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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
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.
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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