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Gases
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Chapter 5
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Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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Elements that exist as gases at
250C
and 1 atmosphere
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Physical Characteristics of Gases
•
Gases assume the volume and shape of their containers.
•
Gases are the most compressible state of matter.
•
Gases will mix evenly and completely when confined to
the same container.
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Gases have much lower densities than liquids and solids.
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NO2 gas
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Force
Pressure = Area
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(force = mass x acceleration)
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Units of Pressure
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1 pascal (Pa) = 1 N/m2
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1 atm = 760 mmHg = 760 torr
1 atm = 101,325 Pa
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10 miles
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0.2 atm
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4 miles
Sea level
0.5 atm
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1 atm
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Manometers Used to Measure Gas Pressures
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closed-tube
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open-tube
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Apparatus for Studying the Relationship Between
Pressure and Volume of a Gas
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As P (h) increases
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V decreases
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Boyle’s Law
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P  1/V
P x V = constant
P1 x V1 = P2 x V2
Constant temperature
Constant amount of gas
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A sample of chlorine gas occupies a volume of 946 mL at a
pressure of 726 mmHg. What is the pressure of the gas (in
mmHg) if the volume is reduced at constant temperature to 154
mL?
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P x V = constant
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P1 x V1 = P2 x V2
P2 =
P1 = 726 mmHg
P2 = ?
V1 = 946 mL
V2 = 154 mL
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P1 x V1
726 mmHg x 946 mL
=
= 4460 mmHg
154 mL
V2
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Variation in Gas Volume with Temperature at Constant Pressure
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As T increases
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V increases
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Variation of Gas Volume with Temperature
at Constant Pressure
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Charles’ &
Gay-Lussac’s
Law
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VT
V = constant x T
Temperature must be
in Kelvin
V1/T1 = V2 /T2
T (K) = t (°C) + 273.15
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A sample of carbon monoxide gas occupies 3.20 L at 125 °C.
At what temperature will the gas occupy a volume of 1.54 L if
the pressure remains constant?
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V1 /T1 = V2 /T2
V1 = 3.20 L
V2 = 1.54 L
T1 = 398.15 K
T2 = ?
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T1 = 125 (°C) + 273.15 (K) = 398.15 K
T2 =
V2 x T1
=
V1
1.54 L x 398.15 K
3.20 L
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= 192 K
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Avogadro’s Law
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V  number of moles (n)
Constant temperature
Constant pressure
V = constant x n
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V1 / n1 = V2 / n2
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Ammonia burns in oxygen to form nitric oxide (NO) and water
vapor. How many volumes of NO are obtained from one volume
of ammonia at the same temperature and pressure?
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4NH3 + 5O2
4NO + 6H2O
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1 mole NH3
1 mole NO
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At constant T and P
1 volume NH3
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1 volume NO
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Summary of Gas Laws
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Boyle’s Law
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Charles Law
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Avogadro’s Law
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Ideal Gas Equation
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Boyle’s law: P  (at
constant n and T)
V
Charles’ law: V  T (at constant n and P)
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Avogadro’s law: V  n (at constant P and
T)
nT
V
P
nT
nT
V = constant x
=R
R is the gas constant
P
P
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PV = nRT
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The conditions 0 °C and 1 atm are called standard
temperature and pressure (STP).
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Experiments show that at STP, 1 mole of an ideal
gas occupies 22.414 L.
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PV = nRT
R=
(1 atm)(22.414L)
PV
=
nT
(1 mol)(273.15 K)
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R = 0.082057 L • atm / (mol • K)
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What is the volume (in liters) occupied by 49.8 g of HCl at STP?
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T = 0 °C = 273.15 K
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P = 1 atm
PV = nRT
nRT
V=
P
n = 49.8 g x
1.37 mol x 0.0821
V=
L•atm
mol•K
1 mol HCl
= 1.37 mol
36.45 g HCl
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x 273.15 K
1 atm
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V = 30.7 L
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Density (d) Calculations
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PM
d= m =
V
RT
m is the mass of the gas in g
M is the molar mass of the gas
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Molar Mass (M ) of a Gaseous Substance
M=
dRT
P
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d is the density of the gas in g/L
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A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and 27.0
°C. What is the molar mass of the gas?
