CHAPTER 14CHAPTER 14

GAS LAWSGAS LAWS

Boyles Law:Boyles Law: Pressure (kPa) Pressure (kPa) Volume (L) Volume (L)

-for a given mass of gas at constant -for a given mass of gas at constant temperature, the volume of the gas temperature, the volume of the gas varies inversely with pressure.varies inversely with pressure.– Pressure increases, Volume decreasesPressure increases, Volume decreases– Inversely proportionalInversely proportional– Smaller volume- more pressure b/c particles Smaller volume- more pressure b/c particles

collide more oftencollide more often

EX:EX: syringesyringe

PP11VV11=P=P22VV22

PP11VV11=P=P22VV22

where P1 and V1 are the pressure & where P1 and V1 are the pressure & volume before the gas expandsvolume before the gas expands

and P2 and V2 are the pressure & volume and P2 and V2 are the pressure & volume after the gas expands. after the gas expands.

Boyles Law:Boyles Law: Pressure (kPa) Pressure (kPa) Volume (L) Volume (L)

Practice:Practice: If you had a gas that exerted 202 kPa of If you had a gas that exerted 202 kPa of pressure and took up a space of 3.00 liters, & you pressure and took up a space of 3.00 liters, & you decided to expand the space to 7.00 liters, what decided to expand the space to 7.00 liters, what would be the new pressure? (temperature would be the new pressure? (temperature remains constant)remains constant)

Answer: PAnswer: P11VV11 = P = P22VV22

So, P1 = 202 kPa, V1 = 3.00L, V2 = 7.00L, and you So, P1 = 202 kPa, V1 = 3.00L, V2 = 7.00L, and you need to solve for P2, the new pressure. Plug the need to solve for P2, the new pressure. Plug the numbersnumbers into the equation, & you have: into the equation, & you have:

(P(P11VV11)/V)/V22 = P = P22

(202 kPa) x (3.00 L) = (P(202 kPa) x (3.00 L) = (P22) x (7.00 L). P2 = 86.6 ) x (7.00 L). P2 = 86.6 kPa.kPa.

Charles’ Law:Charles’ Law: Temp. (K) Temp. (K) Volume Volume (L)(L)

-the volume of a fixed mass of gas is directly -the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if proportional to its Kelvin temperature if the pressure is kept constant.the pressure is kept constant.

– Temperature increases, Volume increasesTemperature increases, Volume increases– Directly proportionalDirectly proportional– Higher temperature, gas particles speed up Higher temperature, gas particles speed up

and move farther away from one anotherand move farther away from one another

EX:EX: heating a sealed containerheating a sealed container

VV1 1 = V= V22

TT1 1 TT22

VV1 1 = V= V22

TT1 1 TT22

where V1 and T1 are the volume & where V1 and T1 are the volume & temperature before the gas expandstemperature before the gas expands

and V2 and T2 are the volume & and V2 and T2 are the volume & temperature after the gas expands. temperature after the gas expands.

Charles’ Law:Charles’ Law: Temp. (K) Temp. (K) Volume Volume (L)(L)

Practice:Practice: If you took a balloon outside that was at If you took a balloon outside that was at 2020ooC at 2L in volume, & it heated up to 29C at 2L in volume, & it heated up to 29ooC, what C, what would its volume be? Assume constant pressure.would its volume be? Assume constant pressure.

Answer: VAnswer: V11 / T / T11 = V = V22 / T / T22

– VV11 = 2.0L, T = 2.0L, T11 = 20 = 20ooC, TC, T22 = 29 = 29ooC, you must solve for VC, you must solve for V22. .

Wait!!Wait!! You have to convert the temperatures to You have to convert the temperatures to Kelvin So: Kelvin So: TT11 = 20 = 20ooC = 20C = 20ooC + 273 = 293 K C + 273 = 293 K T T22 = 29 = 29ooC = 29C = 29ooC + 273 = 302 K C + 273 = 302 K

– Now, you can plug in the numbers and solve for V2. Now, you can plug in the numbers and solve for V2.

