Active Active ChemistryChemistry

l Kinetic Kinetic MoleculaMolecular Theory r Theory and the and the Gas Gas LawsLaws

Phases of MatterPhases of MatterThere are four phases of matter:There are four phases of matter:

1. Solid1. Solid

2. Liquid2. Liquid

3. Gas3. Gas

4. Plasma4. Plasma

The state of matter depends on the The state of matter depends on the motion of the molecules that make it up.motion of the molecules that make it up.

SolidsSolids

Solids are objects that have definite shapes and volumes. Solids are objects that have definite shapes and volumes. The atoms or molecules are tightly packed, so the solid The atoms or molecules are tightly packed, so the solid keeps its shape. The arrangement of particles in a solid keeps its shape. The arrangement of particles in a solid are in a regular, repeating pattern called a crystal.are in a regular, repeating pattern called a crystal.

Microscopic picture of a solid.

LiquidsLiquids

The particles in a liquid are close together, but are The particles in a liquid are close together, but are able to move around more freely than in a solid. able to move around more freely than in a solid. Liquids have no definite shape and take on the Liquids have no definite shape and take on the shape of the container that they are in.shape of the container that they are in.

Microscopic picture of a liquid.

GasesGases

A gas does not have a definite shape or volume. A gas does not have a definite shape or volume. The particles of a gas have much more energy The particles of a gas have much more energy than either solids or liquids and can move than either solids or liquids and can move around freely.around freely.

Microscopic picture of a gas.

PlasmaPlasmaPlasma is a gas-like mixture of positively and Plasma is a gas-like mixture of positively and

negatively charged particles. It is found in stars, negatively charged particles. It is found in stars, such as the sun, and in fluorescent lighting. such as the sun, and in fluorescent lighting. Plasma occurs when temperatures are high Plasma occurs when temperatures are high enough to cause particles to collide violently and enough to cause particles to collide violently and be ripped apart into charged particles.be ripped apart into charged particles.

Postulates of KMTPostulates of KMT

A gas consists of a collection of small particles A gas consists of a collection of small particles traveling in straight-line motion. traveling in straight-line motion. The molecules in a gas occupy no volume (that is, The molecules in a gas occupy no volume (that is, they are points spread far apart).they are points spread far apart).Collisions between molecules are perfectly elastic Collisions between molecules are perfectly elastic (that is, no energy is gained or lost during the (that is, no energy is gained or lost during the collision). collision). There are no attractive or repulsive forces between There are no attractive or repulsive forces between the molecules. the molecules. The average kinetic energy of a molecule is The average kinetic energy of a molecule is proportional to the Temperature.proportional to the Temperature.Molecules can collide with each other and with the Molecules can collide with each other and with the walls of the container. Collisions with the walls walls of the container. Collisions with the walls account for the pressure of the gas.account for the pressure of the gas.

At the same temperature, lighter gases At the same temperature, lighter gases move faster than heavier gases.move faster than heavier gases.

TemperatureTemperature

Temperature is a measure of the amount of the Temperature is a measure of the amount of the average kinetic energy of the particles in matter. average kinetic energy of the particles in matter. The more kinetic energy the particles have, the The more kinetic energy the particles have, the higher the temperature.higher the temperature. The temperature of The temperature of particles are usually recorded in one of three particles are usually recorded in one of three ways:ways:

1. Fahrenheit (1. Fahrenheit (ºF)ºF)

2. Celsius (2. Celsius (ºC)ºC)

3. Kelvin (K)3. Kelvin (K)Do you remember which is the standard unit????Do you remember which is the standard unit????

FahrenheitFahrenheit

Developed by Daniel Gabriel Fahrenheit, who Developed by Daniel Gabriel Fahrenheit, who is best known for inventing the alcohol is best known for inventing the alcohol thermometer and mercury thermometer in the thermometer and mercury thermometer in the early 1700’s. It is based on 32early 1700’s. It is based on 32º for the º for the freezing point of water and 212º for the freezing point of water and 212º for the boiling point of water. The interval between boiling point of water. The interval between the freezing and boiling points are divided the freezing and boiling points are divided into 180 parts. into 180 parts.

