gases. pressure is caused by the collisions of molecules with the walls of a container is equal to...
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GasesGases
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PressurePressureIs caused by the collisions of molecules with
the walls of a container is equal to force/unit area SI units = Newton/meter2 = 1 Pascal (Pa) 1 atmosphere = 101,325 Pa 1 atmosphere = 1 atm = 760 mm Hg = 760
torr
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Measuring Measuring PressurePressure
The first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17th century.The device was called a “barometer”
Baro = weight Meter = measure
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An Early An Early BarometerBarometer
The normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high.
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Standard Temperature and Standard Temperature and PressurePressure
“STP”“STP”
P = 1 atmosphere, 760 torr T = C, 273 Kelvins The molar volume of an ideal gas is 22.42 liters at STP
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Converting Celsius to KelvinConverting Celsius to KelvinGas law problems involving temperature require that the temperature be in KELVINS!
Kelvins = C + 273
°C = Kelvins - 273
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Boyle’s LawBoyle’s Law
Pressure is inversely proportional to volume when temperature is held constant.
2211 VPVP
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A sample of helium gas at 25°C is compressed from 200 cm3 to 0.240 cm3. Its pressure is now 3.00 cm Hg. What was the original pressure of the helium?
P1V1 = P2V2
P1 = P2V2/V1
P1 = 3.00 cm Hg x 0.240 cm3/200 cm3
P1 = 3.60 x 10-3 cm Hg
P1 = ?V1 = 200 cm3
P2 = 3.00 cmV2 = 0.240 cm3 Hg
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Charles’s LawCharles’s Law The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.
(P = constant)
2
2
1
1
T
V
T
V
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Gay Lussac’s LawGay Lussac’s Law
The pressure and temperature of a gas are directly related, provided that the volume remains constant.
2
2
1
1
T
P
T
P
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A sample of oxygen gas has a volume of 2.73 dm3 at 21.0 oC. At what temperature would the gas have a volume of 4.00 dm3?
T1 = 294 KV1 = 2.73 dm3
T2 = ?V2 = 4.00 dm3
V1 = V2
T1 T2
T2 = 294 K x 4.00 dm3
----------------------- 2.73 dm3
2.73 dm3 = 4.00 dm3
----------- -------------
294 K T2
T2 = 431 K
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The Combined Gas LawThe Combined Gas Law
The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.
2
22
1
11
T
VP
T
VP
Boyle’s law, Gay-Lussac’s law, and Charles’ law are all derived from this by holding a variable constant.
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A 350 cm3 sample of helium gas is collected at 22.0 oC and 99.3 kPa. What volume would this gas occupy at STP ?
V1 = 350 cm3
P1 = 99.3 kPaT1 = 295 KV2 = ?P2 = 101.3 kPa (standard press)T2 = 273 K (standard temp))
P1 V1 = P2 V2
---------- --------------
T1 T2
(99.3 kPa )(350 cm3 ) = (101.3 kPa) V2 --------------------------------------- ___________________
( 295 K) (273 K)
V2 = 320 cm3
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Avogadro’s LawAvogadro’s Law
For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas.
V = an
a = proportionality constant V = volume of the gas n = number of moles of gas
31. D 32. D 33. D 34. C 35. C 36. B 37. B
------------------------------------
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Ideal Ideal GasesGases
Ideal gases are imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory.
Gases consist of tiny particles that are far apart relative to their size.
Collisions between gas particles and between particles and the walls of the container are elastic collisions
No kinetic energy is lost in elastic collisions
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Ideal Gases Ideal Gases (continued)
Gas particles are in constant, rapid motion. They therefore possess kinetic energy, the energy of motion
There are no forces of attraction between gas particles
The average kinetic energy of gas particles depends on temperature, not on the identity of the particle.
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The Nature of GasesThe Nature of GasesGases expand to fill their containers Gases are fluid – they flow Gases have low density
1/1000 the density of the equivalent liquid or solid
Gases are compressible Gases effuse and diffuse
– Effusion, molecules moving at a high rate of speed will eventually “collide” with a hole and escape.
• Effusion is gas escaping through a hole,
• Example: air escaping through a hole in your tire
• Diffusion, again because the molecules are moving at a high rate of speed, they will spread out– Example: perfume diffusing through air
– Example: Liquids also diffuse: food coloring in water
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Ideal Gas LawIdeal Gas Law
PV = nRT P = pressure in atm V = volume in liters n = moles R = proportionality constant
= 0.08206 L atm/ mol· T = temperature in Kelvins
Holds closely at P < 1 atm
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What volume is occupied by 5.03 g of O2 at 28°C and a pressure of 0.998 atm?
P = 0.998 atm
V= ?
