11

Chapter 12Chapter 12

GasesGases

22

OverviewOverview Gas LawsGas Laws

– Gas pressure and its measurementGas pressure and its measurement– Empirical gas lawsEmpirical gas laws– Ideal gas lawsIdeal gas laws– Stoichiometry and gasesStoichiometry and gases– Gas Mixtures; Law of Partial PressuresGas Mixtures; Law of Partial Pressures

Kinetic and Molecular TheoryKinetic and Molecular Theory– Kinetic Theory of an Ideal GasKinetic Theory of an Ideal Gas– Molecular speeds: diffusion and effusionMolecular speeds: diffusion and effusion– Real gasesReal gases

33

Measurements on GasesMeasurements on Gases

The most readily measured properties of a The most readily measured properties of a gas are: gas are:

Temperature Temperature Volume Volume PressurePressure

44

Measuring PressureMeasuring Pressure

Pressure (P) is the force (F) that acts on a given area Pressure (P) is the force (F) that acts on a given area (A)(A)

One of the most important of the measured quantities One of the most important of the measured quantities for gasesfor gases

Pressure has traditionally been measured in units Pressure has traditionally been measured in units relating to the height of the Hg and is thus expressed as relating to the height of the Hg and is thus expressed as mm Hg = 1 Torr.mm Hg = 1 Torr.

55

Atmospheric Pressure and the Atmospheric Pressure and the BarometerBarometer

Due to gravity, the atmosphere exerts a downward force Due to gravity, the atmosphere exerts a downward force and therefore a and therefore a pressurepressure upon the earth's surface upon the earth's surface

Force = (mass*acceleration) or Force = (mass*acceleration) or F=maF=ma The earth's gravity exerts an acceleration of 9.8 m/sThe earth's gravity exerts an acceleration of 9.8 m/s22 A column of air 1 mA column of air 1 m22 in cross section, extending through in cross section, extending through

the atmosphere, has a mass of roughly 10,000 kg the atmosphere, has a mass of roughly 10,000 kg

66

Atmospheric pressure can be measured by using a Atmospheric pressure can be measured by using a barometerbarometer A glass tube with a length somewhat longer than 760 mm is A glass tube with a length somewhat longer than 760 mm is

closed at one end and filled with mercury closed at one end and filled with mercury

The filled tube is inverted over a dish of mercury such that no air The filled tube is inverted over a dish of mercury such that no air enters the tube enters the tube

Some of the mercury flows out of the tube, but a column of Some of the mercury flows out of the tube, but a column of mercury remains in the tube. The space at the top of the tube is mercury remains in the tube. The space at the top of the tube is essentially a vacuum essentially a vacuum

The dish is open to the atmosphere, and the fluctuating The dish is open to the atmosphere, and the fluctuating pressure of the atmosphere will change the height of the pressure of the atmosphere will change the height of the mercury in the tube mercury in the tube

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The mercury is pushed up the tube until the The mercury is pushed up the tube until the pressure due to the mass of the mercury in the pressure due to the mass of the mercury in the

column balances the atmospheric pressurecolumn balances the atmospheric pressure

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Standard Atmospheric PressureStandard Atmospheric Pressure

Standard atmospheric pressure Standard atmospheric pressure corresponds to typical atmospheric pressure corresponds to typical atmospheric pressure at sea level at sea level

It is the pressure needed to support a It is the pressure needed to support a column of mercury 760 mm in height column of mercury 760 mm in height

In SI units it equals 1.01325 x 10In SI units it equals 1.01325 x 1055 Pa Pa

99

Relationship to other common units of Relationship to other common units of pressure: pressure:

(Note that 1 torr = 1 mm Hg)(Note that 1 torr = 1 mm Hg)

1010

A A manometermanometer is used to measure the is used to measure the pressure of an enclosed gas. Their pressure of an enclosed gas. Their operation is similar to the barometer, and operation is similar to the barometer, and they usually contain mercury.they usually contain mercury.

It consists of a tube of liquid connected to It consists of a tube of liquid connected to enclosed container which makes it possible enclosed container which makes it possible to measure pressure inside the container.to measure pressure inside the container.

