The Nature of GasesThe Nature of Gases

Prentice-Hall Chapter 13.1Prentice-Hall Chapter 13.1

Dr. YagerDr. Yager

ObjectivesObjectives

DescribeDescribe assumptions of kinetic theory as it assumptions of kinetic theory as it applies to gasesapplies to gases

InterpretInterpret gas pressure in terms of kinetic gas pressure in terms of kinetic theorytheory

DefineDefine the relationship between Kelvin the relationship between Kelvin temperature and average kinetic energytemperature and average kinetic energy

Kinetic EnergyKinetic Energy

Things that are moving have kinetic energy Things that are moving have kinetic energy K.E. = ½mvK.E. = ½mv22 ; m = mass, v = velocity ; m = mass, v = velocity

Example: Example:

A 50 kg student is running at 20 m/sec.A 50 kg student is running at 20 m/sec.

The student’s kinetic energy is:The student’s kinetic energy is:

K.E. = ½(50 kg)(20 m/sec)K.E. = ½(50 kg)(20 m/sec)22 = 10,000 joules = 10,000 joules

This is all done in the MKS system of units. This is all done in the MKS system of units.

Kinetic Energy of a ParticleKinetic Energy of a Particle

Theory developed by Boltzmann and MaxwellTheory developed by Boltzmann and Maxwell The energy of a particle and the temperature are The energy of a particle and the temperature are

related:related:

Kelvin in eTemperatur T

Constant Boltzmann k

kT2

3mv

2

1K.E. 2

Some Average Velocities at 20Some Average Velocities at 20ooCC

H H 7078 km/hr7078 km/hr He He 5004 km/hr5004 km/hr HH22 1890 km/hr 1890 km/hr

OO22 1771 km/hr 1771 km/hr

COCO22 1508 km/hr 1508 km/hr

OO22 molecule traveling at 1771 km/hr will travel molecule traveling at 1771 km/hr will travel

from Washington D.C. to Mexico City in 1.9 hrs. from Washington D.C. to Mexico City in 1.9 hrs.

The only way to fly!!!The only way to fly!!!

Gas consists of tiny hard spherical particles Gas consists of tiny hard spherical particles with insignificant volume.with insignificant volume.

Gas particles are in constant motion.Gas particles are in constant motion.

Gas particles are very far apart.Gas particles are very far apart.

There are no attractive or repulsive forces There are no attractive or repulsive forces between particles. between particles.

The motion of one particle is independent of The motion of one particle is independent of all other particles.all other particles.

Kinetic Theory of GasesKinetic Theory of Gases

Particles in a gas are in rapid, Particles in a gas are in rapid, constant motion.constant motion.

13.1

Kinetic Theory of GasesKinetic Theory of Gases The motion of the particles are The motion of the particles are

• rapidrapid• constantconstant• randomrandom

The motion only changes direction after a The motion only changes direction after a collision when particlescollision when particles• hit each otherhit each other• hit the wall of a containerhit the wall of a container

Gas particles travel in straight-line paths.

The gas fills the container.

All collisions between particles in a gas are All collisions between particles in a gas are perfectly elastic.perfectly elastic.

Elastic means that no energy is lost after each Elastic means that no energy is lost after each collision. collision.

Elastic is like hard metal balls hitting each other.Elastic is like hard metal balls hitting each other.

Kinetic Theory of GasesKinetic Theory of Gases

Gas PressureGas Pressure

Gas pressureGas pressure is the result of simultaneous is the result of simultaneous collisions of billions of rapidly moving particles in a collisions of billions of rapidly moving particles in a gas with an object. gas with an object.

The lack of particles is also known as a The lack of particles is also known as a vacuumvacuum..

The gas pressure you experience every day is The gas pressure you experience every day is atmospheric pressureatmospheric pressure, caused by the earth’s , caused by the earth’s gravity acting on the air particles.gravity acting on the air particles.

Atmospheric pressure decreases with altitude.Atmospheric pressure decreases with altitude.

A barometer is a device that is used to measure atmospheric pressure.

The SI unit of pressure is the The SI unit of pressure is the pascal (Pa)pascal (Pa)..

