It’s a Gas

GAS LAWSGAS LAWS

Mr. Trotts2/14/2011

Mr. Trotts2/14/2011

Lesson ObjectivesLesson ObjectivesYou will be able to:•Name and describe 5 characteristics of gases•Identify three differences between ideal gases and real

gases. •Define the term “STP”•List 4 units for pressure measurement •Explain and describe the relationship between

temperature and pressure of gases, according to Charles’ Law.

•Explain and describe the relationship between volume and pressure of gases, according to Boyle’s Law.

•Explain how temperature, pressure, and volume of gases are all related according to the combined gas law.

•Solve mathematic problems about Charles’ Law, Boyle’s Law, and the combined gas law.

Vocabulary: JournalVocabulary: Journal

Pressure VolumeTemperature KelvinBoyle’s Law Charle’s LawIdeal Gas Law STPCombined Gas Law

Pressure VolumeTemperature KelvinBoyle’s Law Charle’s LawIdeal Gas Law STPCombined Gas Law

Test questions: journal

Test questions: journal

1. Describe the 5 characteristics of gases

2. Compare the 3 real and ideal characteristics of gases

1. Describe the 5 characteristics of gases

2. Compare the 3 real and ideal characteristics of gases

What are Characteristics of a

GAS?

What are Characteristics of a

GAS?

: Gas Laws: Gas LawsIn the REAL WORLD:

Gases are fat. (they have mass)Gases hog the sofa.

(they have volume)

Gases are pushy and have an attitude toward

other gases. (they exert forces on each other)

In the REAL WORLD:Gases are fat. (they have mass)Gases hog the sofa.

(they have volume)

Gases are pushy and have an attitude toward

other gases. (they exert forces on each other)

In an IDEAL WORLD:Gases are skinny. (they have no mass)Gases make themselves invisible. (they have no volume)

Gases are not confrontational. (they do not interact… elastic collisions)

In an IDEAL WORLD:Gases are skinny. (they have no mass)Gases make themselves invisible. (they have no volume)

Gases are not confrontational. (they do not interact… elastic collisions)

Image Source: mtv.com

IT’S A GAS…IT’S A GAS…

Daily grade:

1. name those 5 characteristics given 2 slide ago.

2. What were the 3 differences between a real gas (what is really happening) and an ideal gas (assumptions used to make gas laws work)

IT’S A GAS…IT’S A GAS…3. List the physical

characteristics of gases4. Describe the kinetic

molecular theory (KMT)5. List the 3 assumption of

the KMT

3. List the physical characteristics of gases

4. Describe the kinetic molecular theory (KMT)

5. List the 3 assumption of the KMT

Gases have some interesting characteristics that have fascinated scientists for 300 years.The first gas to be studied was air & it was a long time before it was discovered that air was actually a mixture of particles rather than a single gas.

Gases have some interesting characteristics that have fascinated scientists for 300 years.The first gas to be studied was air & it was a long time before it was discovered that air was actually a mixture of particles rather than a single gas.

The Nature of GasesThe Nature of Gases

But this realization did not make the study of gas behavior more difficult.Although air is a mixture of several different gases, it behaves much the same as any single gas.

But this realization did not make the study of gas behavior more difficult.Although air is a mixture of several different gases, it behaves much the same as any single gas.Regardless of their chemical identity, gases tend to exhibit similar physical behaviors

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



Gas particles can be monatomic (Ne), diatomic (N2), or polyatomic (CH4) – but they all have these characteristics in common:

Gas particles can be monatomic (Ne), diatomic (N2), or polyatomic (CH4) – but they all have these characteristics in common: 1) Gases have mass. 1) Gases have mass.

2) Gases are compressible. 2) Gases are compressible. 3) Gases fill their containers. 3) Gases fill their containers. 4) Gases diffuse 4) Gases diffuse 5) Gases exert pressure. 5) Gases exert pressure. 6) Pressure is dependent on

Temp. 6) Pressure is dependent on

Temp.

Kinetic Molecular Theory


There is a theory that modern day chemist’s use to explain the behaviors and characteristics of gases - the Kinetic Molecular Theory of Matter.

• The word kinetic refers to motion.

• The word molecular refers to molecules

There is a theory that modern day chemist’s use to explain the behaviors and characteristics of gases - the Kinetic Molecular Theory of Matter.

