Chapter Five:

GASES

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Contentsp178

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5-1 Pressurep179

Why study gases?

1. An understanding of real world phenomena.

2. An understanding of how science “works.”

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A Gas

• Uniformly fills any container.

• Mixes completely with any other gas.

• Exerts pressure on its surroundings.

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Pressure

• SI units = Newton/meter2 = 1 Pascal (Pa)

• 1 standard atmosphere = 101,325 Pa

• 1 standard atmosphere = 1 atm =

760 mm Hg = 760 torr

Units of Pressure

…is equal to force/unit areap180

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Ex 5.1 Pressure Conversions

The pressure of a gas is measured as 49 torr. Represent

this pressure in both atmospheres and pascals.

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Solution:

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5-2 The Gas Laws of Boyle, Charles, andAvogadro

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Boyle’s Law

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Ex 5.2 Boyle’s LawSulfur dioxide (SO2), a gas that plays a central role in the

formation of acid rain, is found in the exhaust of automobiles

and power plants. Consider a 1.53-L sample of gaseous SO2

at a pressure of 5.6 × 103 Pa. If the pressure is changed to 1.5

× 104 Pa at a constant temperature, what will be the new

volume of the gas?

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Solution:

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Liquid Nitrogen and a Balloon

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Volume and Temperature

What law results from observations

like these?

The volume of a gas depends on the

temperature of the gas (constant P and n).

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Charles’s Lawp184

Absolute zero

Volume and temperature are directly related

(constant P and n).

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Charles’s Law

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Other Laws

Pressure and Volume are inversely related

(constant T and n)

Boyle’s Law

PV = k

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Boyle’s Law

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Ex 5.4 Charles’s Law

A sample of gas at 15℃ and 1 atm has a volume of 2.58

L. What volume will this gas occupy at 38℃ and 1 atm?

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Solution:

Ex 5.5 Avogadro’s Law

Suppose we have a 12.2-L sample containing 0.5 mol

oxygen gas (O2) at a pressure of 1 atm and a

temperature of 25℃. If all this O2 were converted to

ozone (O3) at the same temperature and pressure and

pressure, what would be the volume of the ozone?

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Solution:

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Gas Volume, Pressure, and Concentration

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5-3 The Ideal Gas Lawp186

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Ideal Gas Law

We can bring all of these laws together into one

comprehensive law:

V = bT

PV = k

V = an

PV = nRT

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Ex 5.6 Ideal Gas Law

A sample of hydrogen gas (H2) has a volume of 8.56 L at

a temperature of 0℃ and a pressure of 1.5 atm. Calculate

the moles of H2 molecules present in this gas sample.

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Solution:

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5-4 Gas Stoichiometryp190

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A sample of nitrogen gas has a volume of 1.75 L at STP.

How many moles of N2 are present?

P191Ex 5.11 Gas Stoichiometry

Solution:

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Ex 5.14 Gas Denisty/Molar Mass

The density of a gas was measured at 1.50 atm

and 27℃ and found to be 1.95 g/L. Calculate the

molar mass of the gas.

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Solution:

5-5 Dalton’s Law of Partial Pressuresp194

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .

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Mole fraction

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Ex 5.15 Dalton’s LawP195

Mixtures of helium and oxygen can be used in scuba divingtanks to help prevent “the bends.”For a particular dive, 46L He at 25℃ and 1.0 atm and 12 L O2 at 25℃ and 1.0 atmwere pumped into a tank with a volume of 5.0 L. Calculatethe partial pressure of each gas and the total pressure in thetank at 25℃.Solution:

P198Ex 5.18 Gas Collection over WaterA sample of solid potassium chlorate (KClO3) was

heated in a test tube (see Fig. 5.13) and decomposed by

the following reaction:

The oxygen produced was collected by displacement of

water at 22℃ at a total pressure of 754 torr. Calculate the

partial pressure of O2 in the gas collected and mass of

KClO3 in the sample that was decomposed.

)(3O)(2KCl)(KClO2 23 gss

Solution:

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5-6 The Kinetic Molecular Theory ofGases

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So far we have considered “what happens,”but

not “why.”

In science, “what”always comes before “why.”

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Kinetic Molecular Theory

Assumptions:

1. Gas particles are in rapid motion, colliding

with container walls.

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Kinetic Molecular Theory

Assumptions:

2. Gas particles have negligible size

compared to the distances between them.

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Kinetic Molecular Theory

Assumptions:

3. Gas particles have no attraction for one

another.

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Kinetic Molecular Theory

Assumptions:

4. Absolute temperature of the gas is a

measure of the average kinetic energy of

the gas particles.

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Kinetic Molecular Theory

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Kinetic Molecular Theory

Animation: Visualizing Molecular Motion (many

molecules)

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Kinetic Molecular Theory

Animation: Kinetic Molecular Theory/Heat-

Transfer

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Molecular View of Boyle’s Law

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Molecular View of Charles’s Law

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Molecular View of The Ideal Gas Law

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Video: Collapsing Can

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Kinetic molecular theory(KMT)

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Pressure and Volume (Boyle’s Law)

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Pressure and Temperature

Volume and Temperature (Charles’s Law)

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Volume and Number of Moles (Avogadrao’s Law)

Mixture of gases (Dalton’s Law)

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Deriving the Ideal Gas Law p203

The Meaning of Temperature p204

Root Mean Square Velocity

Ex 5.19 Root Mean Square Velocity P205

Calculate the root mean square velocity for the atoms

in a sample of helium gas at 25℃.Solution:

=

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5-7 Effusion and Diffusionp206

Diffusion is the term used to describe themixing of gases.

The rate of effusion measuresthe speed at which the gas istransferred into the chamber.

Figure 5-22

Effusion

P206Ex 5.20 Effusion RatesCalculate the ratio of the effusion rates of hydrogen gas (H2)

and uranium hexafluoride (UF6), a gas used in the enrichment

process to fuel for nuclear reactors (see Fig. 5.23).

Figure 5.23Solution:

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Effusion

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Diffusion

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Ammonia and HCl

NH3(g) + HCl(g) → NH4Cl(s) White solidp207

Figure 5-24

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We must correct for ideal gas behavior when

the pressure of the gas is high.

smaller volume

the temperature is low.

attractive forces become important

5-8 Real Gases p208

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Plots of PV/nRT Versus Pfor Several Gases (200 K)

Figure 5.25

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Plots of PV/nRT Versus P forNitrogen Gas at Three Temperatures

Figure 5.26

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Real Gases

[ ]P a V nb nRTobs2( / ) n V

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corrected pressure

Pideal

corrected volume

Videal

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5-9 Characteristics of Several Real Gasesp211

A low value for a reflects weak intermolecular

forces among the gas molecules.

Based on the this behavior we can surmise that

the importance of intermolecular increases in

this order.

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p2115-10 Chemistry in the Atmosphere

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Table 5.4 Atmospheric Composition Near SeaLevel (Dry Air)

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Figure 5.31

Concentration for Some SmogComponents vs. Time of Day

A Schematic Diagram of a Scrubber

Figure 5.33

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Photochemical smog p213