DAT General Chemistry: Kinetic Molecular Theory and Real-Gas Behavior

DAT High-Yield Concept

Ideal Conditions: Real gases behave most ideally at Low Pressure and High Temperature (LPHT).
Microscopic Origin of Pressure: Gas pressure is generated entirely by elastic collisions of gas molecules with container walls.
Average Kinetic Energy: Depends only on absolute temperature ( $\text{KE}_{\text{avg}} = \frac{3}{2}RT$ ), independent of molar mass or chemical identity.
Real Gas Deviations: Non-ideal behavior occurs at High Pressure and Low Temperature (HPLT) due to finite molecular volume and intermolecular attractive forces.
Compressibility Factor ( $Z = \frac{PV}{nRT}$ ): $Z = 1$ for ideal gases; $Z < 1$ when intermolecular attractions dominate, and $Z > 1$ when molecular volume dominates.

1. Postulates of Kinetic Molecular Theory (KMT)

The Kinetic Molecular Theory (KMT) provides a microscopic model explaining macroscopic gas behavior. An ideal gas adheres strictly to five core postulates:

Particle Volume: Gas particles are in continuous, random, straight-line motion. The combined volume of individual gas molecules is negligible compared to the total container volume ( $V_{\text{particles}} \approx 0$ ).
Intermolecular Forces: Gas molecules exert no attractive or repulsive forces on one another.
Elastic Collisions: Collisions between gas molecules or with container walls are perfectly elastic; total kinetic energy is conserved.
Pressure Generation: Gas pressure is caused solely by the impulse and frequency of molecular collisions against the walls of the container.
Temperature and Kinetic Energy: The average kinetic energy of gas molecules is directly proportional to the absolute temperature in Kelvin ( $\text{KE}_{\text{avg}} \propto T$ ). At a given temperature, all gases possess the exact same average kinetic energy regardless of molar mass.

2. Ideal Gas Behavior vs. Real Gas Deviations

An ideal gas obeys the ideal gas equation ( $PV = nRT$ ) under all conditions. However, real gas molecules possess non-zero volumes and experience intermolecular forces (such as London dispersion forces or dipole interactions).

Conditions that favor ideal behavior are Low Pressure and High Temperature:

Low Pressure: Gas molecules are separated by vast distances, making particle volume negligible relative to the container volume.
High Temperature: Molecules possess high thermal kinetic energy, overcoming weak intermolecular attractions during brief collisions.

DAT Memory Mnemonic: Ideal conditions = LPHT vs non-ideal deviations = HPLT

3. Microscopic Causes of Real Gas Deviations at HPLT

At High Pressure and Low Temperature (HPLT), real gases deviate significantly from ideality due to two main physical reasons:

Why Real Gases Deviate:

Low Temperature Effect (Intermolecular Attractions): As kinetic energy decreases, intermolecular attractions pull neighboring molecules together. This slows molecules down before hitting container walls, reducing collision force and causing measured pressure to be lower than ideal ( $P_{\text{real}} < P_{\text{ideal}}$ , leading to $Z < 1$ ).
High Pressure Effect (Finite Particle Volume): As the container volume decreases, individual molecular volumes occupy a significant fraction of total space. The free space available for movement is reduced ( $V_{\text{real}} > V_{\text{ideal}}$ , leading to $Z > 1$ ).

Compressibility factor: where a real gas stops behaving ideally — The compressibility factor Z equals PV/nRT, so an ideal gas traces the horizontal line Z = 1 at every pressure. At ordinary temperatures a real gas dips below that line at moderate pressures, where attractions between the molecules hold the sample to a smaller volume than the ideal gas law predicts, and then rises above it at high pressures, where the volume the molecules themselves occupy dominates. Raising the temperature shallows the dip until it disappears, and lowering the pressure returns every curve to Z = 1, which is why the ideal gas law works well for ordinary gases near room conditions.

The pressure dependence of the compressibility factor for N2 at high temperatures, compared with that for an ideal gas. Created using data from the NIST Chemistry WebBook . (Source: Retired Pchem Prof · CC BY-SA 4.0 · Wikimedia Commons)

Property	Ideal Gas	Real Gas (Moderate Pressure)	Real Gas (Very High Pressure)
Particle Volume	Negligible ( $V \approx 0$ )	Small relative to container	Significant fraction of total volume
Intermolecular Forces	Zero	Dominant attractions lower wall impacts	Repulsive/Volume effects dominate
Compressibility Factor ( $Z = \frac{PV}{nRT}$ )	$Z = 1$	$Z < 1$	$Z > 1$

Worked Calculation Example & DAT Exam Trap

Question: Predict whether $\ce{N2}$ gas at $\pu{200 K}$ and $\pu{100 atm}$ has a compressibility factor $Z < 1$ , $Z = 1$ , or $Z > 1$ .

Reasoning:

Calculate ideal molar volume at $\pu{200 K}$ and $\pu{100 atm}$ : $V_{\text{ideal}} = \frac{RT}{P} = \frac{(\pu{0.08206 L*atm/(mol*K)})(\pu{200 K})}{\pu{100 atm}} = \pu{0.164 L/mol}$
At low temperature ( $\pu{200 K}$ ) and moderate high pressure ( $\pu{100 atm}$ ), attractive forces between $\ce{N2}$ molecules predominate.
Attractions pull molecules together, reducing impact force against walls, so $P_{\text{real}} < P_{\text{ideal}}$ . Thus, $Z = \frac{P_{\text{real}}V}{nRT} < 1$ .

DAT Exam Trap: Students often mistakenly think high pressure always yields $Z > 1$ . At moderate high pressures, attractive forces dominate first (causing $Z < 1$ ). Only at extreme pressures where molecules are tightly packed does molecular volume dominate, driving $Z > 1$ .

Critical Thinking Questions

Which gas will behave more ideally at $\pu{25 degC}$ and $\pu{1.0 atm}$ : $\ce{He}$ or $\ce{H2O}$ vapor? Explain using KMT principles.
If two gas samples ( $\ce{Ne}$ and $\ce{CO2}$ ) are at the same temperature of $\pu{300 K}$ , which gas has a higher average velocity, and which has a higher average kinetic energy?
Why do polar gases deviate more from ideality than nonpolar gases under identical pressure and temperature conditions?

References

Sources returned by Google Search grounding during lesson verification.

10.9: Real Gases - Deviations from Ideal Behavior - Chemistry LibreTexts — chem.libretexts.org
The kinetic molecular theory of gases - Khan Academy — khanacademy.org

Kinetic Molecular Theory and Real-Gas Behavior

Summary

Practice Questions

AI Tutor