“KMT and the Behavior of Gases” adapted from Stephen L. Cotton

““KMT and the KMT and the Behavior of Gases”Behavior of Gases”

adapted fromadapted fromStephen L. CottonStephen L. Cotton

The Nature of GasesThe Nature of Gases

KineticKinetic refers to motion refers to motion kinetic energy kinetic energy – the energy an – the energy an

object has because of its motionobject has because of its motion The The kinetic theorykinetic theory states that the states that the

tiny particles in tiny particles in all forms of matterall forms of matter are in are in constant motionconstant motion!!

KMT – Kinetic Molecular KMT – Kinetic Molecular TheoryTheory

1. All matter is composed of 1. All matter is composed of very tiny particles very tiny particles

2. Particles of matter are 2. Particles of matter are continually movingcontinually moving

3. The collisions of these 3. The collisions of these particles are “elastic” (no particles are “elastic” (no loss of energy)loss of energy)

The Nature of GasesThe Nature of Gases Three basic assumptionsThree basic assumptions of the kinetic of the kinetic

theory as it applies to gases:theory as it applies to gases:

#1#1. The particles in a gas are . The particles in a gas are considered to be small, hard spheres considered to be small, hard spheres with insignificant volumewith insignificant volume#2. The motion of the particles in a gas #2. The motion of the particles in a gas are rapid, constant and randomare rapid, constant and random#3. All collisions between particles in a #3. All collisions between particles in a gas are perfectly elastic.gas are perfectly elastic.

- Page 385 Top

The Nature of Gases (no The Nature of Gases (no volume or shape)volume or shape)

Gas PressureGas Pressure –the force exerted by –the force exerted by a gas per unit surface area of an a gas per unit surface area of an objectobject The result of simultaneous collisions The result of simultaneous collisions

of billions of rapidly moving particles.of billions of rapidly moving particles. No particles present? Then there No particles present? Then there

cannot be any collisions, and thus no cannot be any collisions, and thus no pressure – called a pressure – called a vacuumvacuum


Atmospheric pressureAtmospheric pressure results from results from the collisions of air molecules with the collisions of air molecules with objectsobjects Air exerts pressure on earth because Air exerts pressure on earth because

gravity holds the particles in the air gravity holds the particles in the air from Earth’s atmosphere.from Earth’s atmosphere.

BarometerBarometer is the measuring device is the measuring device for atmospheric pressure, which is for atmospheric pressure, which is dependent upon weather & altitudedependent upon weather & altitude

Measuring PressureMeasuring Pressure

The first device for measuring atmosphericpressure was developed by Evangelista Torricelli during the 17th century.

The device was called a “barometer”

Baro = weight Meter = measure Torricelli

An Early An Early BarometerBarometer

760 mm Hg = 101.3 kPa = 1 atmosphere


For gases, it is important to relate For gases, it is important to relate measured values to standardsmeasured values to standards Standard values are defined as a Standard values are defined as a

temperature of 0temperature of 0 o oC and a pressure of C and a pressure of 101.3 kPa, or 1 atm101.3 kPa, or 1 atm

This is called This is called Standard Standard Temperature and PressureTemperature and Pressure, or , or STPSTP


Absolute zeroAbsolute zero (0 K, or –273 (0 K, or –273 ooC) is the C) is the temperature at which the motion of temperature at which the motion of particles particles theoretically ceasestheoretically ceases

Kelvin = °C + 273Kelvin = °C + 273 °C = Kelvin – 273 °C = Kelvin – 273 °C = (°F – 32) x .555°C = (°F – 32) x .555


The Kelvin temperature scale The Kelvin temperature scale reflects a reflects a direct relationshipdirect relationship between temperature and average between temperature and average kinetic energykinetic energyParticles of He gas at 200 K have Particles of He gas at 200 K have

twice the average kinetic energytwice the average kinetic energy as particles of He gas at 100 Kas particles of He gas at 100 K

The Nature of LiquidsThe Nature of Liquids

Liquid particlesLiquid particles are also in motion. are also in motion. a phase of a substance that has a phase of a substance that has

a definite volume but no definite a definite volume but no definite shapeshape


vaporizationvaporization – conversion of a liquid to a gas by adding heat

evaporationevaporation – conversion of a liquid to a gas at room temperature


Evaporation of a liquid in a closed Evaporation of a liquid in a closed container is somewhat differentcontainer is somewhat different vapor pressurevapor pressure – a measure of the a measure of the

force exerted by a gas above a liquid force exerted by a gas above a liquid An increase in the temperature of a

liquid increases the vapor pressure. A decrease in the temperature decreases the vapor pressure.


