kinetic molecular theory ii

11Mr. ShieldsMr. Shields Regents Chemistry Regents Chemistry U05 L04 U05 L04

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Development of KMTDevelopment of KMT

Let’s discuss each of the 5 key assumptions of the KMT:Let’s discuss each of the 5 key assumptions of the KMT:

1.1. Gas particles do not attract or repel one anotherGas particles do not attract or repel one another

HH22

HH22

HH22

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Forces of Attraction – Assumption 1Forces of Attraction – Assumption 1

Consider what would happen if molecules did exertConsider what would happen if molecules did exertsignificant attractive forcessignificant attractive forces on one another… on one another…

(1)(1) Molecules would slow down as they shot past Molecules would slow down as they shot past one another as a result of the “drag” exertedone another as a result of the “drag” exerted on them by these forces of attractionon them by these forces of attraction

(2) As gas molecules attracted one another(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 solidsliquids and then eventually into solids

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Forces of Attraction – Assumption 1Forces of Attraction – Assumption 1

In the “REAL WORLD” forces of attraction between AtomsIn the “REAL WORLD” forces of attraction between AtomsOr molecules Or molecules do existdo exist

- - In some of these “In some of these “REAL GASES”REAL GASES” these forces of these forces of attraction are attraction are strongstrong and in others they may be very and in others they may be very weakweak

KMT assumes they are non-existent. Therefore gasesKMT assumes they are non-existent. Therefore gasesact act independentlyindependently of one another of one another

These gases are known as “These gases are known as “IDEAL GASES”IDEAL GASES”

In fact, to be considered an ideal gas, the gas must meetAll 5 assumptions of KMT.

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Volume – Assumption 2Volume – Assumption 2

2. The volume occupied by Gas particles is negligibly2. The volume occupied by Gas particles is negligibly small compared to the overall volume of the gassmall compared to the overall volume of the gas container.container.

Lot’s of empty spaceLot’s of empty space

““lots of empty space” is a relative lots of empty space” is a relative term. Let’s consider the volume term. Let’s consider the volume of empty space around molecules of empty space around molecules in the gas state vs. the liquid in the gas state vs. the liquid statestate

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How much more space is there in a gas than in a liquid?How much more space is there in a gas than in a liquid?

1 mol of H1 mol of H22O in the liquid state = 0.018 liters (O in the liquid state = 0.018 liters (i.e. 18 ml;i.e. 18 ml; Density of water is 1g/mlDensity of water is 1g/ml))

Ratio of gas to liquid is thus 22.4L/0.018L = 1250Ratio of gas to liquid is thus 22.4L/0.018L = 1250

1 mole of H1 mole of H22O in the gaseous state = 22.4 Liters/mol O in the gaseous state = 22.4 Liters/mol (V(VBB) which is also 6.023 x 10) which is also 6.023 x 102323 molecules (N molecules (NAA) or 18 g () or 18 g (the the

Molar Mass of WaterMolar Mass of Water))

So the empty space between molecules in the gasSo the empty space between molecules in the gasphase is approximately phase is approximately 1,250x1,250x the empty space the empty spacebetween molecules in the liquid phase.between molecules in the liquid phase.

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This explains why…This explains why…

1.1. Gases are easily compressible when an externalGases are easily compressible when an external force is applied. Why?force is applied. Why?

2. The density of gases is much lower than other2. The density of gases is much lower than other states of matter. Why?states of matter. Why?

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Motion – Assumption 3Motion – Assumption 33. Gas Particles are in constant rapid random straight3. Gas Particles are in constant rapid random straight line motionline motion

Explains why…Explains why…

1.1. Gases quickly fill large empty spacesGases quickly fill large empty spaces

2. Gases quickly mix together to form Homogeneous 2. Gases quickly mix together to form Homogeneous mixturesmixtures

3. Why smaller molecules, which move faster than3. Why smaller molecules, which move faster than larger molecules, mix more quicklylarger molecules, mix more quickly

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Molecular Velocities vs. Mass Molecular Velocities vs. Mass

Molecule H2

(Small)He H2O N2 O2 CO2

(large)

Avg. Speed(m/sec)

1960 1360 650 520 490 415

Molecular weight

2.0 4.0 18.0 28.0 32.0 44.0

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Distribution of Molecular Velocities

Molecules of a given gas do not move atMolecules of a given gas do not move atOne specific velocity at specific temperature.One specific velocity at specific temperature.

OO22 is heavier than H is heavier than H22

so its avg. velocity is lessso its avg. velocity is less

Maxwell-BoltzmanMaxwell-Boltzman

Notice that as avg. vel. increases the velocity Notice that as avg. vel. increases the velocity distribution curve flattensdistribution curve flattens

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Motion – Assumption 3Motion – Assumption 3

Lastly …Not only are Gas Particles in constant, rapid, and Gas Particles in constant, rapid, and random motion but …random motion but …

Particles move in a straight lineuntil they collide with anotherparticle or the walls of thecontainer.