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A A closed tubeclosed tube manometer is used to measure manometer is used to measure pressures pressures belowbelow atmospheric atmospheric

An An open tubeopen tube manometer is used to measure manometer is used to measure pressures pressures slightly above or belowslightly above or below atmospheric atmospheric

In a closed tube manometer the pressure is just In a closed tube manometer the pressure is just the difference between the two levels (in mm of the difference between the two levels (in mm of mercury)mercury)

1212

In an open tube manometer the difference in In an open tube manometer the difference in mercury levels indicates the pressure mercury levels indicates the pressure difference in difference in reference to atmospheric reference to atmospheric pressure pressure

1313

ManometerManometer

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Other liquids can be employed in a manometer Other liquids can be employed in a manometer besides mercury. besides mercury.

The difference in height of the liquid levels The difference in height of the liquid levels is is inversely proportional to the densityinversely proportional to the density of the liquid of the liquid i.e. the greater the density of the liquid, the smaller i.e. the greater the density of the liquid, the smaller the difference in height of the liquid the difference in height of the liquid

The high density of mercury (13.6 g/ml) allows The high density of mercury (13.6 g/ml) allows relatively small manometers to be built relatively small manometers to be built

1616

The Gas LawsThe Gas Laws

Boyle's LawBoyle's Law: For a fixed amount of : For a fixed amount of gas and constant temperature, PV = gas and constant temperature, PV = constant. constant.

1717

The volume of some amount of a gas was The volume of some amount of a gas was 1.00 L when the pressure was 10.0 atm; 1.00 L when the pressure was 10.0 atm; what would the volume be if the pressure what would the volume be if the pressure decreased to 1.00 atm?decreased to 1.00 atm?

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The Gas LawsThe Gas Laws

Charles's LawCharles's Law: at constant pressure : at constant pressure the volume is linearly proportional to the volume is linearly proportional to temperature. V/T = constanttemperature. V/T = constant

1919

A gas occupied a volume of 6.54 L at 25°C A gas occupied a volume of 6.54 L at 25°C what would its volume be at 100°C? what would its volume be at 100°C?

2020

The Gas LawsThe Gas Laws

Avagadro’s law Avagadro’s law for a fixed pressure and for a fixed pressure and temperature, the volume of a gas is directly temperature, the volume of a gas is directly proportional to the number of moles of that proportional to the number of moles of that gas. V/n = k = constant. gas. V/n = k = constant.

2121

The volume of 0.555 mol of some gas was The volume of 0.555 mol of some gas was 100.0 L; what would be the volume of 15.0 100.0 L; what would be the volume of 15.0 mol of the same gas at the same T and P? mol of the same gas at the same T and P?

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The three historically important gas laws The three historically important gas laws derived relationships between two derived relationships between two physical properties of a gas, while physical properties of a gas, while keeping other properties constant:keeping other properties constant:

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These different relationships can be These different relationships can be combined into a single relationship to make combined into a single relationship to make a more general gas law:a more general gas law:

2424

If the proportionality constant is called "R", If the proportionality constant is called "R", then we have:then we have:

2525

Rearranging to a more familiar form:Rearranging to a more familiar form: This equation is known as theThis equation is known as the ideal-gas ideal-gas

equationequation

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Values for R are determined by the values Values for R are determined by the values used for volume and pressure. The value used for volume and pressure. The value that we will use is that we will use is

0.0821 l atm/mole K0.0821 l atm/mole K

2727

When any of the other three quantities in the When any of the other three quantities in the ideal gas law have been determined the last ideal gas law have been determined the last one can be calculated. one can be calculated.

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2929

Calculate the pressure inside a TV picture Calculate the pressure inside a TV picture tube, if it's volume is 5.00 liters, it's tube, if it's volume is 5.00 liters, it's temperature is 23.0temperature is 23.0C and it contains 0.0100 C and it contains 0.0100 mg of nitrogen. mg of nitrogen.

3030

Further Applications of Ideal-Gas Further Applications of Ideal-Gas Equation Equation

The density of a gasThe density of a gas the density of a the density of a gas can be related to the pressure from gas can be related to the pressure from the ideal gas law using the definition of the ideal gas law using the definition of density: d = mass/vol. density: d = mass/vol.

3131

Estimate the density of air at 20.0Estimate the density of air at 20.0C and C and 1.00 atm by supposing that air is 1.00 atm by supposing that air is predominantly Npredominantly N22. .

3232

Rearrangement permits the determination of Rearrangement permits the determination of molecular mass of a gas from a measure of molecular mass of a gas from a measure of the density at a known temperature and the density at a known temperature and pressure. pressure.

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A certain gas was found to have a density of A certain gas was found to have a density of 0.480 g/L at 2600.480 g/L at 260C and 103 Torr. Determine C and 103 Torr. Determine the MM of the compound. the MM of the compound.