The conversion to Celsius is: The conversion to Celsius is:

ººF = (9/5 F = (9/5 ººC) + 32C) + 32

CelsiusCelsius

Scale developed by Anders Celsius in the early to Scale developed by Anders Celsius in the early to mid-1700’s, working from the invention of mid-1700’s, working from the invention of Fahrenheit's thermometers. The Celsius scale Fahrenheit's thermometers. The Celsius scale is based on 0is based on 0º for the freezing point of water º for the freezing point of water and 100º as the boiling point. The interval and 100º as the boiling point. The interval between the freezing and boiling points are between the freezing and boiling points are divided into 100 parts.divided into 100 parts.

The conversion to Fahrenheit is: ºC= (5/9)(ºF-32) The conversion to Fahrenheit is: ºC= (5/9)(ºF-32)

The conversion to Kelvin is: K=ºC +273The conversion to Kelvin is: K=ºC +273

KelvinKelvinDeveloped by William Thompson Kelvin in 1848, Developed by William Thompson Kelvin in 1848,

KelvinKelvin isis a temperature scale having an absolute a temperature scale having an absolute zero below which temperatures do not exist. At 0K, zero below which temperatures do not exist. At 0K, all molecules cease any type of motion (as in the all molecules cease any type of motion (as in the temperature of outer space). It corresponds to a temperature of outer space). It corresponds to a temperature of -273°C. The Kelvin degree is the temperature of -273°C. The Kelvin degree is the same size as the Celsius degree, so the freezing same size as the Celsius degree, so the freezing point of water is at 273K and the boiling point is at point of water is at 273K and the boiling point is at 373K.373K.

The Behavior of GasesThe Behavior of Gases

The behavior of gases can be explained by the The behavior of gases can be explained by the way their particles interact with each other and way their particles interact with each other and the environment around them. the environment around them.

The particles are constantly colliding with one The particles are constantly colliding with one another and other objects. Since the molecules another and other objects. Since the molecules have mass, there is a certain amount of have mass, there is a certain amount of pressure being applied. pressure being applied.

As the volume of the gas and/or the temperature As the volume of the gas and/or the temperature of the gas change, so does its behavior.of the gas change, so does its behavior.

Gas LawsGas LawsThe result of a force distributed over an area.The result of a force distributed over an area.

SI unit for pressure = pascal (Pa) = N/mSI unit for pressure = pascal (Pa) = N/m22

(one kilopascal = kPa= 1000 Pa)(one kilopascal = kPa= 1000 Pa)

Factors that Affect Pressure of an Factors that Affect Pressure of an Enclosed GasEnclosed Gas

TemperatureTemperature

VolumeVolume

Number of ParticlesNumber of Particles

TemperatureTemperature

Raising the temperature of a gas Raising the temperature of a gas will increase its pressure if the will increase its pressure if the volume of the gas and the number volume of the gas and the number of particles are constantof particles are constant

VolumeVolume

Reducing the volume of a gas Reducing the volume of a gas increase its pressure if the increase its pressure if the temperature of the gas and the temperature of the gas and the number of particles are constantnumber of particles are constant..

Number of ParticlesNumber of Particles

Increasing the number of particles Increasing the number of particles will increase the pressure of a gas will increase the pressure of a gas if the temperature and the volume if the temperature and the volume are constant.are constant.

General Properties of GasesGeneral Properties of Gases

There is a lot of “free” space There is a lot of “free” space in a gas.in a gas.

Gases can be expanded Gases can be expanded infinitely.infinitely.

Gases fill containers uniformly Gases fill containers uniformly and completely.and completely.

Gases diffuse and mix rapidly.Gases diffuse and mix rapidly.

Real GasesReal Gases

Ideal GasIdeal Gas Real Gas . Real Gas .

No intermolecularNo intermolecular small attractionsmall attraction

attraction betweenattraction between between particlesbetween particles

particlesparticles

Gas particles haveGas particles have Gas particles haveGas particles have

no volumeno volume a volumea volume

This implies:This implies:

If the volume of space occupied is If the volume of space occupied is large and the pressure is low, the large and the pressure is low, the behavior of a gas is very close to that behavior of a gas is very close to that of an ideal gas.of an ideal gas.

We will not deal with gases at We will not deal with gases at conditions that make them non-ideal conditions that make them non-ideal in this class.in this class.

