Master AP Chemistry Topic 3.6 with this free practice quiz. Test your skills on real gases, high pressure conditions, particle volume, and effect of IMFs to prepare for your AP exam.
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Introduction to Deviation from Ideal Gas Behaviour
The ideal gas law, PV = nRT, describes the relationship between pressure (P), volume (V), amount of gas (n), and absolute temperature (T). R is the ideal gas constant. This equation assumes that gas particles have negligible volume and experience no intermolecular attractions or repulsions.
Real gases do not perfectly satisfy these assumptions. Gas particles occupy space, and intermolecular forces influence their motion. As a result, real gases can deviate from the predictions of the ideal gas law, particularly at high pressures and low temperatures.
The extent of deviation depends on the gas’s identity and the conditions under which it is measured. Under conditions of low pressure and sufficiently high temperature, many real gases behave approximately ideally because particles are relatively far apart and intermolecular attractions have less influence on their motion.
The Assumptions Behind the Ideal Gas Law
The ideal gas law is based on the kinetic molecular theory (KMT), which models gases using two key assumptions.
First, gas particles have negligible volume compared with the volume of their container. This means the space available for particle motion is approximately equal to the container’s total volume.
Second, gas particles experience no intermolecular attractions or repulsions. They move independently, and their collisions with the container walls determine the gas pressure.
These assumptions work well when particles are far apart. However, real gas particles have finite sizes and interact through intermolecular forces, including London dispersion forces, dipole–dipole attractions, and hydrogen bonding where applicable.
When these effects become significant, the gas no longer behaves exactly as the ideal gas model predicts.
How Intermolecular Attractions Cause Deviation
Intermolecular attractions become particularly important at low temperatures and under conditions approaching condensation.
As temperature decreases, gas particles have lower average kinetic energy. Although intermolecular forces do not necessarily become stronger, the particles have less kinetic energy relative to the attractive forces acting between them. Attractions therefore have a greater influence on their motion.
Consider a particle moving toward the wall of a container. In an ideal gas, neighboring particles do not affect its motion. In a real gas, attractions from nearby particles can pull it slightly away from the wall. Consequently, its collision with the wall may transfer less momentum than expected.
The combined effect of these interactions is a lower measured pressure than the ideal gas law predicts at the same temperature, volume, and amount of gas.
This effect is especially significant when a gas is close to condensing into a liquid, because particles are relatively close together and attractive interactions become influential.
Gases with stronger intermolecular attractions generally show greater deviations under comparable conditions. For example, NH₃ has hydrogen bonding, whereas CH₄ experiences only London dispersion forces. NH₃ can therefore show more pronounced attraction-related deviations under suitable comparable conditions.
How Particle Volume Causes Deviation
The second cause of non-ideal behavior is the finite volume occupied by gas particles.
In the ideal gas model, particles are treated as point-like objects with negligible volume. In reality, atoms and molecules occupy space, so not all the volume inside a container is freely available for particle motion.
At low pressures, particles are widely separated, and their combined volume is small compared with the container volume. The assumption of negligible particle volume is therefore reasonable.
At extremely high pressures, particles are forced much closer together. Their own volume becomes a significant fraction of the container’s volume, reducing the space available for movement.
As a result, a real gas becomes more difficult to compress than an ideal gas. At the same temperature and pressure, the real gas may occupy a larger volume than the ideal gas prediction. Alternatively, if the volume is held constant, the pressure may be higher than the ideal prediction when particle-volume effects dominate.
This behavior becomes particularly important under extreme compression, when the finite size of particles can no longer be ignored.
Conditions That Increase or Reduce Deviation
The degree of deviation depends on pressure, temperature, and the nature of the gas particles.
At high pressures, particles are closer together. Both intermolecular attractions and particle volume become more significant, although the finite volume of particles becomes particularly important at extreme compression.
At low temperatures, particles move more slowly on average, making intermolecular attractions more influential relative to their kinetic energy. Deviations caused by attractions become especially significant near condensation.
At high temperatures, particles have greater average kinetic energy. Their motion is less affected by intermolecular attractions, so many gases behave more ideally.
At low pressures, particles are far apart, making both their finite volume and their intermolecular interactions relatively insignificant.
Small particles with weak intermolecular attractions, such as helium atoms, generally behave more ideally than particles with stronger attractions or larger molecular volumes under comparable conditions.
The most favorable conditions for ideal behavior are therefore high temperature and low pressure.
Interpreting Quantitative Deviations
The ideal gas law provides a reference against which the behavior of real gases can be compared.
PV = nRT
where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is absolute temperature in kelvin.
For a given sample, the ideal gas law predicts a particular relationship between pressure, volume, and temperature. If experimental measurements do not match this relationship exactly, the difference reflects non-ideal behavior.
One useful comparison is the ratio PV/nRT. For an ideal gas, this ratio equals 1.
- A ratio below 1 indicates that attractive interactions may be lowering the measured pressure relative to the ideal prediction under the specified conditions.
- A ratio above 1 indicates that particle-volume effects or other repulsive contributions are producing a higher pressure than the ideal prediction.
These interpretations are most straightforward when comparing gases at the same temperature and amount, and when identifying which non-ideal effect dominates.
A ratio close to 1 does not necessarily prove that a gas is perfectly ideal. Different effects can partially offset each other, producing a value close to the ideal prediction even though the particles still interact.
Worked example: Comparing pressure predictions
Suppose 1.00 mol of a gas occupies 2.00 L at 300 K. Use R = 0.0821 L atm mol⁻¹ K⁻¹.
The ideal pressure is calculated using:
P = nRT/V
Substituting the values:
P = (1.00 × 0.0821 × 300)/2.00
P = 12.3 atm
Suppose the measured pressure is 11.5 atm under these conditions.
The measured pressure is lower than the ideal prediction. This is consistent with intermolecular attractions reducing the pressure exerted on the container walls.
The difference is approximately 0.8 atm. The result alone does not establish that attractions are the only cause, but it supports the interpretation that their effect is significant under the conditions studied.
Connecting Particle Behavior to Experimental Observations
AP Chemistry Topic 3.6 emphasizes explaining macroscopic observations using particulate-level reasoning.
A statement such as “the gas deviates from ideal behavior at low temperature” is incomplete without explaining why. A stronger explanation connects the temperature change to particle motion, intermolecular attractions, and the measured pressure.
Similarly, explaining high-pressure deviation requires recognizing that particles occupy finite space. As compression increases, the space available for particle motion becomes increasingly restricted, so the ideal model becomes less accurate.
When analyzing experimental data, consider the conditions first. A gas near condensation is likely to show important attraction-related effects, whereas a gas under extreme compression is more likely to show significant particle-volume effects.
The two effects can compete. Attractions tend to reduce pressure relative to the ideal prediction, while finite particle volume tends to increase pressure when compression makes particle size significant. The observed behavior depends on which effect dominates.
These relationships connect Topic 3.6 with Topic 3.1, Intermolecular and Interparticle Forces; Topic 3.4, Ideal Gas Law; and Topic 3.5, Kinetic Molecular Theory. They also provide the basis for explaining why the ideal gas law is a useful model rather than a perfectly accurate description of every gas under every condition.