Gas Laws

Kinetic TheoryKinetic Theory

True for ideal gases. True for ideal gases.

1. Gas molecules don’t 1. Gas molecules don’t attract or repel each otherattract or repel each other

2. Particles are smaller than 2. Particles are smaller than the space between themthe space between themThey don’t have volumeThey don’t have volume

Kinetic TheoryKinetic Theory3. Constant Random motion3. Constant Random motion

4. No kinetic energy is lost when 4. No kinetic energy is lost when molecules collide—elastic collisionmolecules collide—elastic collision

5.5. All gases have same energy at a All gases have same energy at a particular temperature.particular temperature.

**Actual gases don’t really obey all **Actual gases don’t really obey all of these assumptions—But it’s of these assumptions—But it’s close enough!!**close enough!!**

B. Real GasesB. Real Gases

Particles in a REAL gas…Particles in a REAL gas… have their own volumehave their own volume attract each otherattract each other

Gas behavior is most ideal…Gas behavior is most ideal… at low pressuresat low pressures at high temperaturesat high temperatures in nonpolar atoms/moleculesin nonpolar atoms/molecules

C. Characteristics of GasesC. Characteristics of Gases

Gases expand to fill any container.Gases expand to fill any container. random motion, no attractionrandom motion, no attraction

Gases are fluids (like liquids).Gases are fluids (like liquids). no attractionno attraction

Gases have very low densities.Gases have very low densities. no volume = lots of empty spaceno volume = lots of empty space

C. Characteristics of GasesC. Characteristics of Gases

Gases can be compressed.Gases can be compressed. no volume = lots of empty spaceno volume = lots of empty space

Gases undergo diffusion & effusion.Gases undergo diffusion & effusion. random motionrandom motion

The Gas LawsThe Gas Laws Describe HOW gases behave.Describe HOW gases behave. Can be predicted by the Can be predicted by the

theory.theory. Amount of change can be Amount of change can be

calculated with calculated with mathematical equations.mathematical equations.

E. PressureE. Pressure

area

forcepressure

Which shoes create the most pressure?

E. PressureE. Pressure BarometerBarometer

measures atmospheric pressuremeasures atmospheric pressure

Mercury Barometer

Aneroid Barometer

E. PressureE. Pressure ManometerManometer measures contained gas pressuremeasures contained gas pressure

U-tube Manometer Bourdon-tube gauge

E. PressureE. Pressure

2m

NkPa

KEY UNITS AT SEA LEVELKEY UNITS AT SEA LEVEL

101.325 kPa (kilopascal)101.325 kPa (kilopascal)

1 atm 1 atm

760 mm Hg760 mm Hg

760 torr 760 torr

14.7 psi14.7 psi

F. STPF. STP

Standard Temperature & PressureStandard Temperature & Pressure

0°C0°C 273 K273 K

1 atm1 atm 101.325 kPa101.325 kPa-OR--OR-

STP

The effect of adding The effect of adding gasgas..

Doubling the the number Doubling the the number of gas particles doubles of gas particles doubles the pressure.the pressure.

(of the same volume at the (of the same volume at the same temperature). same temperature).

Pressure and the number Pressure and the number of molecules are directly of molecules are directly

related related More molecules means more More molecules means more

collisions.collisions. Fewer molecules means fewer Fewer molecules means fewer

collisions.collisions. Gases naturally move from Gases naturally move from

areas of high pressure to low areas of high pressure to low pressure because there is pressure because there is empty space to move in.empty space to move in.

1 atm

If you double the number of If you double the number of moleculesmolecules

If you double the number of If you double the number of moleculesmolecules

When we blow up a balloon we When we blow up a balloon we are adding gas molecules.are adding gas molecules.

You double the pressureYou double the pressure..

2 atm

As you remove As you remove molecules from a molecules from a containercontainer

4 atm

As you remove As you remove molecules from a molecules from a container the pressure container the pressure decreasesdecreases

2 atm

As you remove As you remove molecules from a molecules from a container the pressure container the pressure decreasesdecreases

Until the pressure inside Until the pressure inside equals the pressure equals the pressure outsideoutside

Molecules naturally Molecules naturally move from high to low move from high to low pressurepressure

1 atm

Changing the size of the Changing the size of the containercontainer

In a smaller container In a smaller container molecules have less room to molecules have less room to move.move.

Hit the sides of the container Hit the sides of the container more often.more often.

As volume decreases pressure As volume decreases pressure increases.increases.

1 atm

4 Liters

As the As the pressure on a pressure on a gas increasesgas increases

2 atm

2 Liters

As the As the pressure on a pressure on a gas increases gas increases the volume the volume decreasesdecreases

Pressure and Pressure and volume are volume are inversely inversely relatedrelated

TemperatureTemperature Raising the temperature of a gas Raising the temperature of a gas

increases the pressure if the increases the pressure if the volume is held constant.volume is held constant.

