9.3 - Kinetic molecular theory and real gases

What does kinetic molecular theory explain?

How microscopic particle motion produces macroscopic gas behavior.

How does kinetic molecular theory relate to the ideal gas law?

The ideal gas law describes relationships among variables; KMT explains the particle behavior behind them.

How do ideal-gas particles move?

In constant random motion, traveling in straight lines between collisions.

What does KMT assume about particle volume?

Particle volume is negligible compared with container volume.

What does KMT assume about forces between particles?

There are no significant attractions or repulsions between particles between collisions.

What causes pressure according to KMT?

Particles transferring momentum to the container walls during collisions.

What does KMT assume about collisions?

They are elastic, so total kinetic energy is conserved in collisions.

What determines the average translational kinetic energy of gas particles?

Absolute temperature.

What is the kinetic energy equation for one particle?

KE = ½mv².

At the same temperature, do different gases have the same average translational kinetic energy?

Yes.

At the same temperature, do different gases necessarily have the same average speed?

No. Lighter particles move faster on average.

Why do lighter particles move faster at the same temperature?

They require a greater speed to have the same average kinetic energy as heavier particles.

Do all particles in one gas sample move at the same speed?

No. Their speeds form a distribution.

What does the Maxwell–Boltzmann distribution show?

The distribution of molecular speeds in a gas sample.

How does increasing temperature change a Maxwell–Boltzmann speed distribution?

It shifts toward higher speeds and becomes broader with a lower peak.

How does decreasing temperature change a Maxwell–Boltzmann speed distribution?

It shifts toward lower speeds and becomes narrower with a higher peak.

What remains constant under normalized speed-distribution curves?

The total area, representing all particles.

At the same temperature, which gas has a speed distribution shifted farther right: a lighter or heavier gas?

The lighter gas.

How does average translational kinetic energy depend on Kelvin temperature?

It is directly proportional to Kelvin temperature.

If Kelvin temperature doubles, what happens to average translational kinetic energy?

It doubles.

For a given gas, how does a characteristic molecular speed depend on Kelvin temperature?

It is proportional to the square root of Kelvin temperature.

If Kelvin temperature quadruples, what happens to a characteristic molecular speed?

It doubles.

At the same temperature, how does characteristic speed depend on molar mass?

It is inversely proportional to the square root of molar mass.

At the same temperature, if gas B has four times the molar mass of gas A, how do their characteristic speeds compare?

Gas A moves twice as fast as gas B.

At constant moles and volume, why does heating increase pressure?

Particles move faster and transfer momentum to the walls more rapidly.

At constant moles and temperature, why does compression increase pressure?

Particles encounter the walls more frequently in the smaller space.

At constant temperature and volume, what happens if the number of ideal-gas particles doubles?

Pressure doubles.

At constant temperature, pressure, and gas identity, why does adding moles increase volume?

More space is needed to maintain the same pressure.

At equal temperature, volume, and particle number, do light and heavy ideal gases exert different pressures?

No. They exert equal pressures.

Why does a heavier ideal gas not automatically exert greater pressure at the same temperature and particle number?

Heavier particles move more slowly, balancing their greater mass.

At constant temperature and volume, how does replacing 100 light particles with 100 heavy particles affect ideal-gas pressure?

Pressure stays the same.

At constant temperature and volume, how do 200 heavy particles compare with 100 light plus 100 heavy particles?

They produce equal ideal-gas pressure.

What two main properties make real gases differ from ideal gases?

Particles occupy space and interact through intermolecular forces.

Under what conditions do gases behave most ideally?

High temperature and low pressure.

Why does low pressure favor ideal behavior?

Particles are far apart, so their own volume and interactions matter less.

Why does high temperature favor ideal behavior?

Particles have greater kinetic energy, making attractions less important relative to their motion.

Under what conditions do deviations from ideal behavior become more important?

Low temperature and high pressure.

Why do attractive forces matter more at low temperature?

Particles have less kinetic energy, so attractions influence their motion more strongly.

Why does particle volume matter more at high pressure?

Particles occupy a larger fraction of the total container volume.

At a fixed temperature, volume, and amount, how can attractions affect pressure compared with the ideal prediction?

They can lower the measured pressure.

What is the compressibility factor?

Z = PV/(nRT).

What value of Z represents ideal-gas behavior?

Z = 1.

What does Z < 1 generally indicate?

Attractions dominate, producing a smaller PV value than the ideal prediction.

What does Z > 1 generally indicate?

Excluded-volume or repulsive effects dominate, producing a larger PV value than the ideal prediction.

At fixed pressure, temperature, and moles, what does Z < 1 mean about volume?

The real-gas volume is smaller than the ideal-gas prediction.

At fixed pressure, temperature, and moles, what does Z > 1 mean about volume?

The real-gas volume is larger than the ideal-gas prediction.

What equation accounts for molecular attractions and particle volume?

The van der Waals equation.

What is the van der Waals equation?

[P + a(n/V)²](V − nb) = nRT.

What does a represent in the van der Waals equation?

A correction for attractive interactions between particles.

What does a larger a value generally indicate?

Stronger attractive interactions.

What does b represent in the van der Waals equation?

A correction for the volume excluded by the particles.

Why does the van der Waals equation use V − nb?

The space available for particle motion is less than the total container volume.

Why does the van der Waals equation add a(n/V)² to pressure?

It corrects for the pressure reduction caused by attractive forces.

When does the van der Waals equation approach the ideal gas law?

When attraction and excluded-volume corrections become negligible.