Transcript Chapter 5 Gases

Chemistry: A Molecular Approach, 1st Ed.
Nivaldo Tro
Roy Kennedy
Massachusetts Bay Community College
Wellesley Hills, MA
2008, Prentice Hall
Air Pressure & Shallow Wells
 water 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 Pressure
 pressure is the force
exerted over an area
 on average, the air exerts
the same pressure that a
column of water 10.3 m
high would exert
 14.7 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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Force
Pressure 
Area
3
Gases 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
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The Effect of Gas Pressure
 the pressure exerted by a gas can cause some amazing and
startling effects
 whenever there is a pressure difference, a gas will flow
from area of high pressure to low pressure
 the bigger the difference in pressure, the stronger the flow
of the gas
 if 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 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 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 Pressure
 use a barometer
 column 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
8
Common Units of Pressure
Unit
pascal (Pa), 1 Pa  1
Average Air Pressure at
Sea Level
N
m
2
101,325
kilopascal (kPa)
101.325
atmosphere (atm)
1 (exactly)
millimeters of mercury (mmHg)
inches of mercury (inHg)
torr (torr)
760 (exactly)
29.92
760 (exactly)
pounds per square inch (psi, lbs./in2)
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14.7
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Examples
 A 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
Manometers
 the 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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Manometer
for this sample, the gas has a larger
pressure than the atmosphere, so
Pressure gas  Pressure atmosphere  Pressure h
Pressure gas (mmHg)  Pressure atmosphere(mmHg)  difference in Hg levels (mm)
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Boyle’s Law
 pressure of a gas is inversely proportional to its
volume
 constant T and amount of gas
 graph P vs V is curve
 graph P vs 1/V is straight line
 as P increases, V decreases by the same factor
 P x V = constant
 P1 x V1 = P2 x V2
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Boyle’s Experiment
 added 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 Air
in Column
(in)
48
44
40
36
32
28
24
22
Difference in
Hg Levels
(in)
0.0
2.8
6.2
10.1
15.1
21.2
29.7
35.0
14
Boyle's Expt.
140
120
80
60
40
20
0
0
10
20
30
40
50
60
3
Volume of Air, in
Inverse Volume vs Pressure of Air, Boyle's Expt.
140
120
100
Pressure, inHg
Pressure, inHg
100
80
60
40
20
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Inv. Volume, in-3
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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)
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Boyle’s Law and Diving
 since water is denser than air,
for each 10 m you dive below
the surface, the pressure on
your lungs increases 1 atm
 at 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
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Examples
 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 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’ Law
 volume is directly proportional to
temperature
 constant P and amount of gas
 graph of V vs T is straight line
 as T increases, V also increases
 Kelvin T = Celsius T + 273
 V = constant x T
 if T measured in Kelvin
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V1 V2

T1 T2
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Charles’ Law – A Molecular View
 the 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
Charles' Law & Absolute Zero
0.6
Volume (L) of 1 g
torr
Volume (L) of 1 g
torr
Volume (L) of 0.5
torr
Volume (L) of 0.5
1500 torr
0.5
O2 @ 1500
O2 @ 2500
g O2 @ 1500
g SO2 @
0.4
Volume, L
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
0.3
0.2
0.1
0
-300
-200
-100
0
100
200
Temperature, °C
23
Examples
 A 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 Law
 volume directly proportional to the
number of gas molecules
 V = constant x n
 constant P and T
V 1 V2

n1 n 2
 more gas molecules = larger volume
 count number of gas molecules by
moles
 equal volumes of gases contain equal
numbers of molecules
 the gas doesn’t matter
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Examples
 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?
 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
• 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
atm  L
• we will use 0.08206 mol  K 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
P   V   R
n   T 
or PV  nRT
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Examples
 How 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
Conditions
 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
 STP
 standard pressure = 1 atm
 standard temperature = 273 K
 0°C
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Examples
 A gas occupies 10.0 L at 44.1 psi and 27°C. What volume will it
occupy at standard conditions?
Molar 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
 notice: the gas is immaterial
 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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Molar Volume
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Density at Standard Conditions
 density is the ratio of mass-to-volume
 density of a gas is generally given in g/L
 the mass of 1 mole = molar mass
 the volume of 1 mole at STP = 22.4 L
Molar Mass, g
Density 
22.4 L
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Gas Density
1 mol
mass
mass 
 moles  moles 
molar mass
molar mass
mass in grams
density 
volume in liters
PV  nR T
mass
PV 
RT
molar mass
mass
P  (molar mass)
 density 
V
RT
 density is directly proportional to molar mass
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Molar Mass of a Gas
 one 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
mass in grams
Molar Mass 
moles
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Examples
 Calculate the density of a gas at 775 torr and 27°C if
0.250 moles weighs 9.988 g
 A 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