Lesson 1.13: States of matter - Gases (Part 4). The kinetic theory of gases

Aim: To study the kinetic theory of gases.

Video 1

The kinetic theory of gases• The kinetic theory of gases is a generally

accepted and applied theory explaining the properties of gases.

Video 2

The first postulate of the kinetic theory (Particle Volume)

• Gases consist of microscopic particles, the distance between which is such that the actual volume of particles is negligible compared to the volume of the spaces between them.

(The gas particles are considered to have mass, but no volume.)

- Example (Compressibility of gases) In oxygen gas, 99.96% of the total volume is empty space. In normal conditions 1 cm3 of oxygen gas contains 2.7 x 1019 molecules, separated by an average distance of about 3.7 nm, which is thirteen times the diameter of an oxygen molecule.

Video 3

The second postulate of the kinetic theory (Particle Intermolecular Forces)

• Intermolecular forces are very weak in gases and do not affect their observed properties. Attractive and repulsive forces between gas molecules are negligible.

• Example: Expand spontaneously of gases

Video 4

The third postulate of the kinetic theory (Particle motion)

- Gas particles are in constant, random, straight-line motion except when they collide with each other or with the container walls.

Collisions among molecules are perfectly elastic. Energy can be transferred between gas particles during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.

Video 5

The fourth postulate of the kinetic theory (Particle Collisions)

The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy

- At a higher temperature, gas particles hit the walls of the container with greater energy.- An increase in temperature causes a simultaneous increase in gas pressure. Video 6

Maxwell-Boltzmann Distribution

• The total area under the curve = the total number of molecules in a given sample.

• At any temperature, very few molecules have speeds close to zero, and very few molecules have extremely high speeds.

• The distribution is temperature dependent. At low temperature, the maximum (the most probable speed) is higher and the curve has little spread.

• As temperature increase, not only does the peak shift toward the right, but the curve also flattens out.

• The distribution of speeds is unchanged, even though energy and velocity exchanges between the molecules are proceeding continually (as long as the temperature remains constant).

• The number of molecules with high kinetic energy approximately doubles with every 10 degree rise in temperature.

• The distribution depends on the molecular mass. Light gases have a higher average speed and a wider distribution of speeds than heavier gases.

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U1 u2 kinetic energy / molecular velocities

Low T

High T

The distribution of speedsfor nitrogen gas molecules

at three different temperatures

urms = 3RTM

Apparatus for studying molecular speed distribution

The properties of gases and the gas laws

• Compressibility of Gases• Boyle’s Law

• P collision rate with wall

• Collision rate number density

• Number density 1/V• P 1/V

• Charles’ Law• P collision rate with

wall• Collision rate

average kinetic energy of gas molecules

• Average kinetic energy T

• P T

• Avogadro’s Law

P collision rate with wall

Collision rate number density

Number density nP n

• Dalton’s Law of Partial Pressures

Molecules do not attract or repel one another

P exerted by one type of molecule is unaffected by the presence of another gas

Ptotal = Pi

The relationship between the speeds and masses of gas molecules

• The kinetic teory of gases explains Graham’s law of effusion.

• A heavier molecule moves more slowly than a lighter one.

• It collides with a porous barrier less frequently.

• The probability of penetration of the barrier is lower for a heavier molecule.

The distribution of speedsof three different gases

at the same temperature

Activity (Changes in the state of gases)

• What change or changes in the state of a gas brings about each of the following effects?

1. The number of impacts per unit time on a given container wall increases.

2. The average energy of impact of molecules with the wall of the container decreases.

3. The average distance between gas molecules increases.

4. The average speed of molecules in the gas mixture is increased.

T V P

- -

-

- -

Note;T: Temperature, V: Volume, P: Pressure, for increase, for decrease

Conclusion

• At the end of the lesson the students should be able to:

1. state and explain the basic assumptions of the kinetic theory of gases as applied to an ideal gas