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Lesson 4: Kinetic Molecular Theory
Part c: Get Real
Part a: Characteristics of the Model
Part b: Explaining Ideal Gas Behavior
Part c: Get Real
Ideal vs. Real Gases
This unit has focused on ideal gas behavior. An ideal gas is a simplified model of a gas that attempts to approximate a real-world gas. The ideal gas model provides a great approximation of a samples of gas under the conditions of low pressure and high temperature. The lower the pressure and the higher the temperature, the more likely a gas sample will follow the gas laws discussed in this chapter. The opposite of these conditions are conducive to the formation of liquids. That is, placing high pressure upon a gas and/or cooling it to lower temperatures are means of condensing the gas sample into a liquid. The less that a gas sample is like a liquid, the more it tends to act like an ideal gas.
We discussed the five assumptions of the kinetic molecular theory on a previous page. These assumptions or postulates describe the nature of an ideal gas. A gas acts ideally insofar as these assumptions are true. Of the five assumptions, the two that are most problematic are:
- Particles of gas are infinitesimally small points in space. The volume they occupy can be neglected.
- The forces exerted between gas particles are non-existent or negligible.
While these two assumptions are approximately true of reality, a real gas particle doesn’t move about its container neglecting attributes about itself and its motion that aren’t true. And because these two assumptions do not perfectly describe a real gas, efforts have historically been made to adjust and correct the model to correct for these two approximations. On this page, we will learn of the corrections made by Dutch scientist Johannes van der Waals.
Providing Corrections for Particle Volume
Gas particles do have volume. They are not points in space. The effect this reality has upon an ideal gas is that the volume available to particles is slightly less than the volume of the container. Van der Waal implemented a small correction to the V in P•V=n•R•T in order to account for particles occupying some space within the container. The correction had this form:
P•(V - correction factor) = n•R•T
The amount of correction that is made is dependent on the type of gas and the number of particles of the gas. The correction factor has come to have the form of n•b where n is the number of moles of gas and b is a fudge factor that depends on the gas type and is determined experimentally. In general, larger gases tend to have larger values of b. Van der Waal’s corrected the ideal gas law for the fact that particles occupy space.
Providing Corrections for Interparticle Forces
Gas particles do attract one another. They do not move about the container without feeling the forces from other particles. So, the Van der Waal’s second correction was to account for the fact that particles do attract each other. These attractions reduce the frequency at which particle-wall collisions occur. Because interparticle attractions lead to reduced pressures, the correction includes a term subtracted from the gas pressure. The correction would have this form:
(P - correction factor)•(V -n•b) = n•R•T
The amount of correction that needs to be made is dependent upon how densely packed the particles are within the volume of the container. The more densely packed they are, the more numbers of particle pairs that would exert forces on each other. Van der Waal reasoned that the correction factor is proportional to the square of the n/V ratio where n is the number of moles of particles and V is the container volume. The correction factor also includes a fudge factor a that is determined experimentally and is a different value for different gases. With the second correction factor, van der Waal’s equation becomes
You will notice that van der Waal’s equation is approximately a P•V= n•R•T equation with some small corrections to account for real gas behavior.
The Fudge Factors
Both correction factors listed above utilize a couple of constants that are dependent upon the identity of the gas. These constants are determined by experimental investigations of samples of specific gases. Values for 20 common gases are shown in the table below.
There are a couple of trends in this data that are worth highlighting. Both have to do with particle size. The constant a was part of van der Waal’s correction for the fact that there are interparticle attractions. Interparticle attractions is an important enough topic in Chemistry that we have devoted a large portion of Chapter 11 to the topic. For many particles, particularly those that are nonpolar, the strength of interparticle attractions increases with increasing size. An inspection of the noble gases in rows 10 through 14 show that the values of a increase as the size of the atoms increase. Similarly, rows 17 through 19 show three hydrocarbons that are alike in every way with the exception of the number of atoms and thus the size. We notice that the values of a increase as the size of these molecules increase.
The constant b was part of van der Waal’s correction for the fact that particles are not points in space but rather occupy a small bit of the space available in the container. A very noticeable trend is that larger particles like radon (row 14), propane (row 18), butane (row 19), and sulfur hexafluoride (row 20) have the largest values of b. Smaller particles like hydrogen (row 1), helium (row 9), and neon (row 10) have the smallest values of b.