One standard One standard atmosphere (atm)atmosphere (atm) is the is the pressure required to support 760 mm of pressure required to support 760 mm of mercury in a mercury barometer at 25°C.mercury in a mercury barometer at 25°C.

Gas Pressure UnitsGas Pressure Units

A pressure gauge records a pressure of 450 kPa. A pressure gauge records a pressure of 450 kPa. What is this measurement expressed in What is this measurement expressed in atmospheres and millimeters of mercury?atmospheres and millimeters of mercury?

4.4atm101.3kPa

atm 1 x 450kPa

Hg mm 3.4x10Hg mm 3400101.3kPa

Hg mm 760 x 450kPa 3

Your TurnYour Turn

What pressure in kPa and atm does a gas exert What pressure in kPa and atm does a gas exert at 385 mm Hg ?at 385 mm Hg ?

51.3kPaHg mm 760

101.3kPa x Hg mm 385

0.507atmHg mm 760

atm 1 x Hg mm 385

Kinetic Energy and TemperatureKinetic Energy and Temperature

Kinetic energy is proportional to temperature:Kinetic energy is proportional to temperature:

The particles in any collection of atoms or The particles in any collection of atoms or molecules at a given temperature have a wide molecules at a given temperature have a wide range of kinetic energies. Most of the particles range of kinetic energies. Most of the particles have kinetic energies somewhere in the middle have kinetic energies somewhere in the middle of this range.of this range.

kT2

3K.E.

Absolute ZeroAbsolute Zero

Lowest theoretical temperature: Lowest theoretical temperature:

-273.15-273.1500C or 0 K C or 0 K

This is where all particle motion ceases to exist!This is where all particle motion ceases to exist!

Lowest temperature ever reached is 0.5 Lowest temperature ever reached is 0.5 nanokelvin or 0.0000000005Knanokelvin or 0.0000000005K

In this vacuum chamber, scientists cooled sodium vapor to nearly absolute zero.

1. According to the kinetic theory, the 1. According to the kinetic theory, the particles in a gas particles in a gas

a.a. are attracted to each other.are attracted to each other.

b.b. are in constant random motion.are in constant random motion.

c.c. have the same kinetic energy.have the same kinetic energy.

d.d. have a significant volume.have a significant volume.

1. According to the kinetic theory, the 1. According to the kinetic theory, the particles in a gas particles in a gas

a.a. are attracted to each other.are attracted to each other.

b.b. are in constant random motion.are in constant random motion.

c.c. have the same kinetic energy.have the same kinetic energy.

d.d. have a significant volume.have a significant volume.

2. The pressure a gas exerts on another 2. The pressure a gas exerts on another object is caused by object is caused by

a.a. the physical size of the gas particles.the physical size of the gas particles.

b.b. collisions between gas particles and the collisions between gas particles and the

object.object.

c.c. collisions between gas particles.collisions between gas particles.

d.d. the chemical composition of the gas.the chemical composition of the gas.

2. The pressure a gas exerts on another 2. The pressure a gas exerts on another object is caused by object is caused by

a.a. the physical size of the gas particles.the physical size of the gas particles.

b.b. collisions between gas particles and the collisions between gas particles and the

object.object.

c.c. collisions between gas particles.collisions between gas particles.

d.d. the chemical composition of the gas.the chemical composition of the gas.

3. The average kinetic energy of the 3. The average kinetic energy of the particles in a substance is directly particles in a substance is directly proportional to theproportional to the

a.a. Fahrenheit temperature.Fahrenheit temperature.

b.b. Kelvin temperature.Kelvin temperature.

c.c. molar mass of the substance.molar mass of the substance.

d.d. Celsius temperature.Celsius temperature.

3. The average kinetic energy of the 3. The average kinetic energy of the particles in a substance is directly particles in a substance is directly proportional to theproportional to the

a.a. Fahrenheit temperature.Fahrenheit temperature.

b.b. Kelvin temperature.Kelvin temperature.

c.c. molar mass of the substance.molar mass of the substance.

d.d. Celsius temperature.Celsius temperature.