• The word kinetic refers to motion.

• The word molecular refers to molecules



The theory states that the tiny particles in all forms of matter in all forms of matter are in constant motion.This theory is used to explain the behaviors common among gasesThere are 3 basic assumptions of the KMT as it applies to gases.

The theory states that the tiny particles in all forms of matter in all forms of matter are in constant motion.This theory is used to explain the behaviors common among gasesThere are 3 basic assumptions of the KMT as it applies to gases.

KMT Assumption #1KMT Assumption #1

A gas is composed of small hard particles.The particles have an insignificant volume and are relatively far apart from one another. There is empty space between particles.No attractive or repulsive forces between particles.

A gas is composed of small hard particles.The particles have an insignificant volume and are relatively far apart from one another. There is empty space between particles.No attractive or repulsive forces between particles.


The particles in a gas move in constant random motion.Particles move in straight paths and are completely independent of each of otherParticles path is only changed by colliding with another particle or the sides of its container.

The particles in a gas move in constant random motion.Particles move in straight paths and are completely independent of each of otherParticles path is only changed by colliding with another particle or the sides of its container.


All collisions a gas particle undergoes are perfectly elastic.No energy is lost from one particle to another, and the total kinetic energy remains constant.

All collisions a gas particle undergoes are perfectly elastic.No energy is lost from one particle to another, and the total kinetic energy remains constant.

6. Compare the density of several gases at STP

7. Describe why gases are compressible

8. Describe the expansion of gases

6. Compare the density of several gases at STP

7. Describe why gases are compressible

8. Describe the expansion of gases

Gases have mass.Gases have mass.

• Gases seem to be weightless, but they are classified as matter, which means they have mass.

• The density of a gas – the mass per unit of volume – is much less than the density of a liquid or solid, however.

• Gases seem to be weightless, but they are classified as matter, which means they have mass.

• The density of a gas – the mass per unit of volume – is much less than the density of a liquid or solid, however.

Gases have mass.Gases have mass.

It’s this very low density that allows us to be able to walk through the room without concerning ourselves with air resistance.Since it is so easy to “swim” across the room we don’t put much thought into the mass of a gas.Really it is only noticeable if we have a large collection of gas in a container.

It’s this very low density that allows us to be able to walk through the room without concerning ourselves with air resistance.Since it is so easy to “swim” across the room we don’t put much thought into the mass of a gas.Really it is only noticeable if we have a large collection of gas in a container.

The Kinetic-Molecular theory explanation of it is that we assume that gases are composed of a collection of particles. You can’t see these particles directly, so they are very tiny, and to notice any mass you must weigh a collection of the particles.It is usually necessary to have a mole or more of gas particles to have significant a significant change in mass.

The Kinetic-Molecular theory explanation of it is that we assume that gases are composed of a collection of particles. You can’t see these particles directly, so they are very tiny, and to notice any mass you must weigh a collection of the particles.It is usually necessary to have a mole or more of gas particles to have significant a significant change in mass.

2nd– Gases “R” squeezable

2nd– Gases “R” squeezable

If you squeeze a gas, its volume can be reduced considerablyA gases low density allows for there to a lot of empty space between gas molecules.

If you squeeze a gas, its volume can be reduced considerablyA gases low density allows for there to a lot of empty space between gas molecules.

Gas particles have a high velocity, relative to their masses.This gives them a lot of energy and movement. The movement causes the gases to spread out, which leaves a lot of space between molecules.That empty space can be compressed by pressure allowing gas particles less room to move around thus decreasing the volume.

Gas particles have a high velocity, relative to their masses.This gives them a lot of energy and movement. The movement causes the gases to spread out, which leaves a lot of space between molecules.That empty space can be compressed by pressure allowing gas particles less room to move around thus decreasing the volume.

This empty space can be compressed simply by adding pressure.We can use this ability of a gas to do work for us. Think of a shocks on a car. You really are riding on a pillow of air.A bump in the road compresses the gas in the shocks until the bump’s energy is absorbed.

This empty space can be compressed simply by adding pressure.We can use this ability of a gas to do work for us. Think of a shocks on a car. You really are riding on a pillow of air.A bump in the road compresses the gas in the shocks until the bump’s energy is absorbed.

