Gases

Regardless of their chemical Regardless of their chemical identity, gases tend to exhibit identity, gases tend to exhibit similar physical behaviorssimilar physical behaviors

Gas particles can be monatomic Gas particles can be monatomic (Ne), diatomic (N(Ne), diatomic (N22), or polyatomic ), or polyatomic (CH(CH44) – but they all have some ) – but they all have some common characteristics:common characteristics:

The Nature of GasesThe Nature of Gases

1.1. Gases have mass.Gases have mass.2.2. Gases are compressible.Gases are compressible.3.3. Gases fill their containers.Gases fill their containers.4.4. Gases diffuse.Gases diffuse.5.5. Gases exert pressure.Gases exert pressure.6.6. Pressure is related to Pressure is related to

temperaturetemperature

Kinetic Molecular TheoryKinetic Molecular Theory Theory used to explain the Theory used to explain the

behaviors and experimental behaviors and experimental characteristics of ideal gases – characteristics of ideal gases –

• The theory states that the tiny The theory states that the tiny particles in all forms of matter particles in all forms of matter are in continuous motion.are in continuous motion.

There are 3 basic assumptions of There are 3 basic assumptions of the KMT as it applies to ideal the KMT as it applies to ideal gases.gases.

KMT Assumption #1KMT Assumption #1 A gas is composed of small A gas is composed of small

particles.particles. The particles have an insignificant The particles have an insignificant

volume and are relatively far volume and are relatively far apart from one apart from one another. another.

There is empty space There is empty space between particles. between particles.

No attractive or repulsive No attractive or repulsive forces between particles. forces between particles.

The particles in a gas move in The particles in a gas move in constant random motion.constant random motion.

Particles move in straight paths Particles move in straight paths and are completely independent and are completely independent of each otherof each other

Particles path is only Particles path is only changed by colliding with changed by colliding with another particle another particle or the sides or the sides of its container.of its container.

KMT Assumption #2KMT Assumption #2

All collisions a gas particle All collisions a gas particle undergoes are perfectly elastic.undergoes are perfectly elastic.

They exert a pressure but don’t They exert a pressure but don’t lose any energy during the lose any energy during the collisions.collisions.

KMT Assumption #3KMT Assumption #3

Gases have mass.Gases have mass. Gases are classified as matter, therefore, Gases are classified as matter, therefore,

they must have mass.they must have mass.

Gases are squeezableGases are squeezable

The gas particles empty space The gas particles empty space can be compressed by can be compressed by added pressure added pressure giving the gas particles giving the gas particles less room to bounce around thus less room to bounce around thus decreasing the decreasing the overall volume.overall volume.

Gases are squeezableGases are squeezable There are a huge number of There are a huge number of

applicationsapplications• Storm door closersStorm door closers• Pneumatic tube delivery devicesPneumatic tube delivery devices• TiresTires• Air tanksAir tanks

Gases fill their containersGases fill their containers Gases expand until they take up Gases expand until they take up

as much room as they possibly as much room as they possibly can. can.

Gases fill their containersGases fill their containers The random bouncing motion of The random bouncing motion of

gases allows for the gases allows for the mixing up and spreading mixing up and spreading of the particles until of the particles until they are uniform throughout they are uniform throughout the entire container. the entire container.

Gases diffuseGases diffuse Gases can move through each Gases can move through each

other rapidly.other rapidly.• The movement of one substance The movement of one substance

through another is called through another is called diffusion.diffusion.

Because of all of the empty space Because of all of the empty space between gas molecules, gas between gas molecules, gas molecules can pass between each molecules can pass between each other until the gases mix other until the gases mix uniformly.uniformly.

Gases diffuseGases diffuse

Gases diffuseGases diffuse

Gases diffuseGases diffuse

Gases diffuseGases diffuse This doesn’t happen at the same This doesn’t happen at the same

speeds for all gases though.speeds for all gases though.•Some gases diffuse more rapidly Some gases diffuse more rapidly then other gases based on their then other gases based on their size and their energy.size and their energy.