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Elastic Collision – Assumption 4Elastic Collision – Assumption 4

4. 4. NO KE IS LOSTNO KE IS LOST when gas molecules collide with each 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

AA BB

Total KE before (55J) = Total KE before (55J) = Total KE after (55J)Total KE after (55J)

20J (A)20J (A) 35J (B)35J (B)

32J (A)32J (A) 23J (B)23J (B)

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Collision types – Assumption 4Collision types – Assumption 4

Elastic Elastic CollisionCollision

A bouncing basketball is an example A bouncing basketball is an example Of an inelastic collisionOf an inelastic collision

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Consider what would happen if moleculesConsider what would happen if moleculeslacked only an infinitesimal fractional part oflacked only an infinitesimal fractional part ofbeing perfectly elastic.being perfectly elastic.

Let’s look at HLet’s look at H22 at 0 deg. C … at 0 deg. C …

Approx. Velocity = 1.84 x 10Approx. Velocity = 1.84 x 1055 cm/sec (i.e 7244 ft/sec) cm/sec (i.e 7244 ft/sec)

Assume Approx. Distance between collisions = 1.84 x 10Assume Approx. Distance between collisions = 1.84 x 10-5-5 cm cm(Clausius’ mean free path; distance traveled between collisions)(Clausius’ mean free path; distance traveled between collisions)

This leads to aboutThis leads to about 10 billion10 billion collisions/sec collisions/sec (1x10 (1x101010))

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If If ideal gas moleculesideal gas molecules were even were even slightly inelasticslightly inelastic & &lost a little KE with each collision then at this collisionlost a little KE with each collision then at this collisionrate molecules would soon come to rest.rate molecules would soon come to rest.

As they slow down they would condense first to aAs they slow down they would condense first to aliquidliquid and then to a and then to a solidsolid as they loose energy… as they loose energy…

BUT THIS DOESN’T HAPPENBUT THIS DOESN’T HAPPEN

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KE and Temp – Assumption 5KE and Temp – Assumption 55. The avg. KE of a gas is directly proportional to Temp5. The avg. KE of a gas is directly proportional to Tempin in KELVINKELVIN ( (note: not true for any other Temp scalenote: not true for any other Temp scale))

i.e. the average kinetic energy of a collection of gasi.e. the average kinetic energy of a collection of gasparticles depends only on the particles depends only on the temperaturetemperature of the gas of the gas and and nothing elsenothing else. .

- As T increases KE increases and so does Velocity- As T increases KE increases and so does Velocity

- Recall KE = ½ mv- Recall KE = ½ mv22

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KE and Temp – Assumption 5KE and Temp – Assumption 5

- If Velocity is increasing with increasing T then theIf Velocity is increasing with increasing T then the RATE OF COLLISIONSRATE OF COLLISIONS with the container wall must with the container wall must be increasingbe increasing

- If velocity is increasing then the - If velocity is increasing then the forceforce of each of each molecular impact with the wall becomes moremolecular impact with the wall becomes more forceful (higher velocity = higher energy)forceful (higher velocity = higher energy)

THIS RESULTS IN INCREASED PRESSURE SINCETHIS RESULTS IN INCREASED PRESSURE SINCE

(P=F/A)(P=F/A)

(Force = the sum of the energy of all collisions with (Force = the sum of the energy of all collisions with The wall of the container)The wall of the container)

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The 5 KMT AssumptionsThe 5 KMT Assumptions

1.1. Gas particles do not attract or repel one anotherGas particles do not attract or repel one another

2. The volume occupied by Gas particles is negligibly small 2. The volume occupied by Gas particles is negligibly small compared to the overall volumecompared to the overall volume

3. Gas Particles are in constant random straight line motion3. Gas Particles are in constant random straight line motion

4. No KE is lost when gas molecules collide with each other 4. No KE is lost when gas molecules collide with each other (totally elastic)(totally elastic)

5. The avg. KE of a gas is directly proportional to Temp in5. The avg. KE of a gas is directly proportional to Temp inKelvin.Kelvin.

OK … Let’s review the 5 assumptions of the KMTOK … Let’s review the 5 assumptions of the KMT

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Ideal vs. Real GasIdeal vs. Real Gas

Gases that behave according to the 5 KMT assumptionsGases that behave according to the 5 KMT assumptionsAre Known as Are Known as IDEAL GASESIDEAL GASES. .

Gases that do not behave according to the KMT areGases that do not behave according to the KMT areKnown as Known as REAL GASESREAL GASES

Some Some simple gasessimple gases approach IDEAL GAS behavior (He, approach IDEAL GAS behavior (He, Ne, HNe, H22, N, N22 are examples) but many do not. are examples) but many do not.

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Ideal vs. Real GasIdeal vs. Real Gas

Real GasesReal Gases can however be made to approach ideal gas can however be made to approach ideal gasBehavior under the following conditions:Behavior under the following conditions:

- - High TempHigh Temp and and Low pressureLow pressure (Why is that?)(Why is that?)

Deviation from Ideal behavior occurs under theseDeviation from Ideal behavior occurs under theseConditions (i.e gas becomes more like a real gas):Conditions (i.e gas becomes more like a real gas):

- - Low TempLow Temp and and High pressureHigh pressure

Remember these!!Remember these!!

2121

- 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. KMTMacro vs. KMTKMT WorldKMT WorldWe’ve talked about

the Molecular (KMT)world now let’sdiscuss theMacroscopic World.

In the Macroscopicworld we’ll talkabout:

kinetic molecular theory ii

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