2.0L 2.0L == V V22

293 K 293 K 302 K and V302 K and V22 = 2.1L = 2.1L

Gay-Lussac's LawGay-Lussac's Law :: Temp. (K) Temp. (K) PressurePressure (kPa)(kPa)

-the pressure of a fixed mass of gas is -the pressure of a fixed mass of gas is directly proportional to its temperature directly proportional to its temperature if the volume is kept constant.if the volume is kept constant.

– Temperature increases, Pressure increasesTemperature increases, Pressure increases– Directly proportionalDirectly proportional

PP1 1 = P= P22

TT1 1 TT22

Combined Gas Law:Combined Gas Law:

-combined the three gas laws into a single -combined the three gas laws into a single expression.expression.

VV11PP1 1 = V= V22PP22

TT1 1 TT22

The The Vice PresidentVice President is higher than the is higher than the

TreasurerTreasurer

CHARLES’ LAW

GAY-LUSSAC’S LAW

BOYLE’S LAW

COMBINED GAS LAW DOESN‘T:COMBINED GAS LAW DOESN‘T:

ACCOUNT FOR THE AMOUNT OF GASACCOUNT FOR THE AMOUNT OF GAS

IT JUST LOOKS AT PRESSURE, VOLUME, IT JUST LOOKS AT PRESSURE, VOLUME, & TEMPERATURE& TEMPERATURE

Ideal Gas Law:Ideal Gas Law:--allows you to solve for the number of moles allows you to solve for the number of moles

of a gas(n).of a gas(n).PV = nRTPV = nRT

P=pressure in kPa or atmP=pressure in kPa or atmV=volume in LV=volume in LT=temperature in KT=temperature in Kn=#of molesn=#of molesR=Ideal gas constant (R) is 8.31 (L x kPa)R=Ideal gas constant (R) is 8.31 (L x kPa)

(K x mol)(K x mol) 0.0821 (L x atm)0.0821 (L x atm)

(K x mol)(K x mol)

Ideal Gas Law:Ideal Gas Law:PV = nRTPV = nRTPractice:Practice:A sample of OA sample of O22 gas has a volume of 4.52L at a temp. of gas has a volume of 4.52L at a temp. of

1010ooC and a pressure of 110.5 kPa. Calculate the C and a pressure of 110.5 kPa. Calculate the number of moles of Onumber of moles of O22 gas present in this sample. gas present in this sample.

Answer:Answer: Rearrange to solve for n (number of moles): Rearrange to solve for n (number of moles): n = PV/RT. n = PV/RT. P = 110.5 kPa, P = 110.5 kPa, V = 4.52L, V = 4.52L, T = 10T = 10ooC + 273 = 283K, and C + 273 = 283K, and R = 8.31 L x kPa/K x mol. R = 8.31 L x kPa/K x mol.

n= (110.5 kPa)(4.52L)/(8.31L kPa/K mol)(283 K) = .212 n= (110.5 kPa)(4.52L)/(8.31L kPa/K mol)(283 K) = .212 moles. moles.

Do NowDo Now If 4.50 g of methane gas (CHIf 4.50 g of methane gas (CH44) is in a 2.00-L ) is in a 2.00-L

container at 35°C, what is the pressure container at 35°C, what is the pressure inside the container?inside the container?

Solution:Solution: PV=nRT - Ideal Gas Law Equation. PV=nRT - Ideal Gas Law Equation.

P = ?P = ?

V = 2.00 LV = 2.00 L

R = 8.31 R = 8.31 L * kPaL * kPa

T = 308 KT = 308 Kmol * K

n = 4.50 g CH4 x 1 mol / 16.0 g CH4 = 0.281 mol

Do NowDo Now If 4.50 g of methane gas (CHIf 4.50 g of methane gas (CH44) is in a 2.00-L ) is in a 2.00-L

container at 35°C, what is the pressure container at 35°C, what is the pressure inside the container?inside the container?

Solution:Solution: PV=nRT - Ideal Gas Law Equation. PV=nRT - Ideal Gas Law Equation.

P = 3.60 x 10P = 3.60 x 1022 kPa. kPa.

V = 2.00 LV = 2.00 L

R = 8.31 R = 8.31 L * kPaL * kPa

T = 308 KT = 308 Kmol * K

n = 4.50 g CH4 x 1 mol / 16.0 g CH4 = 0.281 mol

Mathematical RelationshipMathematical Relationship

Each slice weighs 0.5 lbs. Eight slices make up a pie.

