Pressure – Volume Pressure – Volume RelationshipRelationship

A4 – A8A4 – A8

PressurePressure

Force applied to one unit of surface areaForce applied to one unit of surface area

Pressure = Pressure = ForceForce Area Area

Which hurts more?Which hurts more?

High heeled shoe, why?High heeled shoe, why?

More thoughts…More thoughts…1.1. When on thin ice should you lay When on thin ice should you lay

out and crawl or run like mad?out and crawl or run like mad?2.2. More pressure – a woman in high More pressure – a woman in high

heels or an elephant? heels or an elephant? 3.3. How many different ways could How many different ways could

you increase tire pressure? you increase tire pressure? 4.4. Which way will the book exert the Which way will the book exert the

most pressure flat or up and most pressure flat or up and down?down?

5.5. Which is the best tool for chopping Which is the best tool for chopping wood – a hammer or an ax of the wood – a hammer or an ax of the same weight? same weight?

6.6. Mud tires – Skinny or Wide? Mud tires – Skinny or Wide? 7.7. Bed of nails – 200 or 20 more Bed of nails – 200 or 20 more

comfortable? comfortable?

In a gas, pressure is…In a gas, pressure is…Caused by particles colliding with the sides of Caused by particles colliding with the sides of the container. the container.

The more collisions The more collisions particles have the particles have the greater the greater the pressure.pressure.

Units of PressureUnits of Pressure

psi (pounds per square inch)psi (pounds per square inch)

atm (atmospheres)atm (atmospheres)

mmHg (mm of Mercury)mmHg (mm of Mercury)

kPa (kiloPascal)kPa (kiloPascal)

Pa (Pascal)Pa (Pascal)

torrtorr

VolumeVolumeThe amount of space occupied by a The amount of space occupied by a

substancesubstanceIf a gas is a non-rigid container then its If a gas is a non-rigid container then its

volume can change.volume can change.Ex of non-rigid: balloonEx of non-rigid: balloon

If a gas is in a rigid container then its volume If a gas is in a rigid container then its volume cannot change.cannot change.

Rigid container: steel canisterRigid container: steel canister

Units of VolumeUnits of Volume

mL (milliliters)mL (milliliters)

L (Liters)L (Liters)

cmcm33 or cc (cubic centimeters) or cc (cubic centimeters)

How are pressure How are pressure and volume related and volume related when temperature when temperature is held constant?is held constant?

Robert Boyle (Robert Boyle (1627-91 )1627-91 )

BoyleBoyle’’s Laws Law

At constant temperature, the product of At constant temperature, the product of the pressure and the volume of a gas the pressure and the volume of a gas

sample is a constant value.sample is a constant value.

BoyleBoyle’’s Laws Lawexplained using kinetic molecular theoryexplained using kinetic molecular theory

Relates pressure to volumeRelates pressure to volume

When you make the volume of a container When you make the volume of a container smaller:smaller:

Particles get closer togetherParticles get closer together

Therefore having more collisionsTherefore having more collisions

Which results in higher pressure.Which results in higher pressure.

So when V decreases, Pressure increases.So when V decreases, Pressure increases.

BoyleBoyle’’s Laws Law

An example of this:An example of this:

Think about the marshmallows in the syringe. Think about the marshmallows in the syringe. You pushed down on the syringe what You pushed down on the syringe what

happened to the marshmallows?happened to the marshmallows?

They got smaller – why? By pushing down They got smaller – why? By pushing down on the syringe you were increasing pressure, on the syringe you were increasing pressure, forcing the air particles in the marshmallow to forcing the air particles in the marshmallow to

get closer together.get closer together.

An inverse relationship is when one variable An inverse relationship is when one variable increases and the other variable decreases. increases and the other variable decreases. They arenThey aren’’t doing the same thing.t doing the same thing.

BoyleBoyle’’s Laws Law

In Equation form:In Equation form:

PP11VV11 = P = P22VV22

Temperature must be held constant!Temperature must be held constant!

We also assume that the number of gas We also assume that the number of gas molecules remains constant.molecules remains constant.