Mass = 5.03 g O2 / 1 mol O2 / =
/ 32 g O2 /
n= 0.157 moles
R = 0.08206 L atm mol K
T = 28°C + 273 = 301 K
PV = nRT
(0.998 atm) V = (0.157 mol) (0.08206 L atm ) ( 301 K) mol K
=3.89 L
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Standard Molar Standard Molar VolumeVolume
Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.
- Amedeo Avogadro
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Density and the Ideal Gas Density and the Ideal Gas LawLaw
Combining the formula for density with the Ideal Gas law, substituting and rearranging algebraically:
M = Molar Mass
P = Pressure
R = Gas Constant
T = Temperature in Kelvins
dRT = molar
P mass
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Gas Stoichiometry #1If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios.
3 H2(g) + N2(g) 2NH3(g)
3 moles H2 + 1 mole N2 2 moles NH3 3 liters H2 + 1 liter N2 2 liters NH3
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Gas Stoichiometry #2How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen?
3 H2(g) + N2(g) 2NH3(g)
12 L H2
L H2
= L NH3 L NH3
3
28.0
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Gas Stoichiometry #3Gas Stoichiometry #3How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?
2 KClO3(s) 2 KCl(s) + 3 O2(g)
= L O2
50.0 g KClO3 1 mol KClO3
122.55 g KClO3
3 mol O2
2 mol KClO3
22.4 L O2
1 mol O2
13.7
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Gas Stoichiometry #4Gas Stoichiometry #4
PnRT
V
How many liters of oxygen gas, at 37.0C and 0.930 atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate?
2 KClO3(s) 2 KCl(s) + 3 O2(g)
= “n” mol O2
50.0 g KClO3 1 mol KClO3
122.55 g KClO3
3 mol O2
2 mol KClO3 0.612 mol O2
atm0.930
K))(310Kmol
atmL1mol)(0.082(0.612
= 16.7 L
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Dalton’s Law of Partial Dalton’s Law of Partial PressuresPressures
For a mixture of gases in a container,
PTotal = P1 + P2 + P3 + . . .
This is particularly useful in calculating the pressure of gases collected over water.
nTotal = n1 + n2 + n3 + . . .
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Mixture of gas and water vapor.
PT = pgas + pvap(H2O)
Dalton’s law of partial pressurescollecting gases over water
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Hydrogen gas is collected over water at a total pressure of 95.0 kPa and a temperature of 25 C. What is the partial pressure of hydrogen gas? According to a water vapor pressure table, the vapor pressure of water at 25C is 3.17 kPa.
Ptotal = Pgas + P water vapor 95.0 kPa = X + 3.17 kPa
X = 91.8 kPa
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• e.g., If 6.00 g of O2 and 9.00 g of CH4 are placed in a 15.0-L container
• at 0ºC, what is the partial pressure of each gas and the total pressure in
• the container.
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Kinetic Energy of Gas Kinetic Energy of Gas ParticlesParticles
At the same conditions of temperature, all gases have the same average kinetic energy.
2
2
1mvKE
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The Meaning of TemperatureThe Meaning of Temperature
Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)
(KE)32avg RT
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Kinetic Molecular Kinetic Molecular TheoryTheory
Particles of matter are ALWAYS in motion
Volume of individual particles is zero.
Collisions of particles with container walls cause pressure exerted by gas.
Particles exert no forces on each other.
Average kinetic energy Kelvin temperature of a gas.
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Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.
DiffusionDiffusion
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EffusionEffusionEffusion: describes the passage of gas into an evacuated chamber.
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Kinetic Molecular Theory• Gases have certain properties that can be explained by the KMT. • Low Density, because the molecules are moving at a high rate of speed and
are not held back by electrostatic attractions, they, spread out. And because gases have small volume as well as being spread out, they have low density
• Compressibility, because the molecules have space between them, they can be forced to compress unlike liquids and solids where there is little space between the molecules
• Expansion, because the molecules are moving at a high rate of speed, they will spread out if given the opportunity
• Diffusion, again because the molecules are moving at a high rate of speed, they will spread out
– Example: perfume diffusing through air– Example: Liquids also diffuse: food coloring in water
• Effusion, molecules moving at a high rate of speed will eventually “collide” with a hole and escape.
– Effusion is gas escaping through a hole,– Example: air escaping through a hole in your tire
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Rate of effusion for gas 1Rate of effusion for gas 2
2
1
MM
Distance traveled by gas 1Distance traveled by gas 2
2
1
MM
Effusion:Effusion:
Diffusion:Diffusion:
Graham’s LawGraham’s LawRates of Effusion and DiffusionRates of Effusion and Diffusion
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Real GasesReal Gases
[ ]P a V nb nRTobs2( / ) n V
corrected pressurecorrected pressure corrected volumecorrected volume
PPideaidea
ll
VVideaidea
ll
Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).