3rd – Gases fill their containers

3rd – Gases fill their containers

Gases expand until they take up as much room as they possibly can.Gases spread out to fill containers until the concentration of gases is uniform throughout the entire space.This is why that nowhere around you is there an absence of air.

Gases expand until they take up as much room as they possibly can.Gases spread out to fill containers until the concentration of gases is uniform throughout the entire space.This is why that nowhere around you is there an absence of air.

The Kinetic-Molecular theory alludes to this by the fact that these particles are in constant random motion.Gases move in a straight line until it they collide with other particles or the sides of the container, which causes them to change directions until they collide with something else.This bouncing off of everything around them spread the particles out until they are uniform throughout the entire container.

The Kinetic-Molecular theory alludes to this by the fact that these particles are in constant random motion.Gases move in a straight line until it they collide with other particles or the sides of the container, which causes them to change directions until they collide with something else.This bouncing off of everything around them spread the particles out until they are uniform throughout the entire container.

If I opened up a bag of popcorn in front of the class you would soon be able to smell it in the back.The popcorn smell is a high energy molecule or group of molecules that is in the gas state.There are really two properties going on here:- This property of gases

spreading out until they have filled the room

- And the property of diffusion

If I opened up a bag of popcorn in front of the class you would soon be able to smell it in the back.The popcorn smell is a high energy molecule or group of molecules that is in the gas state.There are really two properties going on here:- This property of gases

spreading out until they have filled the room

- And the property of diffusion

Explain why when adding air to a balloon it will stop at a certain volume, and then when adding more air gets bigger and stops at a new volume

Explain why when adding air to a balloon it will stop at a certain volume, and then when adding more air gets bigger and stops at a new volume

9. What is meant by gases diffuse?

10.Explain how gases exert pressure

9. What is meant by gases diffuse?

10.Explain how gases exert pressure

4th – Gases diffuse4th – Gases diffuse

Gases can move through each other rapidly.The movement of one substance through another is called diffusion.Because of all of the empty space between gas molecules, another gas molecule can pass between them until each gas is spread out over the entire container.

Gases can move through each other rapidly.The movement of one substance through another is called diffusion.Because of all of the empty space between gas molecules, another gas molecule can pass between them until each gas is spread out over the entire container.

The same logic from the observation that gases spread out applies here.If the gases are in constant random motion the fact that they are moving and colliding with everything around them then they will mix with other gases uniformly. This doesn’t happen at the same speeds for all gases though.Some gases diffuse more rapidly then other gases based on their size and their energy.

The same logic from the observation that gases spread out applies here.If the gases are in constant random motion the fact that they are moving and colliding with everything around them then they will mix with other gases uniformly. This doesn’t happen at the same speeds for all gases though.Some gases diffuse more rapidly then other gases based on their size and their energy.

Diffusion explains why gases are able to spread out to fill their containers.It’s why we can all breath oxygen anywhere in the room.It also helps us avoid potential odoriferous problems.

Diffusion explains why gases are able to spread out to fill their containers.It’s why we can all breath oxygen anywhere in the room.It also helps us avoid potential odoriferous problems.

5th – Gases exert pressure

5th – Gases exert pressure

The sum of all of the collisions makes up the pressure the gas exerts.

The sum of all of the collisions makes up the pressure the gas exerts.

Gas particles exert pressure by colliding with objects in their path.

Gas particles exert pressure by colliding with objects in their path.

The Kinetic-Molecular theory alludes to this by the fact that these particles are colliding with anything in their path.Imagine a gas in a container as a room of hard rubber balls.The collisions of the balls bouncing around exert a force on the object that with which they collide.The definition of a pressure is a force per unit area – so the total of all of the tiny collisions makes up the pressure exerted by the gas.

The Kinetic-Molecular theory alludes to this by the fact that these particles are colliding with anything in their path.Imagine a gas in a container as a room of hard rubber balls.The collisions of the balls bouncing around exert a force on the object that with which they collide.The definition of a pressure is a force per unit area – so the total of all of the tiny collisions makes up the pressure exerted by the gas.

The gases push against the walls of their containers with a force.The pressure of gases is what keeps our tires inflated, makes our basketballs bounce, makes hairspray come out of the can, etc.

The gases push against the walls of their containers with a force.The pressure of gases is what keeps our tires inflated, makes our basketballs bounce, makes hairspray come out of the can, etc.