The molecules hit the walls The molecules hit the walls harder.harder.

The only way to increase the The only way to increase the temperature at constant pressure temperature at constant pressure is to increase the volume.is to increase the volume.

If you start with 1 liter of gas If you start with 1 liter of gas at 1 atm pressure and 300 Kat 1 atm pressure and 300 K

and heat it to 600 K one of 2 and heat it to 600 K one of 2 things happensthings happens

300 K

Either the volume Either the volume will increase to 2 will increase to 2 liters at 1 atmliters at 1 atm

300 K600 K

300 K 600 K

•Or the pressure will Or the pressure will increase to 2 atm.increase to 2 atm.•Or someplace in Or someplace in betweenbetween

Daltons’ Law of Partial Daltons’ Law of Partial PressuresPressures

The total pressure inside a The total pressure inside a container is equal to the partial container is equal to the partial pressure due to each gas.pressure due to each gas.

The partial pressure is the The partial pressure is the contribution by that gas.contribution by that gas.

PPTotalTotal = = PP11 + + PP22 + + PP33

For exampleFor example

We can find out the pressure in We can find out the pressure in the fourth container.the fourth container.

By adding up the pressure in By adding up the pressure in the first 3.the first 3.

2 atm

1 atm

3 atm

6 atm

ExamplesExamples What is the total pressure in a What is the total pressure in a

balloon filled with air if the balloon filled with air if the pressure of the oxygen is 170 mm pressure of the oxygen is 170 mm Hg and the pressure of nitrogen is Hg and the pressure of nitrogen is 620 mm Hg?620 mm Hg?

In a second balloon the total In a second balloon the total pressure is 1.3 atm. What is the pressure is 1.3 atm. What is the pressure of oxygen if the pressure pressure of oxygen if the pressure of nitrogen is 720 mm Hg? of nitrogen is 720 mm Hg?

Boyle’s LawBoyle’s Law

At a constant temperature At a constant temperature pressure and volume are pressure and volume are inversely related.inversely related.

As one goes up the other As one goes up the other goes downgoes down

PP11 x V x V11=P=P22 x V x V22

Think about it mathematicallyThink about it mathematicallyPressure and Volume are Pressure and Volume are INVERSELYINVERSELY proportional proportional

PP11 x V x V11=P=P22 x V x V22 Pressure is 2 atm at 10L and increases to Pressure is 2 atm at 10L and increases to

4 atm.4 atm. (2 atm)(10L) = (4 atm)(X)(2 atm)(10L) = (4 atm)(X)

•20 = (4) (X)

P

V

A balloon is filled with 25 L A balloon is filled with 25 L of air at 1.0 atm pressure. If of air at 1.0 atm pressure. If the pressure is changed to the pressure is changed to 1.5 atm what is the new 1.5 atm what is the new volume?volume?

A balloon is filled with 73 L A balloon is filled with 73 L of air at 1.3 atm pressure. of air at 1.3 atm pressure. What pressure is needed to What pressure is needed to change to volume to 43 L?change to volume to 43 L?

ExamplesExamples

Charles’ LawCharles’ Law The volume of a gas is The volume of a gas is

directly proportional to the directly proportional to the Kelvin Kelvin temperature if the temperature if the pressure is held constant.pressure is held constant.

VV11 = V = V22

TT11 TT22

Think about it mathematically Think about it mathematically Volume and Temperature are Volume and Temperature are

DIRECTLYDIRECTLY proportional proportional VV11 = = VV2 2

TT11 TT22

Volume is 4L and Temp is 8K and Temp is Volume is 4L and Temp is 8K and Temp is lowered to 4K. What does the volume have lowered to 4K. What does the volume have to be????to be????

44 = = ??

8 48 4

What number does it take to keep both sides What number does it take to keep both sides equalequal

V

T

ExamplesExamples What is the temperature of a What is the temperature of a

gas that is expanded from gas that is expanded from 2.5 L at 25ºC to 4.1L at 2.5 L at 25ºC to 4.1L at constant pressure.constant pressure.

What is the final volume of a What is the final volume of a gas that starts at 8.3 L and gas that starts at 8.3 L and 17ºC and is heated to 96ºC?17ºC and is heated to 96ºC?

Gay Lussac’s LawGay Lussac’s Law

The temperature and the The temperature and the pressure of a gas are pressure of a gas are directly related at constant directly related at constant volume.volume.

