Chapter 5 Gases

Roy KennedyMassachusetts Bay Community College

Wellesley Hills, MA2008, Prentice Hall

Chemistry: A Molecular Approach, 1st Ed.

Nivaldo Tro

Air Pressure & Shallow Wellswater for many homes is

supplied by a well less than 30 ft. deep with a pump at the surface

the pump removes air from the pipe, decreasing the air pressure in the pipe

the outside air pressure then pushes the water up the pipe

the maximum height the water will rise is related to the amount of pressure the air exerts

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Atmospheric Pressurepressure is the force

exerted over an areaon average, the air

exerts the same pressure that a column of water 10.3 m high would exert14.7 lbs./in2

so if our pump could get a perfect vacuum, the maximum height the column could rise is 10.3 m

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Area

Force Pressure

Gases Pushinggas molecules are constantly in

motionas they move and strike a surface,

they push on that surfacepush = 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 exertingpressure = force per unit area

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The Effect of Gas Pressurethe pressure exerted by a gas can cause

some amazing and startling effectswhenever there is a pressure difference, a

gas will flow from area of high pressure to low pressurethe bigger the difference in pressure, the

stronger the flow of the gasif there is something in the gas’s path, the

gas will try to push it along as the gas flows

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Atmospheric Pressure Effects

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 youat the surface the atmospheric pressure is

14.7 psi, but at 10,000 ft it is only 10.0 psirapid 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 Gasresult of the constant

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

the pressure of a gas depends on several factorsnumber of gas particles in a

given volumevolume of the containeraverage speed of the gas

particles

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Measuring Air Pressureuse a barometercolumn of

mercury supported by air pressure

force of the air on the surface of the mercury balanced by the pull of gravity on the column of mercury

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gravity

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Unit Average Air Pressure at Sea Level

pascal (Pa), 101,325

kilopascal (kPa) 101.325

atmosphere (atm) 1 (exactly)

millimeters of mercury (mmHg) 760 (exactly)

inches of mercury (inHg) 29.92

torr (torr) 760 (exactly)

pounds per square inch (psi, lbs./in2) 14.7

2m

N 1 Pa 1

ExamplesA high-performance bicycle tire has a

pressure of 132 psi. What is the pressure in mmHg?

Convert a pressure of 23.8 in Hg to kPa

Manometersthe pressure of a gas trapped in a container can

be measured with an instrument called a manometer

manometers are U-shaped tubes, partially filled with a liquid, connected to the gas sample on one side and open to the air on the other

a competition is established between the pressure of the atmosphere and the gas

the difference in the liquid levels is a measure of the difference in pressure between the gas and the atmosphere

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for this sample, the gas has a larger pressure than the atmosphere, so

(mm) levels Hgin difference (mmHg)Pressure (mmHg)Pressure

Pressure Pressure Pressure

atmospheregas

hatmospheregas

Boyle’s Lawpressure of a gas is inversely

proportional to its volumeconstant T and amount of gasgraph P vs V is curvegraph P vs 1/V is straight line

as P increases, V decreases by the same factor

P x V = constantP1 x V1 = P2 x V2

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Boyle’s Experimentadded Hg to a J-tube

with air trapped inside

used length of air column as a measure of volume

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Length of Airin Column

(in)

Difference inHg Levels

(in)48 0.044 2.840 6.236 10.132 15.128 21.224 29.722 35.0

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Boyle's Expt.

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

Volume of Air, in3

Pre

ssu

re, in

Hg

Inverse Volume vs Pressure of Air, Boyle's Expt.

0

20

40

60

80

100

120

140

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Inv. Volume, in-3

Pre

ss

ure

, in

Hg

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When you double the pressure on a gas,the volume is cut in half (as long as the

temperature and amount of gas do not change)

Boyle’s Law and Divingsince water is denser

than air, for each 10 m you dive below the surface, the pressure on your lungs increases 1 atmat 20 m the total

pressure is 3 atm

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if your tank contained air at 1 atm pressure you would not be able to inhale it into your lungs

ExamplesA 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 balloon is put in a bell jar and the pressure is reduced from 782 torr to 0.500 atm. If the volume of the balloon is now 2780 mL, what was it originally?