Atmospheric PressureAtmospheric PressureThe pressure the earth’s atmosphere exerts The pressure the earth’s atmosphere exerts due to its weight. due to its weight.

PressurePressure

Pressure of air is measured Pressure of air is measured with a with a BAROMETERBAROMETER

Column height measures Column height measures Pressure of atmospherePressure of atmosphere

1 standard atmosphere (atm) 1 standard atmosphere (atm)

= 760 mm Hg = 101.3 kPa (SI = 760 mm Hg = 101.3 kPa (SI unit is PASCAL) unit is PASCAL)

Measuring Pressure of Measuring Pressure of confined gasconfined gas

Manometer- Instrument used Manometer- Instrument used to measure gas pressureto measure gas pressure

Filled with MercuryFilled with Mercury

Pressure ConversionsPressure Conversions

1.00 atm = 101.3 kPa1.00 atm = 101.3 kPa

1.00 atm = 760. mmHg1.00 atm = 760. mmHg

101.3kPa = 760. mmHg101.3kPa = 760. mmHg

Pressure ConversionsPressure Conversions

A. What is 475 mm Hg expressed in atm?A. What is 475 mm Hg expressed in atm?

1.00 atm1.00 atm

760 mm Hg760 mm Hg

B. The pressure of a tire is measured as 29.4 kPa.B. The pressure of a tire is measured as 29.4 kPa.

What is this pressure in mm Hg?What is this pressure in mm Hg?

760 mm Hg 760 mm Hg

101.3kPa101.3kPa = 221 mm Hg

= 0.625 atm475 mm Hg x

29.4 kPa x

Properties of GasesProperties of GasesGas properties can be modeled Gas properties can be modeled

using math. Model depends on—using math. Model depends on—V = volume of the gas (ml, L, cmV = volume of the gas (ml, L, cm33, , etc)etc)T = temperature (K)T = temperature (K)–ALL temperatures MUST be ALL temperatures MUST be

in Kelvin to calculate other in Kelvin to calculate other variables!!! No Exceptions!variables!!! No Exceptions!

n = amount (moles)n = amount (moles)P = pressure (atm, mmHg, kPa)P = pressure (atm, mmHg, kPa)

Standard ConditionsStandard ConditionsStandard Temperature: Standard Temperature: 273 K273 K

Standard Pressure:Standard Pressure:

1.00 atm 1.00 atm (atmosphere)(atmosphere)

760 mm Hg760 mm Hg

760 torr760 torr

101.3 kPa (kilopascal)101.3 kPa (kilopascal)

Referred to asReferred to as STP- STP- SStandard tandard TTemperature emperature

and and PPressureressure

Click here for Demonstration

Pressure and Volume

Pressure and VolumePressure and Volume

When temperature and the # of particles are When temperature and the # of particles are kept constant in a closed container:kept constant in a closed container:

As Volume decreases, PressureAs Volume decreases, Pressure

oror

As Volume increases, Pressure As Volume increases, Pressure

This is an relationshipThis is an relationship

increases

inverse

decrease

Boyle’s LawBoyle’s LawP P αα 1/V 1/V

This means Pressure and This means Pressure and

Volume are INVERSELY Volume are INVERSELY PROPORTIONAL if moles PROPORTIONAL if moles

and temperature are constant and temperature are constant

(do not change). For example, (do not change). For example,

P goes up as V goes down.P goes up as V goes down.

PP1 1 • V• V11 = = PP2 2 • V• V22

Robert Boyle Robert Boyle (1627-1691)(1627-1691)

A Graph of Boyle’s LawA Graph of Boyle’s Law

Boyle’s LawBoyle’s LawIf the gas is compressed to half the volume it If the gas is compressed to half the volume it had, twice as many molecules are present in had, twice as many molecules are present in any given volume.any given volume.

Twice as many impacts per second on the walls Twice as many impacts per second on the walls of the container results in doubling the of the container results in doubling the pressure.pressure.

Boyle’s Law ExampleBoyle’s Law ExampleA balloon filled with Helium has a volume of A balloon filled with Helium has a volume of 457ml at standard atmospheric pressure. After 457ml at standard atmospheric pressure. After the balloon is released, it reaches an altitude of the balloon is released, it reaches an altitude of 6.3km where the pressure is only 65.5kPa. 6.3km where the pressure is only 65.5kPa. What is the volume of the balloon at this What is the volume of the balloon at this altitude?altitude?