Practice with BoylePractice with Boyle’’s Laws LawGiven the following data find the missing Given the following data find the missing

variable.variable.

PP11 = 500mmHg = 500mmHg V V11 = 250mL = 250mL

PP22 = 1000 mmHg V = 1000 mmHg V22 = = ??

Practice with BoylePractice with Boyle’’s Laws LawA certain steel gas tank in a chemistry laboratory has a A certain steel gas tank in a chemistry laboratory has a

volume of 2.5L and it contains oxygen gas at a pressure volume of 2.5L and it contains oxygen gas at a pressure of 45atm. What volume would the gas from such a tank of 45atm. What volume would the gas from such a tank occupy at the classroomoccupy at the classroom’’s pressure, 1 atm? Assume the s pressure, 1 atm? Assume the

temperature remains constant.temperature remains constant.

Volume – Temperature Volume – Temperature RelationshipRelationship

Review - VolumeReview - Volume

The amount of space occupied by a The amount of space occupied by a substancesubstance

Units:Units:

mL (milliliters)mL (milliliters)

L (Liters)L (Liters)

cmcm33 or cc (cubic centimeters) or cc (cubic centimeters)

TemperatureTemperature

Extent of Extent of ““hotnesshotness”” or or ““coldnesscoldness”” of a of a sample, which is related to the kinetic energy sample, which is related to the kinetic energy

of the particlesof the particles

Increase in temperature meansIncrease in temperature means

more movement and greater kinetic energymore movement and greater kinetic energy

UnitsUnits

˚F, ˚C, and K˚F, ˚C, and K

Temperature vs Volume of a Gas

0

2

4

6

8

10

12

-300 -250 -200 -150 -100 -50 0 50 100

Temperature (degrees C)

Volum

e (L)

5 g of oxygen

10 g of oxygen

5 g of nitrogen

10 g of nitrgoen

Lord KelvinLord Kelvin

0K is absolute zero0K is absolute zero

Scientists believe this is the temp Scientists believe this is the temp were all particle motion stops were all particle motion stops and the volume of the gas is 0.and the volume of the gas is 0.

0K = -2730K = -273˚C˚C

Therefore to convert from ˚C to KTherefore to convert from ˚C to K

K = ˚C + 273K = ˚C + 273

WORD!

How are volume How are volume and temperature and temperature

related when related when pressure is held pressure is held

constant?constant?

CharlesCharles’’ Law LawThe volume of a gas sample at constant The volume of a gas sample at constant

pressure is directly proportional to its kelvin pressure is directly proportional to its kelvin temperaturetemperature

CharlesCharles’’ Law Law explained using kinetic molecular theoryexplained using kinetic molecular theory

As you increase the temperature:As you increase the temperature:

Particles move fasterParticles move faster

In order for pressure to remain constant those In order for pressure to remain constant those particles will have to move further awayparticles will have to move further away

Which results in larger volumeWhich results in larger volume

So when Temperature increases, Volume So when Temperature increases, Volume increases.increases.

ChuckChuck’’s Laws Law

0 Kelvin's = -273 C

pv simulaiton

sterling engine

CharlesCharles’’ Law Law

Think about the balloon you put in the hot pot Think about the balloon you put in the hot pot of water. What happened to it?of water. What happened to it?

It got bigger – why? It got bigger – why?

When the balloon is placed in the hot water, When the balloon is placed in the hot water, the air inside the balloon warms. As it warms the air inside the balloon warms. As it warms

the particles move faster causing it to the particles move faster causing it to expand.expand.

CharlesCharles’’ Law LawIn Equation form:In Equation form:

VV11 = = VV22 T T1 1

TT2 2

Pressure must be held constant!Pressure must be held constant!

Number of molecules must be the same.Number of molecules must be the same.

Temperature MUST be in Kelvin!Temperature MUST be in Kelvin!

Practice with CharlesPractice with Charles’’ Law LawIn the party store a balloon contains 3200mL of In the party store a balloon contains 3200mL of

helium gas at 18helium gas at 18C (65 C (65 F). What is the new F). What is the new volume of the balloon when you take it outside volume of the balloon when you take it outside

on a hot summer day 38on a hot summer day 38C (100 C (100 F)? F)?

