Kinetic Molecular TheoryKinetic Molecular TheoryKMTKMT

Chapter 10 Chapter 10

Gas LawsGas Laws

GasesGases

Atmospheric gases are made up of :Atmospheric gases are made up of : NN22 78% 78% OO22 21% 21% Other He, COOther He, CO22, H, H22 etc etc What are the GREENHOUSE gases?What are the GREENHOUSE gases? COCO22

CHCH44

HH22OO Other (CFC’s, NOx, ozone)Other (CFC’s, NOx, ozone)

PressurePressure

Gases fill a container uniformly.Gases fill a container uniformly. Pressure is Force per unit areaPressure is Force per unit area P= F x AP= F x A The force of the collisions of the gas The force of the collisions of the gas

particles with the wall of their container.particles with the wall of their container. Pressure is measured by a barometer, Pressure is measured by a barometer,

or manometer.or manometer. Units???Units???

Models vs LawsModels vs Laws So far we have looked at Gas laws to So far we have looked at Gas laws to

predict the behavior of gases.predict the behavior of gases. Scientists have also developed a Scientists have also developed a

model that helps to explain the model that helps to explain the behavior of gases.behavior of gases.

Models are an approximation!!Models are an approximation!!

Kinetic Molecular TheoryKinetic Molecular Theory

KMT attempts to explain the KMT attempts to explain the properties of an ideal gas.properties of an ideal gas.

KMT is based on speculations of KMT is based on speculations of the behavior of individual gas the behavior of individual gas particles.particles.

States of MatterStates of Matter

GasGasLiquid Liquid SolidSolid

States of MatterStates of Matter

KMT of gasesKMT of gases

The particles are so small compared with The particles are so small compared with the distance between then that the volume the distance between then that the volume of the individual particles can assumed to be of the individual particles can assumed to be zero. (demo)zero. (demo)

The particles are in constant motion. The The particles are in constant motion. The collisions of the particles with the wall of the collisions of the particles with the wall of the container are the cause of the pressure container are the cause of the pressure exerted by the gas.exerted by the gas.

KMT of gasesKMT of gases

The particles are assumed to exert no force The particles are assumed to exert no force on one another. (neither attracted nor on one another. (neither attracted nor repelled).repelled).

The average Kinetic energy of a collection of The average Kinetic energy of a collection of gas particles is assumed to be directly gas particles is assumed to be directly proportional to the Kelvin temperature of the proportional to the Kelvin temperature of the gas.gas.

Why Kelvin????Why Kelvin????

Pressure and Volume (Boyles)Pressure and Volume (Boyles)

For a given sample of For a given sample of gas at constant moles gas at constant moles and temperature, and temperature, pressure and volume pressure and volume are inversely related.are inversely related.

With KMT, a decrease With KMT, a decrease in volume increases in volume increases the number of the number of collisions increasing collisions increasing the pressure.the pressure.

Pressure and TemperaturePressure and Temperature For an Ideal gas pressure is directly related to For an Ideal gas pressure is directly related to

temperature.temperature. In KMT, An increase in temperature increases In KMT, An increase in temperature increases

the speed of the particles allowing the the speed of the particles allowing the particles to hit the wall with greater force and particles to hit the wall with greater force and greater frequency.greater frequency.

Volume and TemperatureVolume and Temperature The ideal Gas at a The ideal Gas at a

constant pressure, the constant pressure, the volume is directly volume is directly proportional to proportional to temperature.temperature.

In KMT, as the In KMT, as the temperature increases, temperature increases, the speed and force of the speed and force of the particles increases. the particles increases. The only way to keep The only way to keep pressure constant is to pressure constant is to increase the volume.increase the volume.

Volume and the number of molesVolume and the number of moles Ideal gas predicts the volume of a Ideal gas predicts the volume of a

gas at constant temperature and gas at constant temperature and pressure depends directly on the pressure depends directly on the number of gas particles present.number of gas particles present.

KMT, points out that the number of KMT, points out that the number of collisions is the pressure and if collisions is the pressure and if there is an increase in the number there is an increase in the number of particles that increases the of particles that increases the number of collisions and pressure. number of collisions and pressure. To keep the pressure constant the To keep the pressure constant the volume must increase.volume must increase.

The Meaning of TemperatureThe Meaning of Temperature

The Kelvin scale indicates the The Kelvin scale indicates the average Kinetic energy of gas average Kinetic energy of gas particles. WHY average?particles. WHY average?

The exact relationship is The exact relationship is PV/n=RT=2/3(KE)PV/n=RT=2/3(KE)aveave

Or (KE)Or (KE)aveave=3/2RT=3/2RT

Average Kinetic energyAverage Kinetic energy

Root Mean SquareRoot Mean Square

The average velocity of gas particles is The average velocity of gas particles is special. special.

The symbol uThe symbol u2(with a line over it)2(with a line over it) is the average is the average

squares of the particle velocities.squares of the particle velocities. The square root of the number is the The square root of the number is the

Root Mean Square velocity.Root Mean Square velocity. uurmsrms

So what do we use RMS for?So what do we use RMS for?

RMS is used to find RMS is used to find the velocity of gas the velocity of gas particles based on particles based on their mass.their mass.

The units for R in this The units for R in this case are:case are:

8.3145J/K mol8.3145J/K mol Take home: speed is Take home: speed is

determined by both determined by both Temperature and Temperature and Mass of particleMass of particle

urms = 3RT/M

Average speed of certain gas Average speed of certain gas molecules at the same temperaturemolecules at the same temperature

Effusion and DiffusionEffusion and Diffusion

Effusion:Effusion: The passage of a gas The passage of a gas

through a tiny orifice.through a tiny orifice.

Diffusion:Diffusion: The rate at which a The rate at which a

gas moves from area gas moves from area of high concentration of high concentration to low concentrationto low concentration

Demo!Demo!

Graham’s law of effusionGraham’s law of effusion Larger molecules Larger molecules

will migrate slower will migrate slower than a smaller than a smaller molecule under a molecule under a constant constant temperature.temperature.

This is in direct This is in direct violation of the violation of the KMT.KMT.

REAL GASESREAL GASES

Graham’s Law and DiffusionGraham’s Law and Diffusion

In diffusion, one may In diffusion, one may expect the gases to expect the gases to act similarly to act similarly to effusion.effusion.

NHNH33(g)+HCl(g)(g)+HCl(g)NHNH44Cl(s)Cl(s)

Plug into Graham’s Plug into Graham’s Law and find the Law and find the relative rates of relative rates of effusion to be 1.5effusion to be 1.5

The actual ratio is less.The actual ratio is less.

Distance NHDistance NH33 = =uurmsrms NH NH33

Distance HCl uDistance HCl urmsrmsHClHCl

Sq root Sq root MMNH3NH3

MMHClHCl

Sq root Sq root 36.536.5 1717=1.5=1.5

Diffusion of a gas is more Diffusion of a gas is more complicated than its rate.complicated than its rate.