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Chemistry: A Molecular Approach , 1 st Ed. Nivaldo Tro. Chapter 5 Gases. 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 - PowerPoint PPT Presentation
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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
Tro, Chemistry: A Molecular Approach 2
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
Tro, Chemistry: A Molecular Approach 3
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
Tro, Chemistry: A Molecular Approach 4
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
Tro, Chemistry: A Molecular Approach 5
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
Tro, Chemistry: A Molecular Approach 6
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
Tro, Chemistry: A Molecular Approach 7
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
Tro, Chemistry: A Molecular Approach 8
gravity
Tro, Chemistry: A Molecular Approach 9
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
Tro, Chemistry: A Molecular Approach 11
Tro, Chemistry: A Molecular Approach 12
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
Tro, Chemistry: A Molecular Approach 13
Boyle’s Experimentadded Hg to a J-tube
with air trapped inside
used length of air column as a measure of volume
Tro, Chemistry: A Molecular Approach 14
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
Tro, Chemistry: A Molecular Approach 15
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
Tro, Chemistry: A Molecular Approach 16
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
Tro, Chemistry: A Molecular Approach 17
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
Tro, Chemistry: A Molecular Approach 19
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
Tro, Chemistry: A Molecular Approach 20
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
Tro, Chemistry: A Molecular Approach 25
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
Tro, Chemistry: A Molecular Approach 27
• 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
Tro, Chemistry: A Molecular Approach 29
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
Tro, Chemistry: A Molecular Approach 31
Tro, Chemistry: A Molecular Approach 32
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
Tro, Chemistry: A Molecular Approach 33
L 22.4
g Mass,Molar Density
Gas Density
density is directly proportional to molar mass
Tro, Chemistry: A Molecular Approach 34
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
Tro, Chemistry: A Molecular Approach 35
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