11.Desribe what happens to the gases in a fixed volume container as the temperature is increased

12.Give examples

11.Desribe what happens to the gases in a fixed volume container as the temperature is increased

12.Give examples

6th – Pressure depends on Temp


The higher the temperature of a gas -the higher the pressure that the gas exertsThe reverse of that is true as well, a the temperature of a gas decreases – the pressure decreases.Think about the pressure of a set of tires on a car

The higher the temperature of a gas -the higher the pressure that the gas exertsThe reverse of that is true as well, a the temperature of a gas decreases – the pressure decreases.Think about the pressure of a set of tires on a car

Pressure Gauge

Pressure Gauge

Today’s temp: 35°FToday’s temp: 35°F

Pressure Gauge

Pressure Gauge

Today’s temp: 85°FToday’s temp: 85°F



The reverse of that is true as well, a the temperature of a gas decreases – the pressure decreases.Think about the pressure of a set of tires on a car

The reverse of that is true as well, a the temperature of a gas decreases – the pressure decreases.Think about the pressure of a set of tires on a car

- the average kinetic energy of the particles that make up an object

- the average kinetic energy of the particles that make up an object

Do you recall the definition of temperature?Do you recall the definition of temperature?

The higher the temperature the more the energyThe more the energy the more impacts the gases administerThe more the impacts or collisions the more the pressure exerted.

The higher the temperature the more the energyThe more the energy the more impacts the gases administerThe more the impacts or collisions the more the pressure exerted.

The pressure increases when temperature increases because the molecules are moving with greater speed and colliding against the sides of their containers more often.Therefore, the pressure inside that container is greater, because there are more collisions.

The pressure increases when temperature increases because the molecules are moving with greater speed and colliding against the sides of their containers more often.Therefore, the pressure inside that container is greater, because there are more collisions.

13. What variables effect the characteristics of gases?

14.Describe these variables15.What is STP?

13. What variables effect the characteristics of gases?

14.Describe these variables15.What is STP?

Measuring GasesMeasuring Gases

The conditions under which a gas is studied is very important to its behavior.Experimental work in chemistry requires the measurement of such quantities as volume, temperature, pressure, and the amount of sample.These quantities are called variables and if they are not accounted for then the results of the experiment might be jeopardized.

The conditions under which a gas is studied is very important to its behavior.Experimental work in chemistry requires the measurement of such quantities as volume, temperature, pressure, and the amount of sample.These quantities are called variables and if they are not accounted for then the results of the experiment might be jeopardized.

Gas variablesGas variables

In order to describe a gas sample completely and then make predictions about its behavior under changed conditions, it is important to deal with the values of:

In order to describe a gas sample completely and then make predictions about its behavior under changed conditions, it is important to deal with the values of: 1) amount of gas 1) amount of gas

2) volume 2) volume 3) temperature 3) temperature 4) pressure 4) pressure

Amount (n)Amount (n)

The quantity of gas in a given sample expressed in terms of moles of gas.This of course is in terms of 6.02 x 1023 molecules of the gas. Don’t forget to convert mass to moles you just divide by the molar mass of the gas.

The quantity of gas in a given sample expressed in terms of moles of gas.This of course is in terms of 6.02 x 1023 molecules of the gas. Don’t forget to convert mass to moles you just divide by the molar mass of the gas.

Volume (V)Volume (V)

The volume of the gas is simply the volume of the container it is contained in.The metric unit of volume is the liter (L)There might also be problems that use cubic meters as the unit for volume.- 1 L = 1 dm3

The volume of the gas is simply the volume of the container it is contained in.The metric unit of volume is the liter (L)There might also be problems that use cubic meters as the unit for volume.- 1 L = 1 dm3

Temperature (T)Temperature (T)

The temperature of a gas is generally measured with a thermometer in Celsius. All calculations involving gases should be made after converting the Celsius to Kelvin temperature.

The temperature of a gas is generally measured with a thermometer in Celsius. All calculations involving gases should be made after converting the Celsius to Kelvin temperature.