Diffusion explains why gases are Diffusion explains why gases are able to spread out to fill their able to spread out to fill their containers.containers.

It’s why we can all breathe It’s why we can all breathe oxygen anywhere in the room.oxygen anywhere in the room.

It also helps us avoid potential It also helps us avoid potential odoriferous problems. odoriferous problems.

Gases exert pressureGases exert pressure Gas particles exert pressure by Gas particles exert pressure by

colliding with objects in their path.colliding with objects in their path. The definition of pressure is the The definition of pressure is the

force per unit area – so the total of force per unit area – so the total of all of the tiny collisions makes up all of the tiny collisions makes up the pressure exer- the pressure exer- ted by the gasted by the gas

Gases exert pressureGases exert pressureIt’s the pressure exerted by the It’s the pressure exerted by the gases that hold the walls of a gases that hold the walls of a container outcontainer outThe pressure of gases is what The pressure of gases is what keeps our tires inflated, makes our keeps our tires inflated, makes our basketballs bounce, makes basketballs bounce, makes hairspray come out of the can, hairspray come out of the can, helps our lungs inflate, allow helps our lungs inflate, allow vacuum cleaners to vacuum cleaners to work, etc.work, etc.

Pressure depends on TempPressure depends on Temp Temperature measures the Temperature measures the

average kinetic energy of the average kinetic energy of the particles in an object.particles in an object.• Therefore, the higher the Therefore, the higher the

temperature the more energy temperature the more energy the gas particle has.the gas particle has.

So the collisions are more often So the collisions are more often and with a higher force.and with a higher force.• Think about the pressure of a set Think about the pressure of a set

of tires on a car.of tires on a car.

Pressure depends on TempPressure depends on Temp

Pressure Gauge

Pressure Gauge

Today’s temp: 35°FToday’s temp: 35°F

Today’s temp: 85°FToday’s temp: 85°F

Pressure depends on TempPressure depends on Temp

Pressure Gauge

Pressure Gauge

Measuring GasesMeasuring Gases Variables that are very important Variables that are very important

to studying the behavior of gases:to studying the behavior of gases: Volume: generally in Liters (1L = Volume: generally in Liters (1L =

1000 mL1000 mL))

Temperature :given in Celsius but Temperature :given in Celsius but must be converted to Kelvin for must be converted to Kelvin for gas law problemsgas law problems

Kelvin = °C + 273

Pressure Pressure 1 atm=760 mmHg=760 Torr = 14.7 psi

= 101.3 kPa amount generally given in molesamount generally given in moles

S T PS T PS T PS T P Since the behavior of a gas is Since the behavior of a gas is

dependent on temperature and dependent on temperature and pressure, it is convenient to pressure, it is convenient to designate a set of standard designate a set of standard conditions, called STP in order conditions, called STP in order to study gas behavior.to study gas behavior.

•Standard Temperature = 0°C or Standard Temperature = 0°C or 273K273K

•Standard Pressure = 1atm or Standard Pressure = 1atm or 760mmHg or 101.3kPa 760mmHg or 101.3kPa (depending on the method of (depending on the method of measure)measure)

Atmospheric PressureAtmospheric PressureAtmospheric PressureAtmospheric Pressure The gases in the air are exerting The gases in the air are exerting

a pressure called atmospheric a pressure called atmospheric pressurepressure

Atmospheric pressure is a Atmospheric pressure is a result of the fact that result of the fact that air has mass and air has mass and is colliding with is colliding with everything.everything.

Atmospheric pressure is Atmospheric pressure is measured with a measured with a barometerbarometer..

Atmospheric pressure varies with altitude

•The lower the altitude, the longer and heavier is the column of air above an area of the earth.

