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Not so long ago, in a chemistry lab far far away…
May the FORCE/area be with you
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Ideal GasesIdeal gases are imaginary gases that perfectly fit all of the assumptions of the
kinetic molecular theory:
1) Gases consist of tiny particles that are far apart relative to their size. Volume of particles assumed to be negligible.
2) Collisions between gas particles and between particles and the walls of the container are elastic collisions. Assume particles are in constant motion.3) There are no forces of attraction between gas
particles
4) The average kinetic energy of gas particles depends on temperature, not on the identity of the particle.
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The 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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PressureIs 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
torr1 atm = 29.92inHg = 14.7 psi = 0.987 bar =
10 m column of water.
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Measuring Pressure
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 Barometer
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 Pressure
“STP”
P = 1 atmosphere, 760 torr T = 0°C, 273 Kelvins The molar volume of an ideal gas is 22.42 liters at STP
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Converting Celsius to KelvinGas law problems involving temperature require that the temperature be in KELVINS!
Kelvins = C + 273
°C = Kelvins - 273
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The Combined Gas Law
The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.
1 1 2 2
1 2
PV PV
T T
Boyle’s law, Gay-Lussac’s law, and Charles’ law are all derived from this by holding a variable constant.
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Boyle’s Law
Pressure is inversely proportional to volume when temperature is held constant.
1 1 2 2PV PV
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Charles’s Law The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.
(P = constant)
1 2
1 2
V V
T T
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Gay Lussac’s Law
The pressure and temperature of a gas are directly related, provided that the volume remains constant.
1 2
1 2
P P
T T
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Avogadro’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 Law
PV = nRT P = pressure in atm V = volume in liters n = moles R = proportionality constant
= 0.08206 L atm/ mol·K T = temperature in Kelvins
Holds closely at P < 1 atm
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Standard Molar Volume
Equal volumes of all gases at the same temperature and pressure contain the same number of molecules.
- Amedeo Avogadro
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Gas Densitymolar mass
molar volume
massDensity
volume
… so at STP…
molar mass
22.4 LDensity
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Density and the Ideal Gas Law
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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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 #2
How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen in a closed container at constant temperature?
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 #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 #4
nRT
VP
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
L atm(0.612mol)(0.0821 )(310K)
mol K0.930atm
= 16.7 L
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Dalton’s Law of Partial Pressures
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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Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.
Diffusion
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EffusionEffusion: describes the passage of gas into an evacuated chamber.
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I look like Abe Lincoln but I’m really Thomas Graham!
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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:
Diffusion:
Graham’s LawRates of Effusion and Diffusion
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Real Gases
[ ]P a V nb nRTobs2( / ) n V
corrected pressure corrected volume
Pidea
l
Videa
l
Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).
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