GasesChapter 11

Kinetic Molecular Theory of Gas

1. Made of tiny particles that are relatively far apart

2. Collisions between the particles does not lose energy

3. Particles are in continuous rapid random motion

4. There is no attraction between particles

5. Temperature of gas depends on average kinetic energy of particles

Ch 10 pg 329-330 Parameters for an ideal gas

Kinetic molecular theory only applies to “ideal” gases. Most gases are only nearly ideal if pressure is not too high and temperature is not to low

Properties of Gas

Expansion: indefinite shape and volume

Fluidity: particle move pass each other

Low density: often floatsCompressibility: can press particle

closer togetherDiffusion and effusion:

◦Diffusion: mixing of gas by random motion

◦Effusion: gas particles passing through tiny opening

Pressure: force/unit area

Caused by the collisions of molecules with the walls of

the containerSI units = Newton/meter2 = 1 Pascal (Pa)1 standard atmosphere = 101.3 kPa1 atm = 760 mmHg = 760 torrSo…

◦1 atm = 760 mmHg = 101.3 kPa 1 mmHg = 1 torr

barometer is a device used to measure atmospheric pressure

Warm up1. What is pressure?2. What units are used to measure

pressure?

Pascal is the SI unit of pressure

1 atm = 760 mmHg = 101.3 kPa

1 mmHg = 1 torr

Continuing Ch 11 Gases notes

Given: atmospheric pressure = 0.830 atmUnknown: a. pressure in mm Hg

b. pressure in kPa

a.

b. 101.325 kPa

0.830 atm at

84.1m

kPa

Pressure Conversions

760 mm Hg

0.830 atm a

631 tm

mm Hg

1 atm = 760 mmHg = 101.3 kPa

Factors that affect gas pressure

1. Kinetic theory2. Pressure 3. Volume4. Temperature

Factors that affect gas pressure

1. Kinetic Theory—As collisions increases, pressure will increase.particles travel in straight line paths

until they collide with other particles or wall of the container.◦Pressure is measured

Unit = kilopascal Standard pressure is

101kPa

2. Pressure (amount of gas)As # of gas particles increases

(without increasing volume), pressure increases and collisions increases◦Filling a tire with air

Gas naturally flows from high to low pressureEx: Aerosol cans—pressureinside can is higher than pressure outside

Factors that affect gas pressure

Relationship Between Pressure, Force, and Area

3. VolumeAs volume decreases, collisions

◦ increase and so pressure…◦ increases

Volume is measured in liters

Factors that affect gas pressure

4. TemperatureAs temperature increases, energy

◦ Increases so collisions…◦ Increase causing pressure of a gas to◦ Increase

Temp is measured in Kelvin◦ K = oC + 273◦ Standard temp = 0oC◦ Kelvin is used because 0 in an equation is

problematic

Factors that affect gas pressure

STP: Standard Temperature and Pressure

P = 1 atmosphere, 760 torr, 101.3 kPa

T = 0ºC, 273 Kelvins (K)◦convert to Kelvin: ºK = ºC + 273

The molar volume of an ideal gas is 22.4L at STP

Dalton’s law of partial pressure

total pressure of a mixture of gases is the sum of their partial pressures

Ptotal= P1 + P2 + P3…

Ex B: pg 367Oxygen gas from decomposition of KClO3

was collected by water displacement. The barometric pressure was 731.0 torr and the pressure of the water vapor was 17.5 torr, find the partial pressure of oxygen. Patm = Po2 + PH2O

731torr =Po2 + 17.5 torr 731 – 17.5 torr = 713.5 torr

Phase Diagram: shows critical points in the change of states of mater

Ch 10 pg 347

Ex C pg 370A sample of oxygen gas has a volume of 150.0 mL when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the temperature remains constant?Given: V1 of O2 = 150.0 mL, P1 of O2 = 0.947 atm, P2 of O2 = 0.987 atmUnknown: V2 of O2 in mL

P1V1 = P2V2

Boyle’s Law: volume of the gas varies inversely with pressure

P1 (V1) = P2 (V2)Boyle’s Law defines the

relationship between pressure and volume

Pressure of a gas increases as the volume◦ decreases…when temp. is constant

1 12

2

PVV

P0.947 atm x 150.0mL = 144mL O2

0.987

Boyle's Law clipCartesian diver

demoFish bubblesBreathing

◦Boyle's Law and breathing

◦https://www.youtube.com/watch?v=NB1aCBId6qA

Sample Boyle’s Law Problem

A hot air balloon contains 30.0 L of He gas at 103 kPa. What is the volume of the balloon when it decreases in pressure to 25.0 kPa due to its rise in altitude? Assume the temp remains constant.◦ What do we know?◦ What are we trying to find?◦ What law applies?◦ Solve◦ Does your answer make sense? (124 L)

