By the end of this lesson, you should be able to...
- Determine which gases are more likely to deviate from ideal behavior and under which conditions (including the role of intermolecular forces).
Up to this point, we have assumed that are gases are behaving ideally. That is, that they follow all five postulates of the Kinetic Molecular Theory (KMT). These postulates were introduced in the first section and are restated below.
- The mean (average) kinetic energy (ε) is proportional to temperature (in Kelvin)
- Particles move in straight lines; their direction is random
- Molecules are small. The volume of the molecules is much smaller than the volume of the container.
- Molecules do not attract or repel each other (no IM forces).
- Molecules experience elastic collisions.
It turns out that there are several conditions which lead gases to behave in a non-ideal manner. These include when the pressure is very high, when the temperature is very low, and when molecules have the potential for strong (or many) intermolecular forces. While all three of these factors work in tandem to cause deviation from ideal behavior,. we will address each of these individually to better see the impact each has.
High Pressure
As we have seen from the ideal gas law, as the pressure of a system increases, it causes the volume to decrease. Thus, at extremely high pressures, the volume of the system becomes very small. When this happens, the relative volume that the gas particles take up in proportion to their container becomes larger. This breaks down postulate 3.
For example, let's examine the effects of high pressure on the relative volume of a collection of neon atoms in a container. The neon atom has an atomic radius of 69.0 pm. Assuming the atomic is spherical, the volume of a single atom would be given as V =
. Thus, for a single neon atom, the volume would be 1.38 x 10
-30
m
3
. That is really tiny! Even if you have one mole of neon atoms, the volume of their combined masses would still only be 8.29 x 10
-7
m
3
, which is equivalent to 0.829 mL. The molar volume of an ideal gas at STP is 22.4 L. That means while the molecules themselves only make up 0.829 mL of space, they spread out to fill a container of 22.4 L. That means the atoms themselves only make up 0.829 x 10
-3
L/22.4 L * 100% = 0.0037% of the total volume of the container.
What happens when we increase the pressure drastically? As the pressure increases, so does the portion of the total volume occupied by the atoms themselves. The volume of a mole of neon atoms is always approximately 0.829 mL since the atoms do not get compressed by the increased pressure. But, total volume goes down. The table below illustrates this effect.
The greater the volume of the container that is occupied the more the molecules have opportunities to collide with each other and interact. We will see shortly that this factor combines with low temperatures and strong IMFs.
Low Temperature
When gases are at lower temperatures their average kinetic energy is lower. They move slower on average as well. Anytime a molecule or atom collides with another, there is a chance that they will interact through intermolecular forces. At "high" enough temperatures, these interactions do not have an effect. But, at "low" temperatures, the molecules have less energy and may get "stuck" together when they collide. This would lead them to behave non-ideally. Eventually, if the temperature is low enough, they no longer behave as gases at all, and instead condense into their liquid form.
If you combine high pressure with low temperature, you can see that we a have a recipe for non-ideal behavior. The molecules take up more space in their container so they collide more with each other. They are slower, so when they collide they stick more. Let's now turn our attention to the effect of intermolecular forces.
Effect of Intermolecular Forces
It is assumed that ideal gases do not exert attractive (or repulsive) intermolecular forces between other things. However, in a scenario where they are close together and moving slowly (high pressure, low temperature), the effects of intermolecular forces exacerbate the problem.
Gas molecules with potential for strong intermolecular forces behave less ideally than gases with low potential. For example, ammonia (NH 3 ), has the capacity to perform hydrogen bonding and is highly polar. So is water (H 2 O). These molecules will behave less ideally than a non-polar molecule or atom, even at the same temperature (e.g. neon, nitrogen, helium).
Additionally, we know that larger molecules have more dispersion forces. Thus, gas molecules like butane (C 4 H 10 ) and propane (C 3 H 8 ) will deviate from ideal behavior more than ethane (C 2 H 6 ) or methane (CH 4 ).
If you combine a high pressure, low temperature set of conditions with a molecule/atom with stronger/more prevalent intermolecular forces, you have the largest deviations from ideal behavior. If you were to try to use the ideal gas law to calculate one property of a gas, it would be wrong. The larger the conditions/molecule deviates, the further off the calculation becomes.
Summary
You are expected to know the trends in non-ideal behavior. You do not need to know by how much one scenario deviates from another. This means, you should be able to compare scenarios that are similar but where one or more of these factors are changed. Try the problem below to see if you understand.