3434

Partial Pressure and Dalton’s Partial Pressure and Dalton’s Law Law

Dalton's LawDalton's Law = the sum of the partial = the sum of the partial pressures of the gases in a mixture = pressures of the gases in a mixture = the total pressure or P = Pthe total pressure or P = PAA + P + PBB + P + PCC

+ ...where P+ ...where Pii = the partial pressure of = the partial pressure of

component i.component i.

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Dalton found that gases obeying the ideal gas Dalton found that gases obeying the ideal gas law in the pure form will continue to act ideally law in the pure form will continue to act ideally when mixed together with other ideal gases. when mixed together with other ideal gases.

The individual partial pressures are used to The individual partial pressures are used to determine the amount of that gas in the determine the amount of that gas in the mixture, mixture, not the total pressurenot the total pressure, P, PAA = n = nAART/V. RT/V.

Since they are in the same container T and V Since they are in the same container T and V will be the same for all gases. will be the same for all gases.

3636

1.00 g of air consists of approximately 0.76 g 1.00 g of air consists of approximately 0.76 g nitrogen and 0.24 g oxygen. Calculate the nitrogen and 0.24 g oxygen. Calculate the partial pressures and the total pressure partial pressures and the total pressure when this sample occupies a 1.00 L vessel when this sample occupies a 1.00 L vessel at 20.0at 20.0C. C.

3737

Partial Pressure and Dalton’s Partial Pressure and Dalton’s Law2Law2

Mole fractionMole fraction another quantity commonly determined another quantity commonly determined for gas mixtures. It is defined the number of moles of for gas mixtures. It is defined the number of moles of one substance relative to the total number of moles in one substance relative to the total number of moles in the mixture or the mixture or

X can be calculated from X can be calculated from – moles of each gas in the mixture or moles of each gas in the mixture or – the pressures of each gasthe pressures of each gas

BA

A

BA

AA PP

Pnnn

X

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Gas Collection by Water Gas Collection by Water DisplacementDisplacement

Certain experiments involve the determination Certain experiments involve the determination of the number of moles of a gas produced in of the number of moles of a gas produced in a chemical reaction a chemical reaction

Sometimes the gas can be collected over Sometimes the gas can be collected over water water

Potassium chlorate when heated gives off Potassium chlorate when heated gives off oxygen: oxygen:

2KClO2KClO33((ss) -> 2KCl() -> 2KCl(ss) + 3O) + 3O22((gg) ) The oxygen can be collected in a bottle that is The oxygen can be collected in a bottle that is

initially filled with water initially filled with water

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The volume of gas collected is measured by The volume of gas collected is measured by first adjusting the beaker so that the water first adjusting the beaker so that the water level in the beaker is the same as in the pan.level in the beaker is the same as in the pan.

When the levels are the same, the pressure When the levels are the same, the pressure inside the beaker is the same as on the water inside the beaker is the same as on the water in the pan (i.e. 1 atm of pressure) in the pan (i.e. 1 atm of pressure)

The total pressure inside the beaker is equal The total pressure inside the beaker is equal to the sum of the pressure of gas collected to the sum of the pressure of gas collected and the pressure of water vapor in equilibrium and the pressure of water vapor in equilibrium with liquid water with liquid water

PPtt = P = POO22 + P + PHH22OO

4141

Suppose KClOSuppose KClO33 was decomposed according was decomposed according

to to

2 KClO2 KClO33((ss)+ )+ 2KCl( 2KCl(ss) + 3O) + 3O22((gg). ).

PPTT = 755.2 Torr and 370.0 mL of gas was = 755.2 Torr and 370.0 mL of gas was

collected over water at 20.0collected over water at 20.0C. Determine the C. Determine the number of moles of Onumber of moles of O22 if the vapor pressure if the vapor pressure

of water is 17.5 torr at this temperature.of water is 17.5 torr at this temperature.

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Stoichiometric Relationships with Stoichiometric Relationships with Gases Gases

When gases are involved in a reaction, When gases are involved in a reaction, gas properties must be combined with gas properties must be combined with stoichiometric relationships.stoichiometric relationships.

Two types exist Two types exist – Volume of gas and volume of gasVolume of gas and volume of gas– Condensed phase and volume of gasCondensed phase and volume of gas

4444

Determine the volume of oxygen gas Determine the volume of oxygen gas needed to react with 1.00 L of hydrogen gas needed to react with 1.00 L of hydrogen gas at the same temperature and pressure to at the same temperature and pressure to produce water.produce water.

