Chapter 5Chapter 5GasesGases

Air Pressure & Shallow Air Pressure & Shallow WellsWells

Gases

•Are mostly empty space

• Occupy containers uniformly and completely

• The densities of gases are much smaller than those of liquids and solid and highly variable depending on temperature and pressure

Because there is a lot of unoccupied space in the structure of a gas, gases do not have a lot of mass in a given volume, the result is they have low density•Expand infinitely

• Diffuse and mix rapidly

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Lower density

Higher density

Gases PushingGases Pushing gas molecules are constantly

in motion as they move and strike a

surface, they push on that surface◦ push = force

if we could measure the total amount of force exerted by gas molecules hitting the entire surface at any one instant, we would know the pressure the gas is exerting◦ pressure = force per unit

area

3

Pressure:Unit area

Force

Atmospheric Pressure Atmospheric Pressure EffectsEffects differences in air pressure

result in weather and wind patterns

the higher up in the atmosphere you climb, the lower the atmospheric pressure is around you◦ at the surface the

atmospheric pressure is 14.7 psi, but at 10,000 ft it is only 10.0 psi

rapid changes in atmospheric pressure may cause your ears to “pop” due to an imbalance in pressure on either side of your ear drum

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The Pressure of a GasThe Pressure of a Gas result of the constant

movement of the gas molecules and their collisions with the surfaces around them

the pressure of a gas depends on several factors◦ number of gas particles in a

given volume◦ volume of the container◦ average speed of the gas

particles

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Measuring Air PressureMeasuring Air Pressure

Barometer

Pa (SI unit)torr

mm Hgatmbar

Units

(exact)

Conversions

1 torr = 1 mm Hg

1 atm = 101 325 Pa

(exact)1 atm = 760 mm Hg

(exact)1 bar = 1 x 105 Pa

1 atm = 14.7 psi

Gases and Gas PressureGases and Gas Pressure

Boyle’s lawBoyle’s law

VP1

(constant n and T)

o pressure of a gas is inversely proportional to its volumeo constant T and amount

of gaso as P increases, V decreases

by the same factor

Two sets of conditionsP1 x V1 = P2 x V2

Charles’s LawCharles’s LawIn Charles’s Law,

• the Kelvin temperature of a gas is directly related to the volume.

• P and n are constant.

• when the temperature of a gas increases, its volume increases.

• For two conditions, Charles’s law is written

• V1 = V2 (P and n constant)

T1 T2

0

0.1

0.2

0.3

0.4

0.5

0.6

-300 -200 -100 0 100 200

Vo

lum

e, L

Temperature, °C

Charles' Law & Absolute Zero

Volume (L) of 1 g O2 @ 1500 torr

Volume (L) of 1 g O2 @ 2500 torr

Volume (L) of 0.5 g O2 @ 1500 torr

Volume (L) of 0.5 g SO2 @ 1500 torr

Charles’s Law can be used to approximate absolute zero. At a temperature of absolutezero (0K), theoretically an ideal gas has no volume.

Boyles’ Law and BreathingBoyles’ Law and Breathing

During an inhalation,• the lungs expand.• the pressure in the

lungs decreases.• air flows towards

the lower pressure in the lungs.

Avogadro’s LawAvogadro’s LawV n (constant T and P)

= kn

V

=nfinal

Vfinal

ninitial

Vinitial

ExamplesExamples

A cylinder with a movable piston has a volume of 7.25 L at 4.52 atm. What is the volume at 1.21 atm?

A gas has a volume of 2.57 L at 0.00°C. What was the temperature at 2.80 L?

A 0.225 mol sample of He has a volume of 4.65 L. How many moles must be added to give 6.48 L?

The Gas LawsThe Gas LawsIdeal Gas: A gas whose behavior follows the gas laws exactly.The physical properties of a gas can be defined by four variables:

P pressure (atm)T temperature (calculation must be in

Kelvin)V volume (L)n number of moles

The Ideal Gas Law, PV = nRT,

- models the behavior of ideal gases. Other gas laws can be derived from the Ideal Gas Law for either one set of conditions or for two sets of conditions (initial and final conditions).To derive gas laws for two sets of conditions, solve the Ideal Gas Law for R PV ---- = R nT

R = 0.08206K mol

L atm

ExamplesExamples

A 0.250 mol sample of argon gas has a volume of 9.00L at a pressure of 875 mmHg. What is the temperature (in oC) of the gas?

What volume is occupied by 25.7 g of carbon dioxide gas at 25.0oC and 371 torr?

The Ideal Gas LawThe Ideal Gas Law

Standard Temperature and Pressure (STP) for Gases

P = 1 atm

T = 0 °C (273.15 K)

since the volume of a gas varies with pressure and temperature, chemists have agreed on a set of conditions to report our measurements so that comparison is easy – we call these standard conditions

Molar VolumeMolar Volume solving the ideal gas equation for the volume of 1 mol

of gas at STP gives 22.4 L◦ 6.022 x 1023 molecules of gas

we call the volume of 1 mole of gas at STP the molar volume◦ it is important to recognize that one mole of different

gases have different masses, even though they have the same volume

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ExamplesExamples

What is the volume occupied by 2.75 moles of N2 gas at STP?

Assuming ideal behavior, which of the following gas samples will have the greatest volume at STP?a. 1 g H2 b. 1 g O2

c. 1 g Ar

Gas Density and Molar Gas Density and Molar MassMass

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MRT

Pd

V

m

MRT

P

V

m

Rearrange

RT

M

mPV

nRTPV

The density of a gas is proportional to its molar mass. As the molar mass of a gas increases, so does the density of the gas. Matter often separates according to its density, with less dense matter floating on matter of higher density

ExamplesExamples Calculate the density of gaseous hydrogen at a

pressure of 1.32 atm and a temperature of -45.0oC.

A sample of gas has a mass of 0.827g. Its volume is 0.270L at a temperature of 88.0oC and a pressure of 975 mmHg. Find its molar mass

Partial PressurePartial Pressure when gases are mixed together, their molecules

behave independent of each other the pressure of a single gas in a mixture of gases is

called its partial pressure we can calculate the partial pressure of a gas if the sum of the partial pressures of all the gases in the

mixture equals the total pressure◦ Dalton’s Law of Partial Pressures

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PT = P1 + P2 + P3 +....

Mole FractionMole Fraction

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the fraction of the total pressure that a single gas contributes is equal to the fraction of the total number of moles that a single gas contributes

total

A

total

A

n

n

P

P

the ratio of the moles of a single component to the total number of moles in the mixture is called the mole fraction,

total

AA n

n

the partial pressure of a gas is equal to the mole fraction of that gas times the total pressure

totalAA PP

ExampleExample

Find the partial pressure of neon in a mixture with total pressure 3.9 atm, volume 8.7 L, temperature 598 K, and 0.17 moles Xe.

Collecting GasesCollecting Gases gases are often

collected by having them displace water from a container

the problem is that since water evaporates, there is also water vapor in the collected gas

the partial pressure of the water vapor, called the vapor pressure, depends only on the temperature

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Vapor Pressure of WaterVapor Pressure of Water

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ExamplesExamples

1.02 L of O2 collected over water at 293 K with a total pressure of 755.2 mmHg. Find mass O2.

0.12 moles of H2 is collected over water in a 10.0 L container at 323 K. Find the total pressure.