Gases

Chapters 13.1 & 14

Where are gases found?

• Atmosphere is made of gases:– 78% nitrogen (N2)

– 21% oxygen (O2)

– 1% other gases, including carbon dioxide

Kinetic-Molecular Theory

• Describes the behavior of gases

• Makes several assumptions about the size, motion, and energy of gas particles.

Assumptions of Kinetic theory:

• There is a lot of empty space in a gas between particles

• Gas molecules are tiny compared to the distances between them– Gas does have a volume

• Particles are in constant, random motion• They move in a straight line until they

collide with other particles or the wall of the container

Assumptions of Kinetic theory:

• No kinetic energy is lost in the collisions– Called elastic collisions – b/c energy is

transferred but the total energy does not change

• All gases have the same average kinetic energy at a given temperature.– There is a direct relationship between temp.

and total energy of a gas system

Properties of All Gases

• Most compressible of the states of matter– b/c it has a low density

• Assume the volume & shape of their container– Fill containers uniformly and completely

• Diffuse and mix rapidly– Will mix evenly & completely when confined

And now, we pause for this commercial message from STP

OK, so it’s really not THIS kind of STP…

STP in chemistry stands for Standard Temperature and

Pressure

Standard Pressure = 1 atm (or an equivalent)

Standard Temperature = 0 oC

(273 K)

STP allows us to compare amounts of

gases between different pressures and temperatures

STP allows us to compare amounts of

gases between different pressures and temperatures

• V = volume of the gas (mL or L)V = volume of the gas (mL or L)• T = temperature (K)T = temperature (K)

–ALL temperatures when dealing ALL temperatures when dealing with gases MUST be in Kelvin!!! with gases MUST be in Kelvin!!! No Exceptions!No Exceptions!

• n = amount (moles)n = amount (moles)• P = pressure (Units will change)P = pressure (Units will change)

What is Pressure?

• The amount of “push” that occurs in a certain area.

• We are surrounded by pressure all the time but we have evolved to “ignore” it. What pressure is that?– Air pressure or Atmospheric Pressure

• Gas particles exert pressure when they collide with the walls of a container.

Pressure• Pressure of air is measured Pressure of air is measured

with a with a BAROMETERBAROMETER (developed by Torricelli in (developed by Torricelli in 1643)1643)

• Hg rises in tube until force of Hg rises in tube until force of Hg (down) balances the force Hg (down) balances the force of atmosphere (pushing up). of atmosphere (pushing up). (Just like a straw in a soft (Just like a straw in a soft drink)drink)

• P of Hg pushing down related P of Hg pushing down related to to • Hg densityHg density• column heightcolumn height

PressureColumn height measures Column height measures

pressure of the pressure of the atmosphereatmosphere

• 1 standard atmosphere 1 standard atmosphere (atm) (atm)

= 760 mm Hg (or torr)= 760 mm Hg (or torr)= 29.92 inches Hg= 29.92 inches Hg= 14.7 pounds/in= 14.7 pounds/in2 2 (psi)(psi)= about 34 feet of water= about 34 feet of water= 101.3 kPa (SI unit is = 101.3 kPa (SI unit is

PASCAL) PASCAL)

Pressure Conversions

A. What is 475 mm Hg expressed in atm?

B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg?

= 1.52 x 103 mm Hg

= 0.625 atm

Effect of Air Pressure

Boyle’s Boyle’s LawLaw

Robert BoyleRobert Boyle• Investigated the Investigated the

relationship between relationship between pressure and volume of pressure and volume of a gas when the a gas when the temperature and amount temperature and amount of a gas is held constantof a gas is held constant

Robert Boyle Robert Boyle (1627-1691). Son of (1627-1691). Son of Earl of Cork, Earl of Cork, Ireland.Ireland.

Boyle’s Law and Kinetic Boyle’s Law and Kinetic Molecular TheoryMolecular Theory

Boyle’s Law and Kinetic Boyle’s Law and Kinetic Molecular TheoryMolecular Theory

How are pressure & volume related?How are pressure & volume related?

Boyle’s Boyle’s LawLawP P αα 1/V 1/V

This means Pressure and Volume This means Pressure and Volume are INVERSELY are INVERSELY PROPORTIONAL if moles and PROPORTIONAL if moles and temperature are constant (do not temperature are constant (do not change).change).

PP11VV11 = P = P22 V V22

PP11VV1 1 = Initial conditions of the gas= Initial conditions of the gas

PP22VV2 2 = Changed conditions of the gas= Changed conditions of the gas

Robert Boyle Robert Boyle (1627-1691). Son of (1627-1691). Son of Earl of Cork, Earl of Cork, Ireland.Ireland.

Effect of Pressure on Volume = Boyle’s Law

5

1

3

1 atm

1

3

2 atm

5

1

3

5 atm

5

Which picture represents what the gas willlook like when the pressure is doubled?

(Assume constant n, T)

Charles’s LawCharles’s Law

Low Temperature High Temperature

Charles’s original balloonCharles’s original balloon

Modern long-distance balloonModern long-distance balloon

Charles’s Law and Kinetic Charles’s Law and Kinetic Molecular TheoryMolecular Theory

Charles’s Law and Kinetic Charles’s Law and Kinetic Molecular TheoryMolecular Theory

How are volume and temperature related?How are volume and temperature related?

Effect of Temperature on Volume

Charles’s Law• If n and P are If n and P are

constant, constant, then then

• V and T are V and T are DIRECTLY DIRECTLY proportionalproportional Jacques Charles (1746-Jacques Charles (1746-

1823) – from France1823) – from FranceIsolated boron and Isolated boron and studied gases studied gases BalloonistBalloonist

1 2

1 2

V V

T T

TEMPS. have to be in KELVIN!!

The volume of a gas increases with and increase in temperature.

Introductory Chemistry; 2nd Ed; by Nivaldo Tro; Prentice Hall Publishing 2006, p356

Which picture represents what the gas willlook like when the temperature is increased?

(Assume constant n, P)

Example of Charles’s Law

• Putting fully blown up balloons in a car during a hot summer’s day.

• What will happen?

• Why?

What happens to the pressure if volume What happens to the pressure if volume were kept constant and temp. was were kept constant and temp. was

changed?changed?What happens to the What happens to the

motion of the motion of the particles?particles?

This is Gay-Lussac’s This is Gay-Lussac’s LawLaw

Joseph Louis Gay-Joseph Louis Gay-Lussac (1778-1850)Lussac (1778-1850)

Kinetic Molecular Theory and Kinetic Molecular Theory and Gay-Lussac’s LawGay-Lussac’s Law

Kinetic Molecular Theory and Kinetic Molecular Theory and Gay-Lussac’s LawGay-Lussac’s Law

Gay-Lussac’s LawGay-Lussac’s Law• If n and V are constant, If n and V are constant,

thenthen• P and T are DIRECTLY P and T are DIRECTLY

proportional.proportional.

Joseph Louis Gay-Joseph Louis Gay-Lussac (1778-1850)Lussac (1778-1850)

1 2

1 2

P P

T T

TEMPS. have to be in KELVIN!!

Combined Gas Law• The good news is that you don’t have to

remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!

No, it’s not related to R2D2

1 1 2 2

1 2

PV P V

T T

Combined Gas Law

If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!

= P1 V1

T1

P2 V2

T2

Boyle’s Law

Charles’ Law

Gay-Lussac’s Law

Combined Gas Law Problems:

Combined Gas Law ProblemA sample of neon gas is collected at a pressure of 2.7 atm and a temperature of 295.0 K. It has a volume of 2.25 L. What would be the volume of this gas at STP?

F:

P1 = 2.7 atm V1 = 2.25 L T1 = 295.0 K

P2 = 1 atm V2= ? T2 = 0oC

Calculation

• P1 = 2.7 atm V1 = 2.25 L T1 = 295.0 K

• P2 = 1 atm V2= ? T2 = 0oC = 273 K

P1 V1 P2 V2

= P1 V1 T2 = P2 V2 T1

T1 T2

V2 = P1 V1 T2

P2 T1

V2 = 2.7 atm x 2.25 L x 273 K

1 atm x 295.0 K

= 5.62 L5.62 L

A student collects a 3.5 L sample of hydrogen gas at 22.0oC and 91.9 kPa. What pressure would the hydrogen be at when the temperature is held constant but the volume decreases to 2.0L?

F: L: I: P: S:

Avogadro’s PrincipleAvogadro’s PrincipleEqual volumesEqual volumes of gases at the of gases at the

samesame TT and and PP have the have the samesame number of molecules (we’ll number of molecules (we’ll use moles = n)use moles = n)..

VV and and nn are are directlydirectly related. related.

Also Also massmass and and nn are directly are directly related b/c of related b/c of molar massmolar mass..

•Twice as many Twice as many moleculesmolecules•Twice the massTwice the mass•Twice the volume Twice the volume @ STP@ STP

Which picture represents what the gas willlook like when the moles of gas is doubled?

(Assume constant P, T)

Experiments show that at STP, 1 mole of an ideal gas occupies 22.4 L

Practice Problems:

Determine the volume of a container that holds 2.4 mol of gas at STP.

How many moles of nitrogen gas will be contained in a 2.00 L flask at STP?

= 54 L

= 0.0893 mol

• What volume, in L, will 4.5 kg of ethylene gas occupy at STP?

= 3.6x103 L

What is an “Ideal” Gas?What is an “Ideal” Gas?• The particles take up NO space

and have NO intermolecular forces interact.

• MOST gases will behave like ideal gases under most conditions

Deviations from Ideal GasesDeviations from Ideal Gases• Real molecules have volume.The ideal gas consumes the entire

amount of available volume. It does not account for the volume of the molecules themselves.

• There are intermolecular forces.An ideal gas assumes there are no

attractions between molecules. Attractions slow down the molecules and reduce the amount of collisions.– Otherwise a gas could not

condense to become a liquid.

Conditions that cause Conditions that cause Deviations from Ideal GasesDeviations from Ideal Gases

Real gases are the LEAST like ideal gases under 2 conditions:

1. Extremely high pressures

2. Extremely low temperatures

• Under these circumstances the gas molecules are too close together to NOT interact and take up space.

IDEAL GAS LAWIDEAL GAS LAW

Brings together gas properties Brings together gas properties of pressure, volume, of pressure, volume, temperature and moles of temperature and moles of gas.gas.

BE SURE YOU KNOW THIS BE SURE YOU KNOW THIS EQUATION!EQUATION!

P V = n R TP V = n R T

Ideal Gas Law

5.4

Charles’s law: V T(at constant n and P)

Avogadro’s principle: V n(at constant P and T)

Boyle’s law: V (at constant n and T)1P

V nT

P

V = constant x = RnT

P

nT

PR is the gas constant

0.0821

is the one most commonly used

L atmR

mol K

Other Gas Law Relationships

• PV = nRT

• Remember

• Also density could be used b/c

If you rearrange the equation above:

M

mRT PV so

(M) massmolar

mn

mD

V

( ) substitute in density Mmolar mass

mRT DRTM

VP P

Using the Ideal Gas LawUsing the Ideal Gas Law

How many moles of NHow many moles of N22 are are required to fill a small required to fill a small room with a volume of room with a volume of 960 cubic feet (27,000 L) 960 cubic feet (27,000 L) to 745 mm Hg at 25 to 745 mm Hg at 25 ooC?C?

K: K: UK: nUK: nV = 27,000 LV = 27,000 L

T = 25 T = 25 ooC + 273 = 298 KC + 273 = 298 K P = 745 mm HgP = 745 mm Hg

= 0.98 atm = 0.98 atm (b/c 1 atm = 760 mmHg)(b/c 1 atm = 760 mmHg)And we always know And we always know ..

PV=nRT

0.0821L atm

Rmol K

PVn

RT

22 2

(0.98 *27000 )

((0.0821 )(298 ))

26461

24.4658

108 N 1.0x10 mol N

atm Ln

L atmK

mol K

mol

mol

Example problem:

Dinitrogen monoxide (N2O), laughing gas, is used by dentists as an anesthetic. If 2.86 mol of gas occupies a 20.0 L tank at 23°C, what is the pressure (mmHg) in the tank in the dentist office?

= 2600 mmHg

Another Example Problem

A 5.0 L cylinder contains oxygen gas at 20.0°C and 735 mm Hg. How many grams of oxygen are in the cylinder?

n=PV/RT = (0.967atm*5.0L)/(0.0821 Latm/molK*293) =

0.201mol(32.00g/1mol) = 6.4g O2

Dalton’s Dalton’s LawLaw

John DaltonJohn Dalton1766-18441766-1844

Dalton’s Law of Partial Pressures

When V and T are constant

P1P2 Ptotal

5.6

++ ==

Kinetic theory of gases and …

• Dalton’s Law of Partial Pressures

Molecules of gases do not attract or repel one another

P exerted by one type of molecule is unaffected by the presence of another gas

Ptotal = sum of all the partial pressures of

individual gases = Pi

5.7

Dalton’s Law of Partial PressuresDalton’s Law of Partial Pressures

What is the total pressure in the flask?What is the total pressure in the flask?

PPtotaltotal in gas mixture = P in gas mixture = PAA + P + PBB + ... + ...

Therefore, Therefore,

PPtotaltotal = P = PHH22OO + P + POO22

PPtotaltotal = 0.32 atm + 0.16 atm = 0.48 atm = 0.32 atm + 0.16 atm = 0.48 atm

Dalton’s Law: total P is sum of Dalton’s Law: total P is sum of PARTIAL PARTIAL PRESSURESPRESSURES

2 H2 H22OO2 2 (l) (l) 2 H 2 H22O (g) + OO (g) + O2 2 (g)(g)The pressure of the water vapor is 0.32 atm and The pressure of the water vapor is 0.32 atm and the pressure of the oxygen gas is 0.16 atm.the pressure of the oxygen gas is 0.16 atm.

Gases in the AirThe % of gases in air Partial pressure (STP)

78.08% N2 593.4 mm Hg

20.95% O2 159.2 mm Hg

0.94% Ar 7.1 mm Hg

0.03% CO2 0.2 mm Hg

PAIR = PN + PO + PAr + PCO = 760 mm Hg 2 2 2

Total Pressure 760 mm Hg

Collecting a gas “over water”

• Animation of this concept

When a gas is collected over water; you always have a mixture of that gas and

water vapor.

Introductory Chemistry; 2nd Ed; by Nivaldo Tro; Prentice Hall Publishing 2006, p372

Table of Vapor Pressures for Water

Solve This!A student collects some

hydrogen gas over water at 20 oC and 768 torr. What is the pressure of the hydrogen gas?

GAS DIFFUSION AND EFFUSIONGAS DIFFUSION AND EFFUSION

• diffusiondiffusion is the is the gradual mixing of gradual mixing of molecules of different molecules of different gases.gases.

• effusioneffusion is the is the movement of movement of molecules through a molecules through a small hole into an small hole into an empty container.empty container.

Example: A leak in a balloon

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

Graham’s law governs Graham’s law governs effusion and diffusion effusion and diffusion of gas molecules.of gas molecules.

Thomas Graham, 1805-1869. Thomas Graham, 1805-1869. Professor in Glasgow and London.Professor in Glasgow and London.

Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass.to its molar mass.

Rate of effusion is Rate of effusion is inversely proportional inversely proportional to its molar mass.to its molar mass.

M of AM of B

Rate for B

Rate for A

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

Molecules effuse thru holes in a Molecules effuse thru holes in a rubber balloon, for example, at a rubber balloon, for example, at a rate (= moles/time) that israte (= moles/time) that is

• proportional to Tproportional to T

• inversely proportional to Minversely proportional to M..

Therefore, He effuses more rapidly Therefore, He effuses more rapidly than Othan O22 at same T. at same T.

HeHe

OO22

Gas DiffusionGas Diffusionrelation of mass to rate of diffusionrelation of mass to rate of diffusion

Gas DiffusionGas Diffusionrelation of mass to rate of diffusionrelation of mass to rate of diffusion

• HCl and NH3 diffuse from opposite ends of tube.

• Gases meet to form NH4Cl

• HCl heavier than NH3

• Therefore, NH4Cl forms closer to HCl end of tube.

• HCl and NH3 diffuse from opposite ends of tube.

• Gases meet to form NH4Cl

• HCl heavier than NH3

• Therefore, NH4Cl forms closer to HCl end of tube.

Which gas molecules will diffuse faster? Why?

a) CO2 or water vapor

b) Argon (Ar) or NH3

c) HCl (g) or SO2 (g)

The ones circled all have the smaller molar mass so their molecules move faster so they will diffuse faster than the other gases.