PP11 • V • V11 = P = P22 • V • V22

Temperature Scales and Interconversions

Kelvin ( K ) - The “Absolute temperature scale” begins at absolute zero and only has positive values.

Celsius ( oC ) - The temperature scale used by science, formally called centigrade and most commonly used scale around the world, water freezes at 0oC, and boils at 100oC.

Temperature ConversionsTemperature Conversions

FormulasFormulas

K = 0C + 2730C = K - 273

Temperature Conversions Temperature Conversions

Ex. 1: The boiling point of Liquid Nitrogen is –1950C, what is the temperature in Kelvin?

Formula: K = 0C + 273

K = -195 + 273 = 78.0 K (3 Sig Dig)

Temperature ConversionsTemperature Conversions

Ex. 2 The normal body temperature is 310. K, what is it in Celsius?

Formula: 0C = K - 273

0C = 310. – 273 = 37.0 0C

Temperature and Volume

Click here for Demonstration

Volume and TemperatureVolume and Temperature

Pressure and the # of particles are constant thenPressure and the # of particles are constant then

As Temperature As Temperature decreasesdecreases, Volume _________ , Volume _________

ororAs Temperature As Temperature increasesincreases, Volume __________, Volume __________

This is a relationshipThis is a relationshipdirect

decreases

increases

Charles’ Law Example Charles’ Law Example A quantity of gas occupies a volume of 506 cmA quantity of gas occupies a volume of 506 cm33 at a temperature of 147at a temperature of 147ooC. Assuming that the C. Assuming that the pressure remains constant, at what pressure remains constant, at what temperature will the volume of the gas be 604 temperature will the volume of the gas be 604 cmcm33??

VV11 = 506cm = 506cm33 VV22= 604cm= 604cm33

TT11 = 147 = 147ooC + 273 =C + 273 = 420K420K TT22= ??= ??

A Graph of Charles’s LawA Graph of Charles’s Law

Charles LawCharles Law

If n (moles) and P are constant, If n (moles) and P are constant,

then V then V αα T T

V and T are directly proportional.V and T are directly proportional.

If one temperature goes up, the volume If one temperature goes up, the volume goes up!goes up!

VV11 VV22

TT11 T T22

=

Jacques Charles Jacques Charles (1746-1823)(1746-1823)

Pressure and TemperaturePressure and Temperature

Volume and the # of particles are constant then:Volume and the # of particles are constant then:

As Temperature As Temperature decreasesdecreases, pressure _______ , pressure _______

oror

As Temperature As Temperature increasesincreases, pressure ________, pressure ________

This is a relationshipThis is a relationship

increase

decrease

direct

Charles’ LawCharles’ LawDoubling the Kelvin temperature of a gas Doubling the Kelvin temperature of a gas makes the gas expand resulting in makes the gas expand resulting in doubling the volume of the gasdoubling the volume of the gas

Gay-Lussac’s LawGay-Lussac’s Law

If n and V are constant, If n and V are constant, then P then P αα T T

P and T are directly proportional.P and T are directly proportional.

If one temperature goes up, the pressure goes up!If one temperature goes up, the pressure goes up!

PP11 PP22

TT11 T T22

=

Guy Lussac’s LawGuy Lussac’s Law

Doubling the Kelvin temperature of a gas Doubling the Kelvin temperature of a gas doubles the average kinetic energy of its doubles the average kinetic energy of its molecules.molecules.

Faster moving molecules strike the wall of Faster moving molecules strike the wall of the container more often and with more the container more often and with more force doubling the Pressure.force doubling the Pressure.

Gas Pressure Volume Temperature Number Law of moles

(P) (V) (T) (n)

Boyles

Charles

Gay-

Lussac

Confusing?Confusing?

Combined Gas LawCombined Gas Law

PP11VV11 P P22VV22

TT11 T T22

All 3 Laws can be found from this one!All 3 Laws can be found from this one!

