kinetic theory of gases 1. gas particles do not attract or repel one another 2. gas particles are...
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Kinetic Theory of Gases
• 1. Gas particles do not attract or repel one another
• 2. Gas particles are much smaller than the distances between them
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Kinetic Theory of Gases
• 3. Gas particles are in constant random motion
• 4. Gas particle collisions with other particles or their container are elastic (no kinetic energy lost)
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Kinetic Theory of Gases
• 5. All gases have the same kinetic energy at a given temperature
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Boyle’s Law• States that pressure and
volume are inversely proportional to one another.–As one variable increases the
other decreases
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Boyle’s Law• P1V1 = P2V2
• P1V1 are the initial set of conditions
• P2V2 are the new set of conditions
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Boyle’s Law• Gas in an engine cylinder is at a
pressure of 3 atm and has a volume of .65 L. The piston is then pushed down reducing the volume to .34 L, what is the new pressure in the balloon?
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Boyle’s Law• P1V1 = P2V2
• (3atm)(.65L) = P2(.34L)• P2 = 5.74 atm• * As you can see the pressure
increases as the volume decreases
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Boyle’s Law
Pressure
V
O
L
U
M
E
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Charles’s Law• States that as temperature
increases, volume increases
• There is a directly proportional relationship between temperature (in K) and pressure. –As one increases the other increases
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Charles’s Law• V1 = V2
T1 T2
If you know three of the four values you can calculate the other
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Charles’s Law• A sample of CO2 at 293oK
occupies a 4.52 L container, what volume would the container have to be reduced to in order to bring the temperature down to the freezing point of 194.5oK?
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Charles’s Law• V1 = V2
T1 T2
4.52L = V2
293oK 194.5oKV1 = 3.00L
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Charles’s Law
Temperature
V
O
L
U
M
E
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Gay-Lussac’s Law
• States that temperature and pressure are directly proportional to one another–As temperature increases so
does the pressure
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Gay-Lussac’s Law
• P1 = P2
T1 T2
If you know three of the four values you can calculate the other
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Gay-Lussac’s Law
• The pressure of a gas is raised from 4.65 atm at 30oC to 32.56 atm? What is the new temperature?
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Gay-Lussac’s Law
• 4.65atm = 32.56atm
303oK T2
T2 = 2121.65 K
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Gay-Lussac’s Law
Temperature
P
R
E
S
S
U
R
E
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Combined Gas Law• Shows the relationship between
pressure, temperature, and volume
• Combines Boyles, Charles’s, and Gay-Lussac’s laws into one equation
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Combined Gas Law• P1V1 = P2V2
T1 T2
• Useful when dealing with many variables at one time
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Combined Gas Law• A gas at 2 atm and 289oK fills a
balloon with an initial volume of .05L. If the temperature is raised to 346oK and the pressure increases to 5.6 atm, what is the new volume of the balloon?
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Combined Gas Law• P1V1 = P2V2
T1 T2 • (2atm)(.05L) = (5.6atm)(V2)
289oK 346oK
V2 = .214 L
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Assignment• P. 422 1-5
• P. 425 6-8
• P. 427 9-13
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Avagadro’s Principle
• Equal volumes of gases that are at the same temperature and pressure have the same number of particles–1 L of He at 303o K and 1 atm and 1
L of Ne at 303o K and 1 atm contain the same number of particles
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Molar Volume• The volume that a gas occupies at
0o C and at 1 atm of pressure–These conditions are known as STP
(standard temperature and pressure)
–Every gas occupies 22.4 L at STP
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Molar Volume–So at STP 1 mole of any gas occupies
22.4 L–This can be used as a conversion factor
when solving stoichiometry problems22.4L1 mol
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Problem• How many particles are in a
sample of gas that has a volume of 3.73L at STP?
• 3.73L x 1 mol x 6.02 x 1023 part= • 22.4 L 1 mol • 9.99 x 1022 particles
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Ideal Gas Law• PV = nRT• Since we now know how to
determine the number of moles of a gas, we can use the above formula to relate four variables: Temp, Pressure, volume, and number of moles
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Ideal Gas Law• The R in the formula is the
ideal gas constant.–Varies with pressure units
–See chart on p 435
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How do ideal gases differ from real gases?
• At low temp or high pressure gases behave differently because of intermolecular force interaction.
• Large molecules and polar molecules also deviate from ideal behavior
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Ideal gas problem• How many moles of a gas
are contained in a 4.5L container at 1235K with a pressure of 3.50 atm?
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Answer• PV = nRT
• (3.5atm)(4.5L) = n(.0821L.atm/mol.K)(1235K)
• n= .15 mol
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Gas Stoichiometry
• Same as stoichiometry for mass/mass or mass/volume problems.–Write what you are given first
–Cancel units until you get to the unit you need
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Sample problem• What volume of H2 will be
needed to react with 2.3 L of O2 in order for complete reaction of hydrogen with oxygen?
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Answer• 2.3L O2 x 2 volumes H2 = 4.6
L H2
1 volumes O2
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Assignment• P. 432 25-27 odd• P. 433 29-33 odd• P. 437 41-45 odd• P. 438 45-49 odd• P. 441 57-59 odd• P. 443 61-65 odd