P1 (V1) = P2 (V2)

More problems to practice…N2O is used as an anesthetic. The

pressure of gas changes from 105 kPa to 40.5 kPa. The ending volume is 6.48 L. What was the original volume due to this change in pressure if temp. is held constant. (2.50 L)

A gas with a volume of 4.00L is at a pressure of 1.30 atm. The gas is allowed to expand to 12.0 L. What is the new pressure in the container if the temp. is held constant? (0.433 atm)

Charles’ Law: Volume is directly proportional to temperature.

V1 / T1 = V2 / T2

As the temperature of the enclosed gas increases, the volume ◦ Increases…when pressure is held

constant.◦ Don’t forget! K = ºC + 273, (temp can’t

be zero)

Ex D pg 372A sample of neon gas occupies a volume of 752 mL at 25°C. What volume will the gas occupy at 50°C if the pressure remains constant?

Given: V1 of Ne = 752 mL, T1 of Ne = 25°C + 273 = 298 K, T2 of Ne = 50°C + 273 = 323 KUnknown: V2 of Ne in mL

1 2

1 2

V V

T T

1 2

21

VTV

T

752mL x 323K = 815mL Ne 298 K

◦ Charles' Law clip◦ Microwave popcorn◦ Warming/cooling balloon over flask◦ Demos◦ https://www.youtube.com/watch?v=

GcCmalmLTiU ◦ https

://www.youtube.com/watch?v=7JKVtbe-hV8◦ https://www.youtube.com/watch?v=Uy-

SN5j1ogk

Sample Charles’ Law ProblemA balloon inflated in a room at 24C has a

volume of 4.00 L. The balloon is then heated to a temperature of 50C. What is the new volume of the balloon if the pressure of the room remains constant throughout the experiment? (4.35 L)

Exactly 5.00 L of air at -50.0C is warmed. If the new volume of the balloon is 8.36 L, to what temperature in C was it heated? Assume pressure is constant. (99.9C)

If a sample of gas occupies a volume of 6.80 L at 325 C, what will its volume be at 25.0C if the pressure does not change? (3.39 L)

Whose law?Balloon test

◦ttps://www.youtube.com/watch?v=JZSajBakGK4

Imploding drum◦https://www.youtube.com/watch?v=

Uy-SN5j1ogk

Marshmallows in a vacuum

Gay-Lussac’s Law: The pressure of a gas is directly proportional to Kelvin temperature

P1/T1 = P2/T2

As the temperature of an enclosed gas increases, the pressure ◦ increases, if the volume is constant.

1 2

1 2

P P

T T

Ex E pg 373The gas in a container is at a pressure of 3.00 atm at 25°C. Directions on the container warn the user not to keep it in a place where the temperature exceeds 52°C. What would the gas pressure in the container be at 52°C?Given: P1 of gas = 3.00 atm, T1 of gas = 25°C + 273 = 298 K, T2 of gas = 52°C + 273 = 325 KUnknown: P2 of gas in atm

1 2

1 2

P P

T T

1 2

21

PTP

T

3.00atm x 325K = 3.27 atm 298 K

Ch 11 Practice Problems11.1: pg 367 section review #1,2,4,611.2: Pg 370 sample C #1

Pg 372 sample D #1,2 Pg 374 sample E #1,2,3 Pg 375 sample F #1-2

11.3: Pg 385 sample I #1-2

More Practice: (do not do now…)Try pg 375 section review # 2-4 and pg 385 section review #3,5,6

Sample Gay-Lussac’s Law ProblemsThe pressure in an empty aerosol can is 103 kPa. If

the can is thrown into a fire and increased in temp. from 25.0C to 928C what will the resulting pressure be. Volume is kept constant since the size of the can does not change. (415 kPa)

Think about the tires on your car. Why do you suppose that tire manufacturers recommend checking the air pressure in your ties before driving more than a mile?

