chemistry and Physics. Needless to say, they would be given to you if you are required to solve a problem using this equation. At this level, only pressure or temperature can be solved for easily. Solving for the volume is nontrivial and involves solving a cubic polynomial equation. Let's show how the van der Waals equation is rearranged to solve for pressure. Begin by dividing both sides of the equation by the volume term, V - nb:
Next, subtract the interparticle interaction term, n2a/V2 from both sides of the equation:
Using the real gas law, let's find the pressure of 2.00 moles of carbon dioxide gas at 298 K in a 5.00 L container. The van der Waals constants for carbon dioxide are: a = 3.592 L2. atm/mol2 and b = 0.04267 L/mol.
Substituting all of the variables into the appropriate terms of the equation, one obtains the pressure of :
Compare this to the pressure calculated using the ideal gas law:
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