Kelvin = C° + 273

Kelvin = C° + 273

Pressure (Pressure (PP))

The pressure of a gas is the force exerted on the wall of the container a gas is trapped in.There are several units for pressure depending on the instrument used to measure it including:

The pressure of a gas is the force exerted on the wall of the container a gas is trapped in.There are several units for pressure depending on the instrument used to measure it including: 1) atmospheres

(atm) 1) atmospheres

(atm) 2) Millimeters of Mercury (mmHg)

2) Millimeters of Mercury (mmHg) 3) Kilopascal (kPa) 3) Kilopascal (kPa)

S T PS T PS T PS T P

The behavior of a gas depends very strongly on the temperature and the pressure at which the gas is held.To make it easier to discuss the behavior of a gas, it is convenient to designate standard conditions, called STP.

The behavior of a gas depends very strongly on the temperature and the pressure at which the gas is held.To make it easier to discuss the behavior of a gas, it is convenient to designate standard conditions, called STP. - Temperature = 0°C or 273K- Temperature = 0°C or 273K

- Pressure = 1atm or 760mmHg or 101.3kPa- Pressure = 1atm or 760mmHg or 101.3kPa

16.What causes atmospheric pressure to vary?

17.1 atmosphere of pressure = how many mmHg, pascals, torres?

16.What causes atmospheric pressure to vary?

17.1 atmosphere of pressure = how many mmHg, pascals, torres?

Atmospheric Atmospheric PressurePressure

The gases in the air are exerting a pressure called atmospheric pressureAtmospheric pressure is a result of the fact that air has mass is and is attracted by gravity producing a force.Knowing this atmospheric pressure and predicting changes in the atmospheric pressure is how forecasters predict the weather.

The gases in the air are exerting a pressure called atmospheric pressureAtmospheric pressure is a result of the fact that air has mass is and is attracted by gravity producing a force.Knowing this atmospheric pressure and predicting changes in the atmospheric pressure is how forecasters predict the weather.

Atmospheric Atmospheric PressurePressure

Atmospheric pressure varies with altitude - the lower the altitude, the longer and heavier is the column of air above an area of the earth.

Look on the back of a box of cake mix for the difference in baking times based on the atmospheric pressure in your region.

Atmospheric pressure varies with altitude - the lower the altitude, the longer and heavier is the column of air above an area of the earth.

Look on the back of a box of cake mix for the difference in baking times based on the atmospheric pressure in your region.

1 atm = 760mmHg = 760 torr = 101.3kPa

Atmospheric PressureAtmospheric Pressure

Low pressure or dropping pressure indicates a change of weather from fair to rain.High pressure is an indication of clear skies and sun.It all has to do with the amount of air pressing down on us.

Low pressure or dropping pressure indicates a change of weather from fair to rain.High pressure is an indication of clear skies and sun.It all has to do with the amount of air pressing down on us.

Boyle’s LawBoyle’s Law

Boyle’s Law:18. Variables = ?19. Constant = ?20. Formula = ?21. Examples of system

Boyle’s Law:18. Variables = ?19. Constant = ?20. Formula = ?21. Examples of system

Gas LawsGas Laws

Studies of the behavior of gases played a major role in the development of physical sciences in the 7th and 8th centuries.The Kinetic Molecular theory marked a significant achievement in understanding the behavior of gases.Observations have become mathematical laws which we can use to predict quantitative outcomes.

Studies of the behavior of gases played a major role in the development of physical sciences in the 7th and 8th centuries.The Kinetic Molecular theory marked a significant achievement in understanding the behavior of gases.Observations have become mathematical laws which we can use to predict quantitative outcomes.

Boyle’s LawBoyle’s Law

Robert Boyle was among the first to note the relationship between pressure and volume of a gas.He measured the volume of air at different pressures, and observed a pattern of behavior which led to his mathematical law.During his experiments Temperature and amount of gas weren’t allowed to change

Robert Boyle was among the first to note the relationship between pressure and volume of a gas.He measured the volume of air at different pressures, and observed a pattern of behavior which led to his mathematical law.During his experiments Temperature and amount of gas weren’t allowed to change

As the pressure increases

As the pressure increases

VolumedecreasesVolume

decreases

22. How does Pressure and Volume of gases relate

graphically?

22. How does Pressure and Volume of gases relate

graphically?

Volu

me

Volu

me

PressurePressure

PV = kPV = k

Temperature, # of particlesremain constant

Temperature, # of particlesremain constant

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

since PV = ksince PV = k

P1V1 = P2V2P1V1 = P2V2

Eg: A gas has a volume of 3.0 L at 2 atm. What is its volume

at 4 atm?