The pressure in a car tire is 198 kPa at 27C. After a long drive the pressure in the tire has increased to 225 kPa. What is the temp of the air in the tire? Assume tire volume is constant. (341 K)

Another problem..A sample of nitrogen gas has a

pressure of 0.58 atm at 539K. If the volume is kept constant and the temp. decreases to 211K, what is the new pressure? (0.23 atm)

Warm up: Who’s law?1.Bag of chips pop when brought to a higher

altitude.2.Burning gun powder increases the pressure

until a cannon explodes. 3.Car tires become slightly smaller in the snow.4.Pumping up a bike tire by adding air.5.Heating corn kernels until they they pop.

https://www.youtube.com/watch?v=0m-Lr4Z2drc

SummaryBoyle’s Law: P1 (V1) = P2 (V2)

◦ Indirectly relatedCharles’ Law: V1 / T1 = V2 / T2

◦ Directly relatedGay-Lussac’s Law: P1/T1 = P2/T2

◦ directly related

https://www.youtube.com/watch?v=JZSajBakGK4

https://www.youtube.com/watch?v=Uy-SN5j1ogk

Combined Gas Law:

Boyle’s Law: P1 (V1) = P2 (V2)

Charles’s Law:

Gay-Lussac’s Law:

Gas law only works when the amount of gas is constant.

1 1 2 2

1 2

PV PV

T T

Combined Gas LawExample F pg 375A helium-filled balloon has a volume of 50.0 L at 25°C and 1.08 atm. What volume will it have at 0.855 atm and 10.0°C?Given: V1 of He = 50.0 L

T1 of He = 25°C + 273 = 298 K T2 of He = 10°C + 273 = 283 K P1 of He = 1.08 atm P2 of He = 0.855 atm

Unknown: V2 of He in L

1 1 2 2

1 2

PV PV

T T

1 1 22

2 1

PVTV

PT

1.08atm x 50.5LHe x 283K 0.855atm x 298 = 60.0L He

Sample Combined Gas Law ProblemsA volume of gas is 30.0L at 313K and

153 kPa. What will the new volume be at standard temp. and pressure (STP)? (39.5 L)

A 5.00L air sample has a pressure of 1.07 atm at a temp of -50.0C. If the temp is raised to 102C and the volume expands to 7.00L, what will the new pressure be? (1.29 atm)

Ideal Gas Law: PV = nRTCombined gas law only works when

amount of gas is constant.You can’t use the combined gas law to

compute how many moles you have of a gas at a fixed volume and a known temperature and pressure, so to calculate that the Ideal Gas Law is used

It is expressed by the following equation:

PV = nRTSolve for R when PVT and n= standard

values.

Ideal Gas Law: PV = nRTP = Pressure (kPa)V = Volume (L)n = amount of gas in moles

(mol)R = constant of (8.31 L kPa/K mol )

determined from STP values

T = Temperature (K)Ex I pg 385What is the pressure in atmospheres exerted by a 0.500 mol sample of nitrogen gas in a 10.0 L container at 298 K?

Ex I pg 385What is the pressure in atmospheres exerted by a 0.500 mol sample of nitrogen gas in a 10.0 L container at 298 K?Given: V of N2 = 10.0 L

n of N2 = 0.500 molT of N2 = 298 K

Unknown: P of N2 in atmnRT

PV nRT PV

(0.500 mol)(0.0821 L atm)(298 K)

101

.0 L.22 atmP

Sample Ideal Gas Law Problems

A deep underground cavern contains 2.24 x 106 L of CH4 (methane gas) at a pressure of 1500 kPa and a temp of 315 K. How many moles of CH4 are in the cavern? (1.3 x 106 mol)

◦How many LITERS are in the cavern? Recall that moles can be converted to

grams when the molar mass is known.

Problems to practice…A child’s lungs can hold 2.20 L of air.

How many moles of air do her lungs hold at a pressure of 102 kPa and a body temp. of 37C? (0.0871 mol)

◦ Use a value of 29.0 g/mol for the molar mass of air and calculate the amount of GRAMS of air. (2.53 g)

Real vs. Ideal GasesIdeal gases must follow all the

gas laws at all conditions of pressure and temp. Particles would have no volume and there is not attraction between particles in the gas…no such gas exists

Real gases have volume and there is often attraction between particles.

Explain this…Whose law??Pack Mate—watch until 1:10Elisa’s poor balloonLiquid nitrogen balloonsHow do you fix a dented ping

pong ball?◦start at 0:45 sec—stop at 1:54

You give ME a practical application of one of the gas laws…

Whose Law?

Gay Lussac Law

Whose law?

BOYLE

Whose Law?

Charles’ Law

Name the law…

Combined Gas Law

Name the law…

Boyle’s Law