Example: Recipes likethe back of a cake box that describes how to cook a cake at a higheraltitude

Atmospheric PressureAtmospheric PressureAtmospheric PressureAtmospheric Pressure

Boyle’s LawBoyle’s Law

Boyle’s Mathematical Law:Boyle’s Mathematical Law:

since PV equals a constantsince PV equals a constant

PP11VV11 = = PP22VV22

PP11VV11 = = PP22VV22

If we have a given amount of a gas at If we have a given amount of a gas at a starting pressure and volume, what a starting pressure and volume, what would happen to the pressure if we would happen to the pressure if we

changed the volume? changed the volume? Or to the volume if we changed the Or to the volume if we changed the

pressure? pressure?

Boyle’s Mathematical Law:Boyle’s Mathematical Law:

List the variables or clues given:List the variables or clues given:

PP11 = 2 atm = 2 atm VV11 = 3.0 L = 3.0 L

PP22 = 4 atm = 4 atm VV22 = ? = ?

P1V1 = V2 P2

Plug in the variables & calculate:Plug in the variables & calculate:

(2 atm)(2 atm)(3.0 L) (3.0 L) ==

(4 atm)(4 atm)(V(V22))

Ex: A gas has a volume of 3.0 L at 2 atm. Ex: A gas has a volume of 3.0 L at 2 atm. What will its volume be at 4 atm?What will its volume be at 4 atm?

Charles’ LawCharles’ Law

Charles’s Mathematical Law:Charles’s Mathematical Law:

since V/T = ksince V/T = k

==VV11 V V22

TT11 T T22

If we have a given amount of a gas at If we have a given amount of a gas at a starting volume and temperature, a starting volume and temperature, what would happen to the volume if what would happen to the volume if

we changed the temperature? we changed the temperature? Or to the temperature if we changed Or to the temperature if we changed

the volume?the volume?

Charles’s Mathematical Law:Charles’s Mathematical Law:

TT11 = 400K = 400K VV11 = 3.0 L = 3.0 L

TT22 = 500K = 500K VV22 = ? = ?

List the variables or clues given:List the variables or clues given:

Plug in the variables & calculate:Plug in the variables & calculate:

3.0L3.0L

400K400K 500K500K X LX L

==

Ex: A gas has a volume of 3.0 L at 400K. Ex: A gas has a volume of 3.0 L at 400K. What is its volume at 500KWhat is its volume at 500K

Gay-Lussac’s LawGay-Lussac’s Law

since P/T = ksince P/T = k

PP11 PP22TT11 T T22

==

If we have a given amount of a gas at If we have a given amount of a gas at a starting temperature and pressure, a starting temperature and pressure, what would happen to the pressure if what would happen to the pressure if

we changed the temperature? we changed the temperature? Or to the temp. if we changed the Or to the temp. if we changed the

pressure? pressure?

Gay-Lussac’s Mathematical Law:Gay-Lussac’s Mathematical Law:

Gay-Lussac’s Mathematical Law:Gay-Lussac’s Mathematical Law:

TT11 = 400K = 400K PP11 = 3.0 atm = 3.0 atm

TT22 = 500K = 500K PP22 = ? = ?

List the variables or clues given:List the variables or clues given:

Plug in the variables & calculate:Plug in the variables & calculate:3.0atm

400K400K 500K500K

X atmX atm==

Ex: A gas has a pressure of 3.0atm at Ex: A gas has a pressure of 3.0atm at 400K. What is its pressure at 500K?400K. What is its pressure at 500K?

Combined Gas Law

Combined and Combined and ideal gas lawsideal gas lawsCombined and Combined and ideal gas lawsideal gas laws

There is a lesser known law There is a lesser known law called Avogadro’s Law which called Avogadro’s Law which relates Volume & moles (n).relates Volume & moles (n).

It turns out that they are It turns out that they are directly related to each other.directly related to each other.

As number of moles increases As number of moles increases then Volume increases.then Volume increases.