Eg: A gas has a volume of 3.0 L at 2 atm. What is its volume

at 4 atm?

What if we had a change in conditions?What if we had a change in conditions?

1)determine which variables you have:


P and V = Boyle’s LawP and V = Boyle’s Law

2)determine which law is being represented:


P1 = 2 atm

V1 = 3.0 L P2 = 4

atm V2 = ?

P1 = 2 atm

V1 = 3.0 L P2 = 4

atm V2 = ?

3) Rearrange the equation for the variable you don’t know

3) Rearrange the equation for the variable you don’t know

4) Plug in the variables and chug it on a calculator:

4) Plug in the variables and chug it on a calculator:

P1V1 = V2P1V1 = V2

P2P2

(2.0 atm)(3.0L) = V2(2.0 atm)(3.0L) = V2

(4atm)(4atm)V2 = 1.5LV2 = 1.5L

Complete practice sheet on Boyle’s Law

Complete practice sheet on Boyle’s Law

Charle’s LawCharle’s Law

Charle’s Law23. Variable’s = ?24. Constant = ?25. Formula = ?26. Example of system

Charle’s Law23. Variable’s = ?24. Constant = ?25. Formula = ?26. Example of system

Charles’s LawCharles’s Law

Jacques Charles determined the relationship between temperature and volume of a gas.He measured the volume of air at different temperatures, and observed a pattern of behavior which led to his mathematical law.During his experiments pressure of the system and amount of gas were held constant.

Jacques Charles determined the relationship between temperature and volume of a gas.He measured the volume of air at different temperatures, and observed a pattern of behavior which led to his mathematical law.During his experiments pressure of the system and amount of gas were held constant.

Volume of balloon at

room temperature

Volume of balloon at

room temperature

Volume of balloon at 5°C

Volume of balloon at 5°C

Temp

27. How does Temperature and Volume of gases relate

graphically?

27. How does Temperature and Volume of gases relate

graphically?V

olu

me V/T = k

Pressure, # of particlesremain constant

Pressure, # of particlesremain constant

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

since V/T = ksince V/T = k

Eg: A gas has a volume of 3.0 L at 127°C. What is its volume at

227 °C?

Eg: A gas has a volume of 3.0 L at 127°C. What is its volume at

227 °C?

V1 V2

T1 T2

=




T and V = Charles’s LawT and V = Charles’s Law



T1 = 127°C + 273 = 400K

V1 = 3.0 L T2 = 227°C + 273 =

5ooK V2 = ?

T1 = 127°C + 273 = 400K

V1 = 3.0 L T2 = 227°C + 273 =

5ooK V2 = ?

4) Plug in the variables:


(500K)(3.0L) = V2 (400K)(500K)(3.0L) = V2 (400K)

V2 = 3.8LV2 = 3.8L

3.0L V23.0L V2

400K 500K400K 500K

=

=5) Cross multiply and

chug5) Cross multiply and

chug

Complete practice sheet on Charle’s Law

Complete practice sheet on Charle’s Law

Gay-Lussac’s LawGay-Lussac’s Law

Gay –Lussac’s Law:28. Variables = ?29. Constant = ?30. Formula = ?31. Example of system

Gay –Lussac’s Law:28. Variables = ?29. Constant = ?30. Formula = ?31. Example of system

Gay Lussac’s LawGay Lussac’s Law

Old man Lussac determined the relationship between temperature and pressure of a gas.He measured the temperature of air at different pressures, and observed a pattern of behavior which led to his mathematical law.During his experiments volume of the system and amount of gas were held constant.

Old man Lussac determined the relationship between temperature and pressure of a gas.He measured the temperature of air at different pressures, and observed a pattern of behavior which led to his mathematical law.During his experiments volume of the system and amount of gas were held constant.

Pressure Gauge

Pressure Gauge

Car before a tripCar before a trip

Think of a tire...Think of a tire...

Let’s get onthe road

Dude!

Car after a long tripCar after a long trip

Think of a tire...Think of a tire...

WHEW!

Pressure Gauge

Pressure Gauge

Temp

Pre

ssu

re

32. How does Pressure and Temperature of gases relate

graphically?

32. How does Pressure and Temperature of gases relate

graphically?