=

Combined Gas LawCombined Gas Law

PP11VV11 P P22VV22

TT11 T T22

Boyle’s Law – Temperature constantBoyle’s Law – Temperature constant

=

Combined Gas LawCombined Gas Law

PP11VV11 P P22VV22

TT11 T T22

Charles’ Law – Pressure constantCharles’ Law – Pressure constant

=

Combined Gas LawCombined Gas Law

PP11VV11 P P22VV22

TT11 T T22

Gay-Lussac’s Law – Volume constantGay-Lussac’s Law – Volume constant

=

IDEAL GAS LAWIDEAL GAS LAW

Brings together gas Brings together gas properties.properties.

Can be derived from Can be derived from experiment and theory.experiment and theory.

BE SURE YOU KNOW THIS BE SURE YOU KNOW THIS EQUATION!EQUATION!

P V = n R TP V = n R T

The Ideal Gas Law

PV = nRTP = pressure (in atmospheres)V = volume (in Liters)n = number of molesR = Universal Gas Law Constant (.0821 L atm/mol K)T = Temperature (in Kelvins)

Using PV = nRTUsing PV = nRTHow much NHow much N22 is required to fill a small room with a is required to fill a small room with a

volume of 960 cubic feet (27,000 L) to 745 mm Hg at volume of 960 cubic feet (27,000 L) to 745 mm Hg at 25 25 ooC?C?

SolutionSolution

1. Get all data into proper units1. Get all data into proper units

V = 27,000 LV = 27,000 L

T = 25 T = 25 ooC + 273 = 298 KC + 273 = 298 K

P = 745 mm Hg (1 atm/760 mm Hg) P = 745 mm Hg (1 atm/760 mm Hg) = 0.98 atm = 0.98 atm

And we always know R, 0.0821 L atm / mol KAnd we always know R, 0.0821 L atm / mol K

Using PV = nRTUsing PV = nRTHow much NHow much N22 is req’d to fill a small room with a volume is req’d to fill a small room with a volume

of 960 cubic feet (27,000 L) to P = 745 mm Hg at 25 of 960 cubic feet (27,000 L) to P = 745 mm Hg at 25 ooC?C?

SolutionSolution

2. Now plug in those values and solve for the unknown.2. Now plug in those values and solve for the unknown.

PV = nRTPV = nRT

n = (0.98 atm)(2.7 x 10 4 L)

(0.0821 L • atm/K • mol)(298 K)n =

(0.98 atm)(2.7 x 10 4 L)

(0.0821 L • atm/K • mol)(298 K)

n = 1.1 x 10n = 1.1 x 1033 mol (or about 30 kg of gas) mol (or about 30 kg of gas)

RT RTRT RT

Using Ideal Gas Using Ideal Gas LawLawExample

What is the volume of 2.3 moles of hydrogen gas at a pressure of 1.2 atm and temperature of 20oC?

Ans: V = nRT/P

V = (2.3 mol)(.0821 L atm/mol K)(293K) 1.2 atm= 46.0 L

Deviations from Deviations from Ideal Gas LawIdeal Gas Law

Real molecules have volume.Real molecules have volume.The ideal gas consumes the entire The ideal gas consumes the entire

amount of available volume. It amount of available volume. It does not account for the volume does not account for the volume of the molecules themselves.of the molecules themselves.There are intermolecular forces.There are intermolecular forces.

An ideal gas assumes there are no An ideal gas assumes there are no attractions between molecules. attractions between molecules. Attractions slow down the Attractions slow down the molecules and reduce the molecules and reduce the amount of collisions.amount of collisions.– Otherwise a gas could not Otherwise a gas could not

condense to become a liquid.condense to become a liquid.

Dalton’s Law of Partial PressuresDalton’s Law of Partial Pressures

The % of gases in air Partial pressure (STP) The % of gases in air Partial pressure (STP)

78.08% N78.08% N22 593.4 mm Hg593.4 mm Hg

20.95% O20.95% O22 159.2 mm Hg159.2 mm Hg

0.94% Ar0.94% Ar 7.1 mm Hg 7.1 mm Hg

0.03% CO0.03% CO22 0.2 mm Hg0.2 mm Hg

PPAIRAIR = P = PN N + P + POO + P + PAr Ar + P + PCO CO = 760 mm Hg= 760 mm Hg 2 2 22 2 2

Total Pressure =Total Pressure = 760 mm Hg760 mm Hg

Dalton’s Law of Partial Dalton’s Law of Partial PressuresPressures

What is the total pressure in the flask?What is the total pressure in the flask?