Assume that the pressure remains constant.Assume that the pressure remains constant.

Practice with CharlesPractice with Charles’’ Law LawIf a sample of gas has a volume of 1000 mL when If a sample of gas has a volume of 1000 mL when

the pressure is 720 mmHg, what is its pressure the pressure is 720 mmHg, what is its pressure when the volume has been reduced to 500mL? when the volume has been reduced to 500mL?

Assume that the pressure remains constant.Assume that the pressure remains constant.

Temperature - Pressure Temperature - Pressure Relationship Relationship

A13A13

PressurePressureForced exerted by a gas Forced exerted by a gas which is caused by particle which is caused by particle colliding with the sides of the colliding with the sides of the container.container.

UnitsUnitspsi (pounds per square inch)psi (pounds per square inch)atm (atmospheres)atm (atmospheres)mmHg (mm of Mercury)mmHg (mm of Mercury)kPa (kiloPascal)kPa (kiloPascal)Pa (Pascal)Pa (Pascal)

TemperatureTemperature

Extent of Extent of ““hotnesshotness”” or or ““coldnesscoldness”” of a of a sample.sample.

Temperature MUST be in Kelvin!Temperature MUST be in Kelvin!

K = K = ˚C + 273˚C + 273

Gay LussacGay Lussac’’s Laws Law

The pressure of a gas sample at constant The pressure of a gas sample at constant volume is directly proportional to its kelvin volume is directly proportional to its kelvin

temperaturetemperature

Gay LussacGay Lussac’’s Laws Law explained using kinetic molecular theoryexplained using kinetic molecular theory

As temperature increasesAs temperature increases

Gas particles move fasterGas particles move faster

If in a rigid container, volume CANNOT changeIf in a rigid container, volume CANNOT change

Resulting in more collisionsResulting in more collisions

Creating a higher pressureCreating a higher pressure

Why does the Why does the label on this label on this can warn the can warn the user to not user to not put it in a put it in a

fire?fire?

What can What can happen to a car happen to a car

tire on a hot tire on a hot summer day, summer day,

especially if you especially if you have traveled for have traveled for many hundreds many hundreds

of miles? of miles?

Gay LussacGay Lussac’’s Laws LawIn Equation form:In Equation form:

PP11 = = PP2 2 T T1 1

TT2 2

Volume must be held constant!Volume must be held constant!

Number of molecules cannot change.Number of molecules cannot change.

Temperature MUST be in Kelvin!Temperature MUST be in Kelvin!

Practice Gay LussacPractice Gay Lussac’’s Laws Law

The gas in an aerosol can is at a pressure of 3.0 The gas in an aerosol can is at a pressure of 3.0 atm and 25 atm and 25 C. Directions on the can warn the C. Directions on the can warn the user NOT to keep the can in a place where the user NOT to keep the can in a place where the temperature can exceed 52temperature can exceed 52C (125C (125F). What F). What

would the gas pressure be at 52would the gas pressure be at 52C that causes C that causes the can to explode?the can to explode?

Practice with BoylePractice with Boyle’’s Laws LawWhat pressure is required to reduce the volume of a sample of What pressure is required to reduce the volume of a sample of

air from 1.0L to .25 L? The original pressure on the air from 1.0L to .25 L? The original pressure on the sample is 1.5 atm. Assume the temperature of the sample is 1.5 atm. Assume the temperature of the

sample remains constant.sample remains constant.

CharlesCharles’’ Law Data Law Data

TempTemp VolumeVolume

-5˚C-5˚C   

-5˚C-5˚C   

-5˚C-5˚C   

-5˚C-5˚C   

-5˚C-5˚C   

-5˚C-5˚C   

-5˚C-5˚C   

-5˚C-5˚C   

TempTemp VolumeVolume

100˚C100˚C   

100˚C100˚C   

100˚C100˚C   

100˚C100˚C   

100˚C100˚C   

100˚C100˚C   

100˚C100˚C   

100˚C100˚C