P/T = k

Volume, # of particlesremain constant

Volume, # of particlesremain constant

Lussac’s Mathematical Law:Lussac’s Mathematical Law:


since P/T = ksince P/T = k

P1 P2

T1 T2

=

Eg: A gas has a pressure of 3.0 atm at 127º C. What is its pressure at 227º C?

Eg: A gas has a pressure of 3.0 atm at 127º C. What is its pressure at 227º C?

T and P = Gay-Lussac’s LawT and P = Gay-Lussac’s Law

T1 = 127°C + 273 =

400K P1 = 3.0 atm T2 = 227°C + 273 =

500K P2 = ?

T1 = 127°C + 273 =

400K P1 = 3.0 atm T2 = 227°C + 273 =

500K P2 = ?







(500K)(3.0atm) = P2 (400K)(500K)(3.0atm) = P2 (400K)

P2 = 3.8atmP2 = 3.8atm

3.0atm P23.0atm P2

400K 500K400K 500K

=

=5) Cross multiply and

chug5) Cross multiply and

chug

Complete practice sheet on Gay-Lussac’s Law

Complete practice sheet on Gay-Lussac’s Law

LAWLAW RELAT-RELAT-IONSHIPIONSHIP LAWLAW CON-CON-

STANTSTANT

Boyle’sBoyle’s PP V V PP11VV1 1 = P= P22VV22 T, nT, n

CharlesCharles’’

VV T TVV11/T/T11 = = VV22/T/T22

P, nP, n

Gay-Gay-Lussac’Lussac’

ssPP T T

PP11/T/T11 = = PP22/T/T22

V, nV, n

Combined Gas LawCombined Gas Law

Combined Gas Law:33.Variables34.Constant35.Formula

Combined Gas Law:33.Variables34.Constant35.Formula

…THEREFORE:…THEREFORE:

Temperature, Volume, and Pressure are all related!

Temperature, Volume, and Pressure are all related!

=

V1

T1

P1V2

T2

P2

PracticePractice100.0 cm3 oxygen at 10.50 kPa changes to 9.91 kPa. What is the new volume of the gas?

1.

=V1

T1

P1 V2

T2

P2

=V1P1 V2P2

(100.0 cm3 O2)x(10.50 kPa) = (9.91 kPa) (V2)x

V2 = (100.0 cm3 O2)x(10.50 kPa)

(9.91 kPa)

= 106 cm3 O2

Boyle’s Law!

(150.0 mL SO2)(748 mmHg)

(140.6 mL SO2)

P2 = =

PracticePractice2. 150.0 mL sulfur dioxide at 748 mmHg changes

to a new volume of 140.6 mL. What is the new pressure of the gas?

V1

T1

V2

T2

=P1 P2

V1 V2=P1 P2

=

798 mmHg

x(748 mmHg)

(150.0 mL SO2) (P2) x (140.6 mL SO2)

Complete practice sheet on Combined Gas Law

Complete practice sheet on Combined Gas Law

The Ideal Gas Law & Co.

The Ideal Gas Law & Co.Mr.

Trotts Feb

2011

Mr. Trotts Feb

2011

A Reminder…

A Reminder…

We that we live in an world where:

Gas particles have no mass

Gas particles have no volume

Gas particles have elastic collisions

We that we live in an world where:

Gas particles have no mass

Gas particles have no volume

Gas particles have elastic collisionsThese assumptions are used when trying to calculate the AMOUNT of a gas we have!

Why are these assumptions important?

Why are these assumptions important?

PV = nRTImage source: thefreedictionary.com

Image source: popartuk.com

PV = nRTPV = nRT

P

V

n

R

T

RESSURE

OLUME

MOLES OF GAS

GAS CONSTANT

EMPERATURE

The MysteRious R

The MysteRious R

Image source: toysrusemail.com

• R is a constant (doesn’t change).

• Number value of R depends on other units.

• Units of R are a combination of many units.