V/n = kV/n = k

Avogadro’s LawAvogadro’s Law

If we combine all of the laws If we combine all of the laws together including Avogadro’s together including Avogadro’s Law we get: Law we get:

Where R is the Where R is the universal gas universal gas constantconstant

NormallyNormallywritten aswritten as

Ideal Gas LawIdeal Gas Law

Because of the different Because of the different pressure units there are 3 pressure units there are 3 possibilities for our ideal gas possibilities for our ideal gas constantconstant

R =.0821R =.0821L•atmL•atmmol•Kmol•K

•If pressure is If pressure is given in mmHg given in mmHg or torror torr

R=62.4R=62.4L•mmHgL•mmHg

mol•Kmol•K• If pressure If pressure

is given in is given in kPakPa

R=8.314R=8.314L•kPaL•kPamol•Kmol•K

•If pressure is If pressure is given in atmgiven in atm

Ideal Gas ConstantIdeal Gas Constant

PracticePractice1.1. Use the Ideal Gas Law to complete Use the Ideal Gas Law to complete

the following table for ammonia the following table for ammonia gas (NHgas (NH33).).

PressureVolum

eTem

pMole

sGrams

2.50 atm 0C 32.0

768 mmHg

6.0 L100

C

Variations of the Ideal Gas LawVariations of the Ideal Gas Law

—We need to know that the unit We need to know that the unit mole is equal to mass divided mole is equal to mass divided by by molar mass.molar mass.

n = m/MMn = m/MMPV = nRTPV = nRT

RTMMm

PV

PVmRT

MM

Variations of the Ideal Gas LawVariations of the Ideal Gas Law

• We can then use the MM We can then use the MM equation to derive a version equation to derive a version that solves for the density of a that solves for the density of a gas.gas.—Remember that D = m/VRemember that D = m/V

MW = MW = dRTdRT or or MW = MW = mRTmRT

PP VP VPKitty cats say meow and they Kitty cats say meow and they

put dirt on their pee!!put dirt on their pee!!

Dalton’s Law of Partial PressureDalton’s Law of Partial Pressure

• States that the total pressure States that the total pressure of a mixture of gases is equal of a mixture of gases is equal to the sum of the partial to the sum of the partial pressures of the component pressures of the component gases.gases.

PPTT=P=P11+P+P22+P+P33+…+…• What that means is that each What that means is that each

gas involved in a mixture gas involved in a mixture exerts an independent exerts an independent pressure on its container’s pressure on its container’s wallswalls

• Three of the primary Three of the primary components of air are COcomponents of air are CO22, N, N22, , and Oand O22. In a sample containing . In a sample containing a mixture of these gases at a mixture of these gases at exactly 760 mmHg, the partial exactly 760 mmHg, the partial pressures of COpressures of CO22 and N and N22 are are given as Pgiven as PCOCO22= 0.285mmHg = 0.285mmHg and Pand PNN22 = 593.525mmHg. = 593.525mmHg. What is the partial pressure of What is the partial pressure of OO22??

Simple Dalton’s Law Simple Dalton’s Law CalculationCalculation

PPTT = P = PCO2CO2 + P + PN2N2 + P + PO2O2

Simple Dalton’s Law Simple Dalton’s Law CalculationCalculation

760mmHg = .285mmHg + 760mmHg = .285mmHg +

593.525mmHg + P593.525mmHg + PO2O2

PPO2O2= 167mmHg= 167mmHg

• Partial pressures are also Partial pressures are also important when a gas is important when a gas is collected through water.collected through water.—Any time a gas is collected Any time a gas is collected

through water the gas is through water the gas is “contaminated” with water “contaminated” with water vapor.vapor.

