1 Mr. ShieldsRegents Chemistry U05 L04

2 Development of KMT Let’s discuss each of the 5 key assumptions of the KMT: 1.Gas particles do not attract or repel one another H2H2H2H2 H2H2H2H2 H2H2H2H2

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

6 Volume – Assumption 2 How much more space is there in a gas than in a liquid? 1 mol of H 2 O in the liquid state = liters ( i.e. 18 ml; Density of water is 1g/ml ) Ratio of gas to liquid is thus 22.4L/0.018L = mole of H 2 O in the gaseous state = 22.4 Liters/mol (V B ) which is also x molecules (N A ) or 18 g ( the Molar Mass of Water ) 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… 1. Gases are easily compressible when an external force is applied. Why? force is applied. Why? 2. The density of gases is much lower than other states of matter. Why? states of matter. Why?

8 Motion – Assumption 3 3. Gas Particles are in constant rapid random straight line motion line motion Explains why… 1.Gases quickly fill large empty spaces 2. Gases quickly mix together to form Homogeneous mixtures mixtures 3. Why smaller molecules, which move faster than larger molecules, mix more quickly larger molecules, mix more quickly

9 Molecular Velocities vs. Mass MoleculeH 2 (Small) HeH2OH2ON2N2 O2O2 CO 2 (large) Avg. Speed (m/sec) Molecular weight

10 Distribution of Molecular Velocities Molecules of a given gas do not move at One specific velocity at specific temperature. O 2 is heavier than H 2 so its avg. velocity is less Maxwell-Boltzman Notice that as avg. vel. increases the velocity distribution curve flattens

11 Motion – Assumption 3 Lastly … Gas Particles in constant, rapid, and 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. other. - Collisions between gas particles or collisions with with the walls of the container are perfectly elastic. - The total energy of both colliding gas particles (the system) is the same after the collision as it was before the collision AB Total KE before (55J) = Total KE after (55J) 20J (A) 35J (B) 32J (A) 23J (B)

13 Collision types – Assumption 4 ElasticCollision 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 H 2 at 0 deg. C … Approx. Velocity = 1.84 x 10 5 cm/sec (i.e 7244 ft/sec) Assume Approx. Distance between collisions = 1.84 x cm (Clausius’ mean free path; distance traveled between collisions) This leads to about 10 billion collisions/sec (1x10 10 )

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 - As T increases KE increases and so does Velocity - Recall KE = ½ mv 2 - Recall KE = ½ mv 2

17 KE and Temp – Assumption 5 - I- I- I- 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 The 5 KMT Assumptions 1.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. OK … Let’s review the 5 assumptions of the KMT

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, H 2, N 2 are examples) but many do not.

20 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 Remember these!!

21 - 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. Macro vs. KMT KMT World We’ve talked about the Molecular (KMT) world now let’s discuss the Macroscopic World. In the Macroscopic world we’ll talk about: