Gases

Chapter 12

22

Importance of GasesImportance of Gases

• Airbags fill with NAirbags fill with N22 gas in an gas in an accident. accident.

• Gas is generated by the Gas is generated by the decomposition of sodium decomposition of sodium azide, NaNazide, NaN33..

• 2 NaN2 NaN33 2 Na + 3 N 2 Na + 3 N22

• Air Bag Video

33General General Properties of Properties of

GasesGases• There is a lot of “free” There is a lot of “free”

space in a gas.space in a gas.

• Gases can be expanded Gases can be expanded infinitely.infinitely.

• Gases fill containers Gases fill containers uniformly and completely.uniformly and completely.

• Gases diffuse and mix Gases diffuse and mix rapidly.rapidly.

44

Properties of Properties of GasesGases

Gas properties can be modeled Gas properties can be modeled using math. Model depends on—using math. Model depends on—

• V = volume of the gas (L, mL, dmV = volume of the gas (L, mL, dm33))• T = temperature (K)T = temperature (K)

–ALL temperatures in the entire ALL temperatures in the entire chapter MUST be in Kelvin!!! No chapter MUST be in Kelvin!!! No Exceptions!Exceptions!

• n = amount (moles)n = amount (moles)• P = pressureP = pressure

(atmospheres or Pascal) (atmospheres or Pascal)

55

PressurPressureePressure of air is Pressure of air is

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

66PressurPressuree

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

77PressurPressureeColumn height measures Column height measures Pressure of atmospherePressure of atmosphere

• 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 = Pa) PASCAL = Pa)

1010

Boyle’s Law and Boyle’s Law and Kinetic Molecular Kinetic Molecular

TheoryTheory

Boyle’s Law and Boyle’s Law and Kinetic Molecular Kinetic Molecular

TheoryTheory

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

1111Boyle’s Boyle’s LawLawThis means Pressure This means Pressure

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

P goes up as V goes P goes up as V goes down.down.

PP11VV11 = P = P22 V V22

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

1212

Boyle’s LawBoyle’s LawBoyle’s LawBoyle’s Law

A bicycle pump is a A bicycle pump is a good example of good example of Boyle’s law. Boyle’s law.

As the volume of the As the volume of the air trapped in the air trapped in the pump is reduced, its pump is reduced, its pressure goes up, pressure goes up, and air is forced into and air is forced into the tire.the tire.

1313

Boyle’s Law Problems

•A high-altitude balloon contains 30.0L of helium gas at 1 atmosphere. What is the volume when the balloon rises to an altitude where the pressure is only 0.25 atm?

1414

Charles’s Law and Charles’s Law and Kinetic Molecular Kinetic Molecular

TheoryTheory

Charles’s Law and Charles’s Law and Kinetic Molecular Kinetic Molecular

TheoryTheory

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

1515

Charles’s Charles’s LawLaw

V and T are directly V and T are directly proportional.proportional.

VV11 V V22

==

TT11 T T22

• If one temperature goes If one temperature goes up, the volume goes up!up, the volume goes up!

Jacques Charles (1746-Jacques Charles (1746-1823). Isolated boron 1823). Isolated boron and studied gases. and studied gases. Balloonist.Balloonist.

1616

Charles’s original balloonCharles’s original balloon

Modern long-distance balloonModern long-distance balloon

A sample of carbon monoxide gas occupies 3.20 L at 125 oC. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant?

V1 = 3.20 L

T1 = 398 K

V2 = 1.54 L

T2 = ?

T2 = V2 x T1

V1

1.54 L x 398 K3.20 L

= = 192 K

5.3

1 2

1 2

V V

T T

A set amount of gas at 89oC occupies a volume of 0.67 L. At what Celsius temperature will the volume become to 1.12 L?

= 330oC

1919What happens to the pressure if What happens to the pressure if volume were kept constant and volume were kept constant and

temp. was changed?temp. was 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)

2020

Gay-Lussac’s LawGay-Lussac’s Law

P and T are directly P and T are directly proportional.proportional.

PP11 P P22

==

TT11 T T22

• If one temperature goes If one temperature goes

up, the pressure goes up!up, the pressure goes up!

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

A gas in a sealed container has a pressure of 125 kPa at a temperature of 30.0oC. If the pressure in the container is increased to 201 kPa, what is the new temperature of the gas?

= 214 oC

A rigid plastic container holds 1.00 L methane gas at 660 torr pressure when the temperature is 22.0oC. How much more pressure will the gas exert if the temperature is raised to 44.6oC?

= 51 torr more

2323

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!

P1 V1 P2 V2

=

T1 T2

No, it’s not related to R2D2

2424

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

2525And 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

2626

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

2727

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

• P2 = 1 atm V2= ? T2 = 0oC

P1 V1 P2 V2

= P1 V1 T2 = P2 V2

T1 T2 T1

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

2828

Learning Check 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?

2929

One More Practice Problem

A balloon has a volume of 785 mL on a fall day when the temperature is 21°C. In the winter, the gas cools to 0°C. What is the new volume of the balloon?

3030

Try This One

A sample of neon gas used in a neon sign has a volume of 15 L at STP. What is the volume (L) of the neon gas at 2.0 atm and –25°C?

3131

Avogadro’s HypothesisEqual volumes of gases at the same Equal volumes of gases at the same T and P have the same number of T and P have the same number of molecules.molecules.

V = n (RT/P) = knV = n (RT/P) = kn

V and n are directly related.V and n are directly related.

twice as many twice as many moleculesmolecules

3333

IDEAL GAS LAWIDEAL GAS LAW

Brings together gas Brings together gas properties.properties.

Can be derived from Can be derived from experiment and theory.experiment and theory.

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

P V = n R TP V = n R T

3434

Using PV = nRTUsing PV = nRTP = PressureP = Pressure

V = VolumeV = Volume

T = TemperatureT = Temperature

N = number of molesN = number of moles

R is a constant, called the R is a constant, called the Ideal Gas ConstantIdeal Gas Constant

Instead of learning a different value for R for all the Instead of learning a different value for R for all the possible unit combinations, we can just possible unit combinations, we can just use oneuse one value and value and convert the units to match R.convert the units to match R.

R = 0.0821R = 0.0821L • atm

mol • K

3535

Using PV = nRTUsing PV = nRTHow much NHow much N22 is required to fill a small room with a is required to fill a small room with a

volume of 27,000 L to P that is 0.98 atm at 25 volume of 27,000 L to P that is 0.98 atm at 25 ooC?C?

SolutionSolution

1. Write down what you are given1. Write down what you are given

V = 27,000 LV = 27,000 L

T = 25 T = 25 ooC + 273 = 298 KC + 273 = 298 K

P = 0.98 atmP = 0.98 atm

And we always know R, 0.0821 L atm / mol KAnd we always know R, 0.0821 L atm / mol K

3636

Using PV = nRTUsing PV = nRTHow much NHow much N22 is required to fill a small room with a volume of is required to fill a small room with a volume of

27,000 L to P that is 0.98 atm at 25 27,000 L to P that is 0.98 atm at 25 ooC?C?

SolutionSolution

2. Now plug in those values and solve for 2. Now plug in those values and solve for the unknown.the unknown.

PV = PV = nnRTRT

n = (0.98 atm)(2.7 x 10 4 L)

(0.0821 L • atm/K • mol)(298 K)n =

(0.98 atm)(2.7 x 10 4 L)

(0.0821 L • atm/K • mol)(298 K)

n = 1.1 x 10n = 1.1 x 1033 mol mol

RT RTRT RT

3737

Learning Check

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 (in atmospheres) in the tank in the dentist office?

3838

Learning Check

A 5.0 L cylinder contains oxygen gas at 20.0°C and 0.97 atm. How many grams of oxygen are in the cylinder?

4040

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

4141Dalton’s Law of Partial Dalton’s Law of Partial PressuresPressures

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 = 0.48 atm = 0.48 atm

Dalton’s Law: total P is sum ofDalton’s Law: total P is sum of PARTIALPARTIAL pressures.pressures.

2 H2 H22OO2 2 (l) (l) 2 H 2 H22O (g) + OO (g) + O2 2 (g)(g)

0.32 atm 0.32 atm 0.16 0.16 atmatm

4242

Dalton’s Dalton’s LawLaw

John DaltonJohn Dalton1766-18441766-1844

4343Collecting a gas “over water”

• Gases, since they mix with other gases readily, must be collected in an environment where mixing can not occur. The easiest way to do this is under water because water displaces the air. So when a gas is collected “over water”, that means the container is filled with water and the gas is bubbled through the water into the container. Thus, the pressure inside the container is from the gas AND the water vapor. This is where Dalton’s Law of Partial Pressures becomes useful.

4444Table of Vapor Pressures for Water p. 395

4545

Solve This!

A student collects some hydrogen gas over water at 20 degrees C and 768 torr. What is the pressure of the gas?

4646

GAS DENSITYGAS DENSITYGAS DENSITYGAS DENSITY

HighHigh densitydensity

Low Low densitydensity

22.4 L of ANY gas AT STP = 1 mole

4747Health NoteWhen a scuba diver is several hundred feet under water, the high pressures cause N2 from

the tank air to dissolve in the blood. If the diver rises too fast, the dissolved N2 will form

bubbles in the blood, a dangerous and painful condition called "the bends". Helium, which is inert, less dense, and does not dissolve in the blood, is mixed with O2 in

scuba tanks used for deep descents.

4848Gases and Gases and StoichiometryStoichiometry

2 H2 H22OO2 2 (l) ---> 2 H(l) ---> 2 H22O (g) + OO (g) + O2 2 (g)(g)

Decompose 1.1 g of HDecompose 1.1 g of H22OO22 in a flask with a in a flask with a volume of 2.50 L. What is the volume of Ovolume of 2.50 L. What is the volume of O22 at STP?at STP?

Bombardier beetle Bombardier beetle uses decomposition uses decomposition of hydrogen peroxide of hydrogen peroxide to defend itself.to defend itself.

4949

Gas Stoichiometry: Practice!

A.What is the volume at STP of 4.00 g of CH4?

B. How many grams of He are present in 8.0 L of gas at

STP?

5050

What if it’s NOT at STP?

• 1. Do the problem like it was at STP. (V1)

• 2. Convert from STP (V1, P1, T1) to the stated conditions (P2, T2)

5151

Try this one!

How many L of O2 are needed to react 28.0 g NH3

at 24°C and 0.950 atm?

4 NH3(g) + 5 O2(g) 4 NO(g) + 6 H2O(g)

5252How many L of O2 are needed to react 28.0 g NH3 at

24°C and 0.950 atm?4 NH3(g) + 5 O2(g) 4 NO(g) + 6 H2O(g)

Find mole of O2

28.0 g NH3 x 1 mol NH3 x 5 mol O2 x 22.4 L O2

17.0 g NH3 4 mol NH3 1 mol O2

At STP, V = 46.1 L V1, P1, and T1

P1 V1 P2 V2

= P1 V1 T2 = P2 V2 T1

T1 T2

V2 = P1 V1 T2 (1 atm) (46.1 L) (297K)

P2 T1 (0.950 atm) (273 K)= 52.8

L

= 46.1 L

AT STP

5353

GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION

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

5454GAS 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

5555

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 M.inversely proportional to M.

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

HeHe

5656

Gas DiffusionGas Diffusionrelation of mass to rate of relation of mass to rate of

diffusiondiffusion

Gas DiffusionGas Diffusionrelation of mass to rate of relation of mass to rate of

diffusiondiffusion

• 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.