How much does this pie weigh? What can I ignore in my calculation?

Mathematical RelationshipMathematical Relationship

Each lego block has dimensions 4 cm x 2 cm x 1 cm

How tall is the stack of lego blocks?

HistoryHistory John Dalton (1766-1844) was John Dalton (1766-1844) was

an English chemist and an English chemist and physicist born in Cumberland, physicist born in Cumberland, England. England.

Early in life, influenced by Early in life, influenced by meteorology. meteorology.

Researched color-blindness Researched color-blindness a.k.a. “Daltonism.”a.k.a. “Daltonism.”

Most notably known for Most notably known for compiling fundamental ideas compiling fundamental ideas into a universal atomic into a universal atomic theory.theory.

His interest in gases and gas His interest in gases and gas mixtures lead him to mixtures lead him to investigate humidity. This investigate humidity. This ultimately lead to Dalton’s ultimately lead to Dalton’s Law.Law.

Observe and Find a PatternObserve and Find a Pattern Partial Pressures of Compressed Air  

(Assuming air is 80% Nitrogen and 20% Oxygen)  

Depth (meters) Absolute Pressure P O2 P N2

0 14.7 2.94 11.76

33 29.4 5.88 23.52

66 44.1 8.82 35.28

99 58.8 11.76 47.04

132 73.5 14.70 58.80

165 88.2 17.64 70.56

198 102.9 20.58 82.32

231 117.6 23.53 94.08

264 132.3 26.46 105.8

297 147.0 29.40 117.6

ExplainExplain

The Ideal Gas Law holds for virtually any The Ideal Gas Law holds for virtually any gas, whether pure or a mixture, at gas, whether pure or a mixture, at ordinary conditions for two reasons:ordinary conditions for two reasons:– Gases mix homogeneously in any Gases mix homogeneously in any

proportions.proportions.– Each gas in a mixture behaves as if it were Each gas in a mixture behaves as if it were

the only gas present.the only gas present. Explain why we can use a gas mixture, Explain why we can use a gas mixture,

such as air, to study the general such as air, to study the general behavior of an ideal gas under ordinary behavior of an ideal gas under ordinary conditions.conditions.

Predict and TestPredict and Test

What is the relationship between the number of What is the relationship between the number of particles in containers A and C and the partial particles in containers A and C and the partial pressures of A and C.pressures of A and C.

Predict what the reading will be for container T.Predict what the reading will be for container T.

Predict and TestPredict and Test

What is the relationship between the number of What is the relationship between the number of particles in containers A and C and the partial particles in containers A and C and the partial pressures of A and C.pressures of A and C.

Predict what the reading will be for container T.Predict what the reading will be for container T.

DeriveDerive

Based on the outcome of the experiment Based on the outcome of the experiment relative to the prediction, make a relative to the prediction, make a judgment about whether the experiment judgment about whether the experiment disproved the hypothesis or not.disproved the hypothesis or not.

Write a mathematical expression that Write a mathematical expression that relates absolute (total) pressure to the relates absolute (total) pressure to the individual gas pressures.individual gas pressures.

– PPtotaltotal = P = P11 + P + P22 + P + P33 + …this is known as + …this is known as Dalton’s Law of Partial Pressures. Dalton’s Law of Partial Pressures. How can we How can we qualitatively explain this mathematical qualitatively explain this mathematical relationship?relationship?

Mathematical ApplicationMathematical Application It was a dark and stormy night and your It was a dark and stormy night and your

“friend” has locked you in the lab without a “friend” has locked you in the lab without a key. You remembered that the oldest key. You remembered that the oldest window in the lab is always cracked open on window in the lab is always cracked open on a diagonal that won’t ever seem to budge a diagonal that won’t ever seem to budge completely. Someone calculated that you completely. Someone calculated that you need a total pressure of 7.10 x 10need a total pressure of 7.10 x 106 6 kPa to kPa to exert a strong enough force to bust open exert a strong enough force to bust open the window. Coincidentally, you have 2.00 the window. Coincidentally, you have 2.00 moles of Ne, 4.00 moles of Xe, and 6.00 moles of Ne, 4.00 moles of Xe, and 6.00 moles of Ar in a 5.00-L vessel at 27°C moles of Ar in a 5.00-L vessel at 27°C standing next to your lab station. Is the standing next to your lab station. Is the total pressure of the mixture enough for you total pressure of the mixture enough for you to escape and make it to the club in time or to escape and make it to the club in time or will you be left alone in the lab synthesizing will you be left alone in the lab synthesizing aspirin to relieve you of your torment?aspirin to relieve you of your torment?