—You can determine the You can determine the pressure of the dry gas by pressure of the dry gas by subtracting out the water subtracting out the water vaporvapor

Dalton’s Law of Partial PressureDalton’s Law of Partial Pressure

PPtottot = P = Patmospheric pressureatmospheric pressure = P = Pgasgas + P + PHH22OO

AtmosphericPressure

AtmosphericPressure

—The water’s vapor pressure The water’s vapor pressure can be determined from a list can be determined from a list and subtract-ed from the and subtract-ed from the atmospheric pressureatmospheric pressure

WATER VAPOR PRESSURESWATER VAPOR PRESSURESTemp Temp ((°°C)C) (mmHg)(mmHg) (kPa)(kPa)

0.00.0 4.64.6 .61.615.05.0 6.56.5 .87.87

10.010.0 9.29.2 1.231.2315.015.0 12.812.8 1.711.7115.515.5 13.213.2 1.761.7616.016.0 13.613.6 1.821.8216.516.5 14.114.1 1.881.8817.017.0 14.514.5 1.941.9417.517.5 15.015.0 2.002.0018.018.0 15.515.5 2.062.0618.518.5 16.016.0 2.132.13

• Determine the partial pressure Determine the partial pressure of oxygen collected by water of oxygen collected by water displace-ment if the water displace-ment if the water temperature is 20.0temperature is 20.0°°C and the C and the total pressure of the gases in total pressure of the gases in the collection bottle is 730 the collection bottle is 730 mmHg.mmHg.

Simple Dalton’s Law Simple Dalton’s Law CalculationCalculation

PPH2O H2O at 20.0at 20.0°°C= 17.5 mmHgC= 17.5 mmHg

PPTT = P = PH2OH2O + P + PO2O2

Simple Dalton’s Law Simple Dalton’s Law CalculationCalculation

730mmHg = 17.5 + P730mmHg = 17.5 + PO2O2

PPO2O2= 712.5 mmHg= 712.5 mmHg

PPH2O H2O = 17.5 mmHg= 17.5 mmHg

PPT T = 730 mmHg= 730 mmHg

Mole FractionMoles of gasx x PT = Px

Total moles

A mixture of 4.00 moles of O2 and 3.00 moles of H2 exert a total pressure of 760 torr. What is the partial pressure of each gas?

4.00 moles of O2 x 760 torr = 434 torr7.00 total moles

3.00 moles of H2 x 760 torr = 326 torr7.00 total moles

Graham’s LawGraham’s Law

• Thomas Graham studied the Thomas Graham studied the effusion and diffusion of gases.effusion and diffusion of gases.– Diffusion is the mixing of gases Diffusion is the mixing of gases

through each other.through each other.– Effusion is the process whereby Effusion is the process whereby

the molecules of a gas escape the molecules of a gas escape from its container through a from its container through a tiny holetiny hole

• Graham’s Law states that the Graham’s Law states that the rates of effusion and diffusion rates of effusion and diffusion of gases at the same of gases at the same temperature and pressure is temperature and pressure is dependent on the size of the dependent on the size of the molecule.molecule.– The bigger the molecule the The bigger the molecule the

slower it moves the slower it slower it moves the slower it mixes and escapes.mixes and escapes.

Graham’s LawGraham’s Law

• The velocities of two different The velocities of two different gases are inversely proportional gases are inversely proportional to the square roots of their to the square roots of their molar masses.molar masses.

Rate of effusion of ARate of effusion of A====

Rate of effusion of BRate of effusion of B

MMMMBB

MMMMAA

If equal amounts of helium and If equal amounts of helium and argon are placed in a porous argon are placed in a porous

container and allowed to escape, container and allowed to escape, which gas will escape faster and which gas will escape faster and

how much faster?how much faster?

Graham’s Law Example Calc.Graham’s Law Example Calc.

Rate of effusion of ARate of effusion of A====

Rate of effusion of BRate of effusion of B

MMBB

MMAA

Graham’s Law Example Calc.Graham’s Law Example Calc.

Rate of effusion of HeRate of effusion of He==

Rate of effusion of ArRate of effusion of Ar

40 g40 g

4 g4 g

Helium is 3.16 times faster than Helium is 3.16 times faster than Argon.Argon.