Kinetic Molecular Theory II

1. Kinetic Molecular Theory II Mr. Shields Regents Chemistry U05 L04

2. H2 H2 H2 Development of KMT Let’s discuss each of the 5 key assumptions of the KMT: • Gas particles do not attract or repel one another

3. Forces of Attraction – Assumption 1 • Consider what would happen if molecules did exert • significant attractive forces on one another… • Molecules would slow down as they shot past • one another as a result of the “drag” exerted • on them by these forces of attraction • (2) As gas molecules attracted one another • they eventually would tend to condense into • liquids and then eventually into solids

4. Forces of Attraction – Assumption 1 In the “REAL WORLD” forces of attraction between Atoms Or molecules do exist - In some of these “REAL GASES” these forces of attraction are strong and in others they may be very weak KMT assumes they are non-existent. Therefore gases act independently of one another These gases are known as “IDEAL GASES” In fact, to be considered an ideal gas, the gas must meet All 5 assumptions of KMT.

5. Volume – Assumption 2 2. The volume occupied by Gas particles is negligibly small compared to the overall volume of the gas container. “lots of empty space” is a relative term. Let’s consider the volume of empty space around molecules in the gas state vs. the liquid state Lot’s of empty space

6. Volume – Assumption 2 How much more space is there in a gas than in a liquid? • 1 mole of H2O in the gaseous state = 22.4 Liters/mol • (VB) which is also 6.023 x 1023 molecules (NA) or 18 g (the Molar Mass of Water) 1 mol of H2O in the liquid state = 0.018 liters (i.e. 18 ml; Density of water is 1g/ml) Ratio of gas to liquid is thus 22.4L/0.018L = 1250 • So the empty space between molecules in the gas • phase is approximately 1,250x the empty space • between molecules in the liquid phase.

7. Volume – Assumption 2 • This explains why… • Gases are easily compressible when an external • force is applied. Why? • 2. The density of gases is much lower than other • states of matter. Why?

8. Motion – Assumption 3 3. Gas Particles are in constant rapid random straight line motion • Explains why… • Gases quickly fill large empty spaces • 2. Gases quickly mix together to form Homogeneous • mixtures • 3. Why smaller molecules, which move faster than • larger molecules, mix more quickly

9. Molecular Velocities vs. Mass

10. Maxwell-Boltzman Distribution of Molecular Velocities Notice that as avg. vel. increases the velocity distribution curve flattens O2 is heavier than H2 so its avg. velocity is less Molecules of a given gas do not move at One specific velocity at specific temperature.

11. Motion – Assumption 3 Lastly … Not only are Gas Particles in constant, rapid, and random motion but … Particles move in a straight line until they collide with another particle or the walls of the container.

12. Elastic Collision – Assumption 4 4. NO KE IS LOST when gas molecules collide with each other. - Collisions between gas particles or collisions with with the walls of the container are perfectly elastic. - Thetotal energy of both colliding gas particles (the system) is the same after the collision as it was before the collision 20J (A) 35J (B) A B 32J (A) 23J (B) Total KE before (55J) = Total KE after (55J)

13. Collision types – Assumption 4 Elastic Collision A bouncing basketball is an example Of an inelastic collision

14. Elastic Collision – Assumption 4 • Consider what would happen if molecules • lacked only an infinitesimal fractional part of • being perfectly elastic. • Let’s look at H2 at 0 deg. C … • Approx. Velocity = 1.84 x 105 cm/sec (i.e 7244 ft/sec) • Assume Approx. Distance between collisions = 1.84 x 10-5 cm • (Clausius’ mean free path; distance traveled between collisions) • This leads to about10 billion collisions/sec (1x1010)

15. Elastic Collision – Assumption 4 • If ideal gas molecules were even slightly inelastic & • lost a little KE with each collision then at this collision • rate molecules would soon come to rest. • As they slow down they would condense first to a • liquid and then to a solid as they loose energy… • BUT THIS DOESN’T HAPPEN

16. KE and Temp – Assumption 5 5. The avg. KE of a gas is directly proportional to Temp in KELVIN (note: not true for any other Temp scale) i.e. the average kinetic energy of a collection of gas particles depends only on the temperature of the gas and nothing else. - As T increases KE increases and so does Velocity - Recall KE = ½ mv2

17. KE and Temp – Assumption 5 • If Velocity is increasing with increasing T then the • RATE OF COLLISIONS with the container wall must • be increasing • - If velocity is increasing then the force of each • molecular impact with the wall becomes more • forceful (higher velocity = higher energy) • THIS RESULTS IN INCREASED PRESSURE SINCE • (P=F/A) • (Force = the sum of the energy of all collisions with • The wall of the container)

18. The 5 KMT Assumptions OK … Let’s review the 5 assumptions of the KMT • Gas particles do not attract or repel one another • 2. The volume occupied by Gas particles is negligibly small compared to the overall volume • 3. Gas Particles are in constant random straight line motion • 4. No KE is lost when gas molecules collide with each other (totally elastic) • 5. The avg. KE of a gas is directly proportional to Temp in • Kelvin.

19. Ideal vs. Real Gas Gases that behave according to the 5 KMT assumptions Are Known as IDEAL GASES. Gases that do not behave according to the KMT are Known as REAL GASES Some simple gases approach IDEAL GAS behavior (He, Ne, H2, N2 are examples) but many do not.

20. Remember these!! Ideal vs. Real Gas Real Gases can however be made to approach ideal gas Behavior under the following conditions: - High Temp and Low pressure(Why is that?) Deviation from Ideal behavior occurs under these Conditions (i.e gas becomes more like a real gas): - Low Temp and High pressure

21. Macro vs. KMT We’ve talked about the Molecular (KMT) world now let’s discuss the Macroscopic World. In the Macroscopic world we’ll talk about: KMT World - Pressure, Volume, Temperature and the number of moles. To see how these are related we’ll discuss the gas laws of - Boyle, Charles, Guy-Lussac, Avogadro and Dalton.