Observe and ExplainObserve and Explain

Gas produced is less dense than water, so it Gas produced is less dense than water, so it replaces the water in the test tube.replaces the water in the test tube.

Gas collected is not pure because it contains Gas collected is not pure because it contains vapor from the water.vapor from the water.

KClO3

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

-for a mixture of gases in a container, the -for a mixture of gases in a container, the total pressure exerted is the sum of the total pressure exerted is the sum of the pressures that each gas would exert if it pressures that each gas would exert if it were alone.were alone.

PPtotaltotal=P=P11 + P + P22 + P + P33 +….. +…..

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

Practice:Practice:

Air contains OAir contains O22, N, N22, CO, CO22, and trace amounts of other , and trace amounts of other gases. What is the partial pressure of Ogases. What is the partial pressure of O22 ( (PPO2O2) at ) at 101.3 kPa of pressure if 101.3 kPa of pressure if PPN2N2 =79.10 kPa, =79.10 kPa, PPCOCO22 =0.040 kPa, and =0.040 kPa, and PPothersothers =0.94 kPa? =0.94 kPa?

Answer:Answer: PPtotaltotal = 101.3 kPa = 101.3 kPa

-P-Ptotaltotal = = PPO2 O2 ++ P PN2N2 + P+ PCOCO22 + + P Pothersothers

-P-PO2O2 = = PPtotaltotal - - ((PPN2N2 + P+ PCOCO22 + + P Pothersothers))

-P-PO2O2 = 101.3 kPa - = 101.3 kPa - (79.10 kPa (79.10 kPa + + 0.040kPa +0.040kPa + 0.94kPa)0.94kPa)

-P-PO2O2 = 21.22 kPa = 21.22 kPa

Ideal vs. Real GasesIdeal vs. Real Gases

An ideal gas is a hypothetical concept. An ideal gas is a hypothetical concept. No gas No gas exactlyexactly follows the ideal gas follows the ideal gas law.law.

Ideal GasesIdeal Gases

Always a gasAlways a gas Not attracted to one anotherNot attracted to one another Have no volumeHave no volume Follow the gas laws for all conditions Follow the gas laws for all conditions

of pressure and temperatureof pressure and temperature Ideal gases Ideal gases DO NOTDO NOT exist!!!!!!!! exist!!!!!!!!

Real GasesReal Gases

Can be liquified and sometimes Can be liquified and sometimes solidified by cooling and applying solidified by cooling and applying pressure pressure

(ideal gases can not)(ideal gases can not)

Have a finite volumeHave a finite volume Are attracted to one another, Are attracted to one another,

especially at low temperaturesespecially at low temperatures

Graham’s Law of EffusionGraham’s Law of Effusion::

the rate of effusion and diffusion of a gas is the rate of effusion and diffusion of a gas is inversely proportional to the square root inversely proportional to the square root of its molar mass .of its molar mass .

– Lighter gas goes faster.Lighter gas goes faster.– Heavier gas goes slower.Heavier gas goes slower.– To figure out how much faster take the square To figure out how much faster take the square

root of the gfm of the heavier gas and divide root of the gfm of the heavier gas and divide by the square root of the gfm of the lighter by the square root of the gfm of the lighter gas.gas.

) (

) (

) (

) (

gaslighter

gasheavier

gasheavier

gaslighter

gfm

gfm

Rate

Rate

Graham’s Law of EffusionGraham’s Law of Effusion::

Practice:Practice:

Does He effuse faster or slower than ODoes He effuse faster or slower than O22? ? What is the relative rate of diffusion of He What is the relative rate of diffusion of He compared to Ocompared to O22? ?

) (

) (

)(

)(

4

32

2 gaslighter

gasheavier

O

He

g

g

Rate

Rate

Answer:Answer: = 2.8, He is 2.8 times much = 2.8, He is 2.8 times much fasterfaster