Charles’ Lawvolume is directly proportional to

temperatureconstant P and amount of gasgraph of V vs T is straight line

as T increases, V also increasesKelvin T = Celsius T + 273V = constant x T

if T measured in Kelvin

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2

2

1

1

T

V

T

V

Charles’ Law – A Molecular Viewthe pressure of gas inside

and outside the balloon are the same

at low temperatures, the gas molecules are not moving as fast, so they don’t hit the sides of the balloon as hard – therefore the volume is small

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Charles’ Law – A Molecular View• the pressure of gas

inside and outside the balloon are the same

•at high temperatures, the gas molecules are moving faster, so they hit the sides of the balloon harder – causing the volume to become larger

Charles’ Law – A Molecular View• the pressure of gas

inside and outside the balloon are the same

•at high temperatures, the gas molecules are moving faster, so they hit the sides of the balloon harder – causing the volume to become larger

23

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 torrVolume (L) of 1 g O2 @ 2500 torrVolume (L) of 0.5 g O2 @ 1500 torrVolume (L) of 0.5 g SO2 @ 1500 torr

The data fall on a straight line.If the lines are extrapolated back to a volume of “0,” they all show the same temperature, -273.15°C, called absolute zero

ExamplesA gas has a volume of 2.57 L at 0.00°C. What

was the temperature at 2.80 L?The temperature inside a balloon is raised from

25.0°C to 250.0°C. If the volume of cold air was 10.0 L, what is the volume of hot air?

Avogadro’s Lawvolume directly proportional to

the number of gas moleculesV = constant x nconstant P and Tmore gas molecules = larger

volumecount number of gas molecules

by molesequal volumes of gases contain

equal numbers of moleculesthe gas doesn’t matter

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2

2

1

1

n

V

n

V

ExamplesA 0.225 mol sample of He has a volume of

4.65 L. How many moles must be added to give 6.48 L?

A chemical reaction occurring in a cylinder equipped with a moveable piston produces 0.621 mol of a gaseous product. If the cylinder contianed 0.120 mol of gas before the reaction and had an initial volume of 2.18L, what was its volume after reaction?

Ideal Gas Law

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• By combing the gas laws we can write a general equation• R is called the gas constant• the value of R depends on the units of P and V

• we will use 0.08206 and convert P to atm and V to L• the other gas laws are found in the ideal gas law if two variables are kept constant• allows us to find one of the variables if we know the other 3

Kmol

Latm

nRTPVor R

Tn

VP

ExamplesHow many moles of gas are in a basketball

with total pressure 24.3 psi, volume of 3.24 L at 25°C?

An 8.50L tire is filled with 0.520 mol of gas at a temperature of 305K. What is the pressure in atm and mmHg of gas in the tire?

Standard Conditionssince 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 conditionsSTP

standard pressure = 1 atmstandard temperature = 273 K

0°C

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ExamplesA gas occupies 10.0 L at 44.1 psi and 27°C. What

volume will it occupy at standard conditions?

Molar Volumesolving the ideal gas equation for the volume

of 1 mol of gas at STP gives 22.4 L6.022 x 1023 molecules of gasnotice: the gas is immaterial

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

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

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Density at Standard Conditionsdensity is the ratio of mass-to-volumedensity of a gas is generally given in g/Lthe mass of 1 mole = molar massthe volume of 1 mole at STP = 22.4 L

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L 22.4

g Mass,Molar Density

Gas Density

density is directly proportional to molar mass

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TRmass)(molar P

density V

mass

TRmassmolar

massVP

TRnVP

litersin volumegramsin mass

density

massmolar mass

moles moles massmolar

mol 1mass

Molar Mass of a Gasone of the methods chemists use to

determine the molar mass of an unknown substance is to heat a weighed sample until it becomes a gas, measure the temperature, pressure, and volume, and use the ideal gas law

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moles

gramsin massMassMolar

ExamplesCalculate the density of a gas at 775 torr

and 27°C if 0.250 moles weighs 9.988 gA sample of gas has a mass of 827 mg. Its

volume is 0.270L at a temperature of 88oC and a pressure of 975 mmHg. Find its molar mass