unit 5: gases and gas laws. kinetic molecular theory particles of matter are always in motion ...
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Unit 5: Unit 5: GasesGases
and Gas and Gas LawsLaws
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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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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 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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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 Gases
Gases 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
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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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PressurePressure
Is 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 standard atmosphere = 101,325 Pa 1 standard 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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The Aneroid BarometerThe Aneroid Barometer
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Converting Celsius to KelvinConverting Celsius to Kelvin
Gas law problems involving temperature require that the temperature be in KELVINS!Kelvins = C + 273
°C = Kelvins - 273
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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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Boyle’s LawBoyle’s Law
Pressure Volume = Constant P1V1 = P2V2 (T = constant)
Pressure is inversely proportional to volume when temperature is held constant.
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A Graph of Boyle’s A Graph of Boyle’s LawLaw
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Why Don’t I Get a Constant Value for PV = k?
1. Air is not made
of ideal gases2. Real gases deviate from ideal behavior at high pressure
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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)
VT
VT
P1
1
2
2 ( constant)
Temperature MUST be in KELVINS!
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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
Temperature MUST be in KELVINS!
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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
Temperature MUST be in KELVINS!
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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.
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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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Standard Molar VolumeStandard Molar Volume
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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 (at low pressures).
V = an
a = proportionality constant V = volume of the gas n = number of moles of gas
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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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Gas DensityGas Density
molar mass
molar volume
massDensity
volume
… so at STP…
molar mass
22.4 LDensity
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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:
MPD
RT
M = Molar Mass
P = Pressure
R = Gas Constant
T = Temperature in Kelvins
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Real Gases Do Not Behave IdeallyReal Gases Do Not Behave Ideally