0.0821 atm · Lmol · K

8.31 kPa · Lmol · K

62.4 mmHg · Lmol · K

Ummm… What?Ummm… What?PV = nRT

Solve for R:

R = P Vn T

R =

Plug in units:

(mm Hg) L)

(mol) (K)

(kPa)(atm) (L)atm)

!!V1

T1

=V2

T2

P1 x V1 = P2 x V2

P1 V1 P2 V2=T1 T2

e

P V = n RT

Used with only ONE SET OF CONDITIONS

When to Use PV = nRT

When to Use PV = nRT

Calculating amount of gas in molesCalculating P, V, or T if moles of gas are known. IMPORTANT! We must have 3 out of 4 pieces of information:

PVnT

Calculating amount of gas in molesCalculating P, V, or T if moles of gas are known. IMPORTANT! We must have 3 out of 4 pieces of information:

PVnT

Practice with the Ideal Gas Law


1. A gas sample occupies 2.62 L at 285ºC and 3.42 atm. How many moles are present in this sample?

PV = nRT

n = P VR T

n =(3.42 atm) (2.62

L)0.0821 L · atm

mol · K

(558 K)= 0.196 mol

But Let’s Be Practical…

But Let’s Be Practical…

We don’t usually measure in moles!

We usually measure quantities in GRAMS!

PV = nRT PVM = gRT

PVM = gRTPVM = gRTRESSUREOLUME

OLAR MASS OF GAS (g/mol)

GAS CONSTANT

EMPERATURE

P

V

M

R

T

g RAMS OF GAS

Image source: popartuk.com



A balloon is filled with 0.2494 g of helium to a pressure of 1.26 atm. If the desired volume of the balloon is 1.250 L, what must the temperature be in ºC?

PVM = gRT T =P V M

g R

T =

(1.26 atm) (1.250 L) 4.00 gmol

0.0821 L · atm

mol · K

(0.2494 g)

= 308 K

35 ºC

- 273

PV=nRT vs. PVM=gRT

PV=nRT vs. PVM=gRT

Use PV=nRT when:You are given moles in the problem.You are searching for moles as an

answer.

Use PVM=gRT when:You are given grams in the

problem.You are searching for grams as an

answer.

Use PV=nRT when:You are given moles in the problem.You are searching for moles as an

answer.

Use PVM=gRT when:You are given grams in the

problem.You are searching for grams as an

answer.

What Else Happens Under Unchanging Conditions?What Else Happens Under Unchanging Conditions?

At constant V and T, pressure is easy to calculate!

Total Pressure = Pressure of gas 1 + Pressure of gas 2 + Pressure of gas 3 + Pressure of gas 4 …

Ptotal = P1 + P2 + P3 + …

“The sum of the individual pressures is equal to the total pressure.”

Partial Pressures PracticePartial Pressures PracticeA sample of hydrogen gas is collected over water at 25ºC. The vapor pressure of water at 25ºC is 23.8 mmHg. If the total pressure is 523.8 mmHg, what is the partial pressure of the hydrogen?

Source: 2003 EOC Chemistry Exam

Ptotal = PH2 + PH2O

23.8 mm Hg

523.8 mm Hg = PH2+

PH2= 500.0 mm Hg

What do Changing Conditions

Affect?What do Changing Conditions

Affect?

If MASS remains constant…

…But VOLUME changes…

Then DENSITY CHANGES! D = M

V

We have learned that we can change 3 variables: Temperature, Volume, and Pressure.

Two Types of Density Problems:Two Types of Density Problems:

At STP: Not at STP:

• molar volume of any gas at STP =

• Density at STP =

molar volume

• Determine new volume (V2

) using Combined Gas Law

molar mass

P1 V1 P2 V2=T1 T2

• Density at non-STP =

molar mass

V222.4LLiters

Practice with Density Problems:

Practice with Density Problems:

Determine the density of ethane (C2H6) at STP:

molar mass

D (at STP) =

molar mass = 30.08 g

molar volume = 22.4 L

D = 30.08 g

22.4 L= 1.34 g/L

Determine the density of C2H6 at 3.0 atm and 41ºC.

molar volume

P1 V1 P2 V2=T1 T2

V2 = P1 V1 T2

T1 P2

V2 = 8.6 L

P1 = 1.0 atm

V1 = 22.4 L

T1 = 273 K

P2 = 3.0 atm

V2 = ?

T2 = 314 K

V2 = (1.0 atm) (22.4 L) (314 K) (273 K) (3.0

atm)

V2 == 8.6 L 8.6 LD = molar mass

V2

D = 30.08 gg8.6 L

3.5 g/L=

It’s a Gas

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