The The boiling pointboiling point (bp) the (bp) the temperature at which the vapor temperature at which the vapor pressure of a liquid is just equal to pressure of a liquid is just equal to the external pressure.the external pressure.

Section 13.2Section 13.2The Nature of LiquidsThe Nature of Liquids

Normal bp of water = 100 Normal bp of water = 100 ooCC However, in Denver = 95 However, in Denver = 95 ooC, since C, since

Denver is 1600 m above sea level and Denver is 1600 m above sea level and average atmospheric pressure is about average atmospheric pressure is about 85.3 kPa (Recipe adjustments?)85.3 kPa (Recipe adjustments?)

In In pressure cookerspressure cookers, which reduce , which reduce cooking time, water boils cooking time, water boils aboveabove 100 100 ooC C due to the increased pressuredue to the increased pressure

- Page 394

Not Boiling Normal Boiling Point @ 101.3 kPa = 100 oC

Boiling, but @ 34 kPa = 70 oC

- Page 394

Questions:

a. 60 oC b. about 20 kPa c. about 30 kPa

The Behavior of The Behavior of GasesGases

Properties of GasesProperties of Gases

Compressibility:Compressibility: a measure of how a measure of how much the volume of matter much the volume of matter decreases under pressure. decreases under pressure.

Gases are easily compressed Gases are easily compressed because of the space between the because of the space between the particles. (remember KMT)particles. (remember KMT)

3 Factors Affecting Gas 3 Factors Affecting Gas PressurePressure

1. Amount of Gas:1. Amount of Gas: by adding gas by adding gas you increase the particles and you increase the particles and number of collisions so the pressure number of collisions so the pressure increases, and vise versa.increases, and vise versa.

2. Volume of Gas:2. Volume of Gas: by increasing by increasing the volume you increase the space the volume you increase the space that the particles can move in. Thus that the particles can move in. Thus the pressure decreases as the number the pressure decreases as the number of collisions decreases, and vice of collisions decreases, and vice versa.versa.

3. Temperature:3. Temperature: as the as the temperature increases the kinetic temperature increases the kinetic energy of the particles increases and energy of the particles increases and they hit the walls of the container and they hit the walls of the container and each other with more energy, each other with more energy, increasing the pressure, and vice increasing the pressure, and vice versa.versa.

Warm temp. Hot temp. Cold temp.

The Gas LawsThe Gas Laws Boyle’s Law:Boyle’s Law: If the temperature is If the temperature is

constant, as the pressure of a gas constant, as the pressure of a gas increases, the volume decreases.increases, the volume decreases.

P1V1 = P2V2

Pressure and VolumePressure and VolumeExperimentExperiment PressurePressure Volume P x VVolume P x V

(atm) (L) (atm x L)(atm) (L) (atm x L)

11 8.0 8.0 2.0 2.0 16 16

22 4.04.0 4.04.0 __________

33 2.02.0 8.08.0 __________

44 1.01.0 1616 __________

Boyle's Law P x V = k (constant) when Boyle's Law P x V = k (constant) when

T remains constantT remains constant

P1V1= 8.0 atm x 2.0 L P1V1= 8.0 atm x 2.0 L = 16 atm L= 16 atm L

P2V2= 4.0 atm x 4.0 L P2V2= 4.0 atm x 4.0 L = 16 atm L= 16 atm L

P1V1 = P2V2 = kP1V1 = P2V2 = k

Use this equation to calculate how a volume changes when pressure changes, or how pressure Use this equation to calculate how a volume changes when pressure changes, or how pressure changes when volume changes.changes when volume changes.

new vol.new vol. old vol. x Pfactor old vol. x Pfactor new P old P x Vfactor new P old P x Vfactor

V2 = V1 x V2 = V1 x P1 P1 P2 = P1 x P2 = P1 x V1V1

P2P2 V2 V2

P and V ChangesP and V Changes

P1

P2

V1 V2

Boyle's LawBoyle's Law

The pressure of a gas is inversely related to The pressure of a gas is inversely related to the volume when T does not changethe volume when T does not change

Then the PV product remains constantThen the PV product remains constant

PP11VV11 = P = P22VV22

PP11VV11= 8.0 atm x 2.0 L = 8.0 atm x 2.0 L = 16 atm L= 16 atm L

PP22VV22= 4.0 atm x 4.0 L = 4.0 atm x 4.0 L = 16 atm L= 16 atm L

PV CalculationPV Calculation

Prepare a data table Prepare a data table

DATA TABLEDATA TABLE

Initial conditionsInitial conditions Final Final conditionsconditions

PP11 = 50 mm Hg= 50 mm Hg PP22 = 200 mm = 200 mm

HgHg

VV11 = 1.6 L= 1.6 L VV22 = ?= ??