PP11 = P = P22

TT11 TT22

P

T

ExamplesExamples What is the pressure inside a What is the pressure inside a

0.250 L can of deodorant that 0.250 L can of deodorant that starts at 25ºC and 1.2 atm if starts at 25ºC and 1.2 atm if the temperature is raised to the temperature is raised to 100ºC?100ºC?

At what temperature will the At what temperature will the can above have a pressure of can above have a pressure of 2.2 atm?2.2 atm?

Putting the pieces Putting the pieces togethertogether

The The Combined Gas LawCombined Gas Law Deals Deals with the situation where only the with the situation where only the number of molecules stays number of molecules stays constant. constant.

PP1 1 x Vx V11 = P = P2 2 x Vx V22

TT11 TT22

Lets us figure out one thing when Lets us figure out one thing when two of the others change.two of the others change.

ExamplesExamples A 15 L cylinder of gas at 4.8 A 15 L cylinder of gas at 4.8

atm pressure at 25ºC is heated atm pressure at 25ºC is heated to 75ºC and compressed to to 75ºC and compressed to 1.7 atm. What is the new 1.7 atm. What is the new volume?volume?

If 6.2 L of gas at 723 mm Hg at If 6.2 L of gas at 723 mm Hg at 21ºC is compressed to 2.2 L at 21ºC is compressed to 2.2 L at 4117 mm Hg, what is the 4117 mm Hg, what is the temperature of the gas?temperature of the gas?

The combined gas law The combined gas law contains all the other gas contains all the other gas laws!laws!

If the temperature remains If the temperature remains constant.constant.

P1 V1

T1

x=

P2 V2

T2

x

Boyle’s Law

The combined gas law contains The combined gas law contains all the other gas laws!all the other gas laws!

If the pressure remains If the pressure remains constant.constant.

P1 V1

T1

x=

P2 V2

T2

x

Charles’ Law

• The combined gas law contains all the other gas laws!

• If the volume remains constant.

P1 V1

T1

x=

P2 V2

T2

x

Gay-Lussac Law

The Fourth PartThe Fourth Part Avagadro’s Hypothesis Avagadro’s Hypothesis Volume is proportional to Volume is proportional to

number of molecules (or number of molecules (or moles) at constant T and P.moles) at constant T and P.

V is proportional to moles.V is proportional to moles. Gets put into the combined Gets put into the combined

gas Lawgas Law

PP1 1 x Vx V11 = P = P2 2 x Vx V22

TT11x nx n11 TT22x nx n22

•For an ideal gas at STP

•P=101KPa

•T=273K

•V=22.4L

•n=1mole

These numbers are constant, so These numbers are constant, so put them into the equation!!!put them into the equation!!!

101.3KPa x 22.4L

273K x 1 mol=

P2 x V2

T2 x n

The left side = 8.31 KPa x L K x mole

Let’s assign it a letter-----R---------called the ideal gas constant

What if we use a different What if we use a different number for standard pressure?number for standard pressure?

Instead of 101.3KPa use 1atm…Instead of 101.3KPa use 1atm…

1 atm x 22.4L

1 mole x 273K=

P2 x V2

n2xT2

So R = .0821 atm x L mole x K

What if we use a different What if we use a different number for standard pressure?number for standard pressure?

Instead of 101.3KPa use Instead of 101.3KPa use 760mHg…760mHg…

x 22.4L

1 mole x 273K=

P2 x V2

n2xT2

So R = 62.4mmHg x L mole x K

760 mm

So…..So…..

R = R = P x VP x V

n x Tn x T

Too hard to memorize…rearrange the Too hard to memorize…rearrange the lettersletters

P x V = n x R x T = The Ideal Gas LawP x V = n x R x T = The Ideal Gas Law

The Ideal Gas LawThe Ideal Gas Law P x V = n x R x TP x V = n x R x T Pressure times Volume equals Pressure times Volume equals

the number of moles times the the number of moles times the Ideal Gas ConstantIdeal Gas Constant (R)(R) times times the temperature in Kelvin.the temperature in Kelvin.

This time R does not depend on This time R does not depend on anything, it is really constant anything, it is really constant

We now have a new way to We now have a new way to count moles. By measuring count moles. By measuring T, P, and V. We aren’t T, P, and V. We aren’t restricted to STP.restricted to STP.

n = PV/RTn = PV/RT

The Ideal Gas LawThe Ideal Gas Law

ExamplesExamples How many moles of air are How many moles of air are

there in a 2.0 L bottle at 19ºC there in a 2.0 L bottle at 19ºC and 747 mm Hg?and 747 mm Hg?

What is the pressure exerted What is the pressure exerted by 1.8 g of Hby 1.8 g of H22 gas exert in a gas exert in a 4.3 L balloon at 27ºC?4.3 L balloon at 27ºC?

