Gases
Name: _______________________
AP Chemistry Lecture Outline
Basics on Gases
composition of the atmosphere:
properties of gases:
vapors: gases of substances that are normally liquids or solids
Equation for pressure:
1 atm = 760 mm Hg = 760 torr = 101.325 kPa = 1.01325 bar
OPEN END
MANOMETER
BAROMETER
CLOSED END
MANOMETER
AIR
PRESSURE
vacuum
SEALED END
air
pressure
mercury
(Hg)
Hg HEIGHT
DIFFERENCE
CONFINED
GAS
The Gas Laws
Boyle’s law:
Charles’s law:
Gay-Lussac’s law:
PV = constant
V/T = constant
P/T = constant
V
V
P
P
T
T
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Avogadro’s law: Equal volumes of gas at the same temperature and pressure have the same
number of particles.
Combined Gas law: merges Boyle’s, Charles’s, and Gay-Lussac’s laws in one equation.
**NOTE: For all gas law calculations, use the
absolute temperature (in K).
Ideal Gas law:
n = number of moles of gas
R = 8.314 L-kPa/mol-K = 0.08206 L-atm/mol-K
Conditions of standard pressure and temperature (STP):
Equation for gas density (in g/L):
d
P
RT
 = molar mass of gas
To solve problems involving volumes of gases in chemical reactions:
1. Use PV = nRT to get any and all gases in terms of moles (i.e., n).
2. Solve the problem using stoichiometry.
EX.
Safety air bags in automobiles are inflated by nitrogen gas generated by the rapid
decomposition of sodium azide, according to
2 NaN3(s)
2 Na(s) + 3 N2(g)
If an air bag has a volume of 36 L and is to be filled with nitrogen at 1.15 atm and
26.0oC, how many grams of sodium azide must be decomposed?
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Dalton’s law of Partial Pressure
Ptot = P1 + P2 + ...
total pressure of mixture
partial pressures:
Other equations:
Total moles of gas in a mixture of gases can be found using:
The mole fraction (X) of a gas in a mixture is found using:
EX.
Find the total pressure exerted by 14 g of carbon monoxide and 14 g of nitrogen in
a 6.0-L container at 25oC.
Collecting Gases over Water
gas being
collected
filled with
water, initially
collected gas
(w/H2O vapor, too)
gas from
reaction
H2O levels
even
before
reaction
during
reaction
reaction
complete
After the reaction is complete, raise or lower the collecting vessel so that the water levels
inside and out are the same. In this way...
3
EX.
For the reaction
CaC2(s) + H2O(l)
C2H2(g) + CaO(s)...
If 0.852 L of acetylene are collected over water at 20.0 oC, find the number of moles
of acetylene collected and the number of grams of calcium carbide used. Assume the
barometric pressure to be 732.0 torr.
EX.
Find the total pressure in container Z.
PX
A
B
C
1.3 L
3.2 atm
2.6 L
1.4 atm
3.8 L
2.7 atm
VX
VZ
Z
2.3 L
X atm
PX,Z
A
B
C
The Kinetic-Molecular Theory (the theory of moving molecules)
1. Gas particles are in constant, random motion.
2. The volume of the particles is negligible compared to the container volume.
3. The attractive-repulsive forces between particles are negligible.
4. Collisions are perfectly elastic (i.e., no energy is lost).
5. KEavg of molecules is proportional to absolute temperature.
At a given temperature, the gas particles of Sample A have the same KE
as the gas particles of Sample B.
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pressure = “how hard” and “how often” gas particles collide with the sides of the container
Particle-Velocity Distribution
(various gases, same T and P)
# of
particles
Particle-Velocity Distribution
(same gas, same P, various T)
# of
particles
(SLOW)
Velocity of particles (m/s) (FAST)
(SLOW)
Velocity of particles (m/s) (FAST)
Equation for the rms (root-mean-square) speed of a gas:
R = 8.314 J/mol-K
 = molar mass, in kg
KEavg for a particle =
EX.
Find the rms velocity of chlorine gas at 80oC.
effusion:
the escape of gas particles through a tiny
hole into an evacuated space
diffusion:
the spread of one substance from
high concentration to low concentration
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For gases, rates of diffusion & effusion obey Graham’s law:
The rate of diffusion of gases is slower than the molecular speeds because of...
-The mean free path is the average distance traveled by a particle between collisions.
-- it is shorter when the pressure is high
EX.
At a given temperature, an unknown noble gas travels 1.26 times faster than oxygen
gas. What is the noble gas?
Real Gases: Deviations from Ideal Behavior
All real gases deviate, to some degree, from PV = nRT. The deviations are most
pronounced at...
Real gas particles... (1)
(2)
ideal gas (ideal gas equation):
real gas (van der Waals equation):
PV  nRT 
P
P
nRT
V
nRT
n2a
 2
V - nb V
The constants a and b are unique for each gas.
-- a is large when interparticle attractions are large
-- b is large for large gas particles
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