1)1) If I have 5.6 liters of gas in a If I have 5.6 liters of gas in a piston at a pressure of 1.5 atm piston at a pressure of 1.5 atm and compress the gas until its and compress the gas until its volume is 4.8 L, what will the volume is 4.8 L, what will the new pressure inside the piston new pressure inside the piston be?be?

2)2) I have added 15 L of air to a I have added 15 L of air to a balloon at sea level (1.0 atm). If balloon at sea level (1.0 atm). If I take the balloon with me to I take the balloon with me to Denver, where the air pressure Denver, where the air pressure is 0.85 atm, what will the new is 0.85 atm, what will the new volume of the balloon be?volume of the balloon be?

3)3) I’ve got a car with an I’ve got a car with an internal volume of 12,000 L. If I internal volume of 12,000 L. If I drive my car into the river and it drive my car into the river and it implodes, what will be the implodes, what will be the volume of the gas when the volume of the gas when the pressure goes from 1.0 atm to pressure goes from 1.0 atm to 1.4 atm?1.4 atm?

Charles Law:Charles Law: As the temperature of As the temperature of an enclosed gas increases, the volume an enclosed gas increases, the volume increases, if the pressure is constant.increases, if the pressure is constant.

When you use temperature in ANY When you use temperature in ANY gas law you must change the gas law you must change the temperature into Kelvintemperature into Kelvin

Kelvin = ºC + 273Kelvin = ºC + 273

Find the volume of 250 mL of Find the volume of 250 mL of a gas at 25 °C if the a gas at 25 °C if the temperature is dropped to 10 temperature is dropped to 10 °C.°C.

Gay-Lussac’s Law:Gay-Lussac’s Law: As the As the temperature of an enclosed gas temperature of an enclosed gas increases, the pressure increases, if increases, the pressure increases, if the volume is constant.the volume is constant.

Calculate the final pressure Calculate the final pressure inside a scuba tank after it inside a scuba tank after it cools from 1.00 x 10cools from 1.00 x 1033 °C to °C to 25.0 °C. The initial pressure 25.0 °C. The initial pressure in the tank is 130.0 atm.in the tank is 130.0 atm.

The Combined Gas Law:The Combined Gas Law: all three all three gas laws combined.gas laws combined.

Convert 250 mL of a gas at Convert 250 mL of a gas at 50 °C and 650 mm Hg 50 °C and 650 mm Hg to STPto STP

A gas starts at 1 atm, 30 °C A gas starts at 1 atm, 30 °C and 1 L. What is the final and 1 L. What is the final temperature if the final temperature if the final amounts are 5 atm and 0.5 L.amounts are 5 atm and 0.5 L.

Ideal Gas Law:Ideal Gas Law: includes the number includes the number of particles (n= moles) and the ideal of particles (n= moles) and the ideal gas constant (related to pressure).gas constant (related to pressure).

1 mole = 6.02 x 101 mole = 6.02 x 1023 23

particlesparticles

R = (22.4 L x 1 atm/1 mol R = (22.4 L x 1 atm/1 mol x 273 K)x 273 K) == 0.0821 L x 0.0821 L x atm/mol x Katm/mol x K

How many moles of a gas How many moles of a gas will you have if 1 liter of will you have if 1 liter of gas is collected 28.0 °C gas is collected 28.0 °C and 1.7 atmospheres and 1.7 atmospheres pressure.pressure.

R = (22.4 L x 760 mmHg/1 R = (22.4 L x 760 mmHg/1 mol x 273 K) = mol x 273 K) = 62.4 L62.4 L x x mmHg/mol x KmmHg/mol x K

R = (22.4 L x 1 atm/1 mol x R = (22.4 L x 1 atm/1 mol x 273 K) = 273 K) = 0.08210.0821 L x L x atm/mol x Katm/mol x K

R = (22.4 L x 101.3 kPa/1 R = (22.4 L x 101.3 kPa/1 mol x 273 K) = mol x 273 K) = 8.318.31 L x L x kPa/mol x KkPa/mol x K

Documents

“KMT and the Behavior of Gases” adapted from Stephen L. Cotton