DensityDensity The gram formula mass of a gas can be The gram formula mass of a gas can be

determined by the density of the gas.determined by the density of the gas. Or Density can be determined by using Or Density can be determined by using

gfm and the ideal gas lawgfm and the ideal gas law D= D= mass mass = = mm Volume VVolume V Molar Mass =Molar Mass = grams grams = = m m

moles n moles n n = n = PV PV RT RT ThereforeTherefore …….…….

ThereforeTherefore Molar Mass = Molar Mass = m m

(PV/RT) (PV/RT) Molar mass =Molar mass = m RT m RT

V P V P Molar mass = Molar mass = D RT D RT

P P

Density ExamplesDensity Examples

What is the density of a OWhat is the density of a O22 at at 800mmHg and 35800mmHg and 35ooC?C?

What is the gram formula What is the gram formula mass of a gas with a density of mass of a gas with a density of 5.68g/L at 705.68g/L at 70ooC and 1.86atm? C and 1.86atm? What gas is it?What gas is it?

Molar mass(Molecular WT)Molar mass(Molecular WT)

PV = nRT n = g/Molar massPV = nRT n = g/Molar mass PV = (g/MM)RTPV = (g/MM)RT MM = (gRT)(PV)MM = (gRT)(PV)

At STPAt STP At STP determining the At STP determining the

amount of gas required or amount of gas required or produced is easy.produced is easy.

22.4 L = 1 mole22.4 L = 1 mole For example: How many liters For example: How many liters

of Oof O22 at STP are at STP are required to required to produce 20.3 g of Hproduce 20.3 g of H22O?O?

Not At STPNot At STP

Use the Ideal Gas Law Use the Ideal Gas Law n = n = PV/RTPV/RT

If you want to find how much If you want to find how much gas - use moles to figure out gas - use moles to figure out volume.volume.

For ExampleFor Example

Example #1Example #1 HCl(g) can be formed by the HCl(g) can be formed by the

following reactionfollowing reaction 2NaCl(aq) + H2NaCl(aq) + H22SOSO44 (aq) (aq)

2HCl(g) + Na2HCl(g) + Na22SOSO44(aq)(aq) What mass of NaCl is needed to What mass of NaCl is needed to

produce 340 mL of HCl at 1.51 produce 340 mL of HCl at 1.51 atm at 20ºC?atm at 20ºC?

Example #2Example #2 2NaCl(aq) + H2NaCl(aq) + H22SOSO44 (aq) (aq)

2HCl(g) + Na 2HCl(g) + Na22SOSO44 (aq) (aq) What volume of HCl gas at 25ºC What volume of HCl gas at 25ºC

and 715 mm Hg will be and 715 mm Hg will be generated if generated if

10.2 g of NaCl react with excess 10.2 g of NaCl react with excess HH22SOSO44??

Ideal Gases don’t existIdeal Gases don’t exist Molecules do take up spaceMolecules do take up space There are attractive forcesThere are attractive forces otherwise there would be no liquidsotherwise there would be no liquids

Real Gases behave like Real Gases behave like Ideal GasesIdeal Gases

When the molecules When the molecules are far apartare far apart

The molecules do not The molecules do not take up as big a take up as big a percentage of the percentage of the spacespace

We can ignore their We can ignore their volume.volume.

This is at low pressureThis is at low pressure

Real Gases behave like Real Gases behave like Ideal gases whenIdeal gases when

When molecules are moving fast.When molecules are moving fast. Collisions are harder and faster.Collisions are harder and faster. Molecules are not next to each Molecules are not next to each

other very long.other very long. Attractive forces can’t play a role.Attractive forces can’t play a role.

DiffusionDiffusion

Effusion Gas escaping through a tiny Effusion Gas escaping through a tiny hole in a container.hole in a container.

Depends on the speed of the molecule.Depends on the speed of the molecule.

Molecules moving from areas of high concentration to low concentration.

Perfume molecules spreading across the room.

Graham’s LawGraham’s Law The rate of effusion and diffusion The rate of effusion and diffusion

is inversely proportional to the is inversely proportional to the square root of the molar mass of square root of the molar mass of the molecules.the molecules.

Kinetic energy = 1/2 mvKinetic energy = 1/2 mv2 2

m is the mass v is the velocitym is the mass v is the velocity..

Chem Express

bigger molecules move slower bigger molecules move slower at the same temp.at the same temp. (by (by Square root)Square root)

Bigger molecules effuse and Bigger molecules effuse and diffuse slowerdiffuse slower

Helium effuses and diffuses Helium effuses and diffuses faster than air - escapes from faster than air - escapes from balloon.balloon.

Graham’s LawGraham’s Law