PPtotaltotal in gas mixture = P in gas mixture = PAA + P + PBB + ... + ...

Therefore, Therefore,

PPtotaltotal = P = PHH22OO + P + POO22 = 0.48 atm = 0.48 atm

Dalton’s Law: total P is sum of PARTIAL pressures. Dalton’s Law: total P is sum of PARTIAL pressures.

2 H2 H22OO2 2 (l) ---> 2 H(l) ---> 2 H22O (g) + OO (g) + O2 2 (g)(g)

0.32 atm 0.16 atm0.32 atm 0.16 atm

Dalton’s Dalton’s LawLaw

John DaltonJohn Dalton1766-18441766-1844

Health NoteHealth NoteWhen a scuba diver is several When a scuba diver is several

hundred feet under water, the hundred feet under water, the high pressures cause Nhigh pressures cause N2 2 from the from the

tank air to dissolve in the blood. tank air to dissolve in the blood. If the diver rises too fast, the If the diver rises too fast, the dissolved Ndissolved N22 will form bubbles in will form bubbles in

the blood, a dangerous and the blood, a dangerous and painful condition called "the painful condition called "the bends". Helium, which is inert, bends". Helium, which is inert, less dense, and does not dissolve less dense, and does not dissolve in the blood, is mixed with Oin the blood, is mixed with O22 in in

scuba tanks used for deep scuba tanks used for deep descents. descents.

Collecting a gas “over Collecting a gas “over water”water”

Gases, since they mix with other gases readily, must be Gases, since they mix with other gases readily, must be collected in an environment where mixing can not occur. collected in an environment where mixing can not occur. The easiest way to do this is under water because water The easiest way to do this is under water because water displaces the air.displaces the air. So when a gas is collected “over water”, So when a gas is collected “over water”, that means the container is filled with water and the gas is that means the container is filled with water and the gas is bubbled through the water into the container. Thus, the bubbled through the water into the container. Thus, the pressure inside the container is from the gas AND the pressure inside the container is from the gas AND the water vapor. water vapor. This is where Dalton’s Law of Partial This is where Dalton’s Law of Partial Pressures becomes useful.Pressures becomes useful.

Table of Vapor Pressures for WaterTable of Vapor Pressures for Water

Solve This!Solve This!

A student collects A student collects some hydrogen some hydrogen gas over water at gas over water at 20 degrees C and 20 degrees C and 768 torr. What is 768 torr. What is the pressure of the the pressure of the gas?gas?

768 torr – 17.5 torr = 750.5 torr

GAS DENSITYGAS DENSITYGAS DENSITYGAS DENSITY

High High densitydensity

Low Low densitydensity

22.4 L of ANY gas AT STP = 1 mole

Gases and StoichiometryGases and Stoichiometry2 H2 H22OO2 2 (l) ---> 2 H(l) ---> 2 H22O (g) + OO (g) + O2 2 (g)(g)

Decompose 1.1 g of HDecompose 1.1 g of H22OO22 in a flask with a in a flask with a

volume of 2.50 L. What is the volume of Ovolume of 2.50 L. What is the volume of O22 at at

STP?STP?

Bombardier beetle Bombardier beetle uses decomposition uses decomposition of hydrogen peroxide of hydrogen peroxide to defend itself.to defend itself.

Gases and Gases and StoichiometryStoichiometry

2 H2 H22OO2 2 (l) ---> 2 H(l) ---> 2 H22O (g) + OO (g) + O2 2 (g)(g)

Decompose 1.1 g of HDecompose 1.1 g of H22OO22 in a flask with a volume of in a flask with a volume of

2.50 L. What is the volume of O2.50 L. What is the volume of O22 at STP? at STP?

SolutionSolution

1.1 g H1.1 g H22OO22 1 mol H 1 mol H22OO22 1 mol O 1 mol O22 22.4 L O 22.4 L O22

34 g H34 g H22OO22 2 mol H 2 mol H22OO22 1 mol O 1 mol O22

= 0.36 L O2 at STP

Gas Stoichiometry: Practice!Gas Stoichiometry: Practice!

A. What is the volume at STP of 4.00 g of CHA. What is the volume at STP of 4.00 g of CH44??

B. How many grams of He are present in 8.0 L B. How many grams of He are present in 8.0 L

of gas at STP?of gas at STP?