4545

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Determine the volume of gas produced at Determine the volume of gas produced at 273.15 K and 1.00 atm if 1.00 kg of calcium 273.15 K and 1.00 atm if 1.00 kg of calcium oxide reacts with a sufficent amount of oxide reacts with a sufficent amount of carbon. Assume complete reaction (i.e. carbon. Assume complete reaction (i.e. 100% yield) 100% yield)

CaO(CaO(ss) + 3C() + 3C(ss) ) CaC CaC22((ss) + CO() + CO(gg).).

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The Behavior of Real GasesThe Behavior of Real Gases

The molar volume is not constant as is The molar volume is not constant as is expected for ideal gases. expected for ideal gases.

These deviations due to an attraction These deviations due to an attraction between some molecules. between some molecules.

Applicable at high pressures and low Applicable at high pressures and low temperatures.temperatures.

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For compounds that deviate from ideality the For compounds that deviate from ideality the van der Waals equation is used:van der Waals equation is used:

where a and b are constants that are where a and b are constants that are characteristic of the gas. characteristic of the gas.

nRT=nb)-(VV

an+P2

2

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The Kinetic Molecular Theory of The Kinetic Molecular Theory of GasesGases

Microscopic view of gases assumes Microscopic view of gases assumes thatthat

– A gas is a collection of molecules (atoms) A gas is a collection of molecules (atoms)

in continuous random motion.in continuous random motion.

– The molecules are infinitely small point-The molecules are infinitely small point-like particles that move in straight lines like particles that move in straight lines until they collide with something.until they collide with something.

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KMT cont.KMT cont.

– Gas molecules do not influence each other Gas molecules do not influence each other except during collision.except during collision.

– All collisions are elastic; the total kinetic energy All collisions are elastic; the total kinetic energy is constant at constant T.is constant at constant T.

– Average kinetic energy is proportional to T.Average kinetic energy is proportional to T.

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The Kinetic Theory – Molecular The Kinetic Theory – Molecular Theory of Gases Theory of Gases

Theory leads to a description of bulk Theory leads to a description of bulk properties i.e. observable properties. properties i.e. observable properties.

The average kinetic energy of the The average kinetic energy of the molecule is molecule is

where Nwhere NAA = Avagadro’s number. = Avagadro’s number.

Ak N2

RT3E

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Average kinetic energy of moving particles Average kinetic energy of moving particles can also be obtained from can also be obtained from

where u = average velocitywhere u = average velocity2mu

2

1E

5454

Ak N2

RT3E 2mu

2

1E

•Combine 1 & 2 to get a relationship between the velocity, temperature and molecular mass.

5555

M

RT3u

5656

Determine average velocity of He at 300 K. Determine average velocity of He at 300 K.

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Predict the ratio of the speeds of a gas if the Predict the ratio of the speeds of a gas if the temperature is increased from 300 K to 450 temperature is increased from 300 K to 450 K. K.

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Graham’s Law: Diffusion and Graham’s Law: Diffusion and Effusion of GasesEffusion of Gases

Diffusion Diffusion the process whereby a gas spreads out the process whereby a gas spreads out through another gas to occupy the space with through another gas to occupy the space with uniform partial pressure.uniform partial pressure.

Effusion Effusion the process in which a gas flows through the process in which a gas flows through a small hole in a container.a small hole in a container.

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Graham’s Law of EffusionGraham’s Law of Effusion the rate of the rate of effusion of gas molecules through a hole is effusion of gas molecules through a hole is inversely proportional to the square root of inversely proportional to the square root of the molecular mass of the gas at constant the molecular mass of the gas at constant temperature and pressure.temperature and pressure.

MWk

Rate

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Graham’s Law for Two GasesGraham’s Law for Two Gases

6161

Determine the molecular mass of an Determine the molecular mass of an unknown compound if it effused through a unknown compound if it effused through a small orifice 3.55 times slower than CHsmall orifice 3.55 times slower than CH44..

6262

A compound with a molecular mass of 32.0 A compound with a molecular mass of 32.0 g/mol effused through a small opening in 35 g/mol effused through a small opening in 35 s; determine the effusion time for the same s; determine the effusion time for the same amount of a compound with a molecular amount of a compound with a molecular mass of 16.0.mass of 16.0.

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