M=
M=
dRT
P
2.21
g
L
4.65 g
= 2.21
d= m =
V 2.10 L
x 0.0821
L•atm
mol•K
g
L
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x 300.15 K
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1 atm
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M = 54.5 g/mol
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Gas Stoichiometry
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What is the volume of CO2 produced at 37 0C and 1.00 atm
when 5.60 g of glucose are used up in the reaction:
C6H12O6(s) + 6O2(g)
g C6H12O6
mol C6H12O6
5.60 g C6H12O6 x
6 mol CO2
1 mol C6H12O6
x
= 0.187 mol CO2
180 g C6H12O6
1 mol C6H12O6
nRT
V=
=
P
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6CO2(g) + 6H2O(l)
mol CO2
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V CO2
L•atm
x 310.15 K
mol•K
1.00 atm
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0.187 mol x 0.0821
= 4.76 L
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Dalton’s Law of Partial Pressures
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V and T are constant
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P2
P1
Ptotal = P1 + P2
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Consider a case in which two gases, A and B, are in a
container of volume V.
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PA =
nART
V
nA is the number of moles of A
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PB =
nBRT
V
nB is the number of moles of B
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PT = PA + PB
PA = XA PT
XA =
nA
nA + nB
XB =
nB
nA + nB
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PB = XB PT
Pi = Xi PT
mole fraction (Xi ) =
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ni
nT
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A sample of natural gas contains 8.24 moles of CH4, 0.421
moles of C2H6, and 0.116 moles of C3H8. If the total pressure
of the gases is 1.37 atm, what is the partial pressure of
propane (C3H8)?
Pi = Xi PT
PT = 1.37 atm
Xpropane =
0.116
8.24 + 0.421 + 0.116
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= 0.0132
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Ppropane = 0.0132 x 1.37 atm = 0.0181 atm
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Collecting a Gas over Water
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2KClO3 (s)
2KCl (s) + 3O2 (g)
PT = PO2 + PH2 O
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Kinetic Molecular Theory of Gases
1. A gas is composed of molecules that are separated from
each other by distances far greater than their own
dimensions. The molecules can be considered to be points;
that is, they possess mass but have negligible volume.
2. Gas molecules are in constant motion in random directions,
and they frequently collide with one another. Collisions
among molecules are perfectly elastic.
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3. Gas molecules exert neither attractive nor repulsive forces
on one another.
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4. The average kinetic energy of the molecules is proportional
to the temperature of the gas in kelvins. Any two gases at
the same temperature will have the same average kinetic
energy
KE = ½ mu2
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Kinetic theory of gases and …
• Compressibility of Gases
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• Boyle’s Law
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P  collision rate with wall
Collision rate  number density
Number density  1/V
P  1/V
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• Charles’ Law
P  collision rate with wall
Collision rate  average kinetic energy of gas
molecules
Average kinetic energy  T
PT
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Kinetic theory of gases and …
• Avogadro’s Law
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P  collision rate with wall
Collision rate  number density
Number density  n
Pn
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• Dalton’s Law of Partial Pressures
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Molecules do not attract or repel one another
P exerted by one type of molecule is unaffected by the
presence of another gas
Ptotal = SPi
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The distribution of speeds
of three different gases
at the same temperature
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The distribution of speeds
for nitrogen gas molecules
at three different temperatures
urms =
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 3RT
M
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Gas diffusion is the gradual mixing of molecules of one gas
with molecules of another by virtue of their kinetic properties.
r1
r2
=

M2
M1
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molecular path
NH4Cl
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NH3
17 g/mol
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HCl
36 g/mol
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Gas effusion is the is the process by which gas under
pressure escapes from one compartment of a container to
another by passing through a small opening.
r1
r2
=
t2
t1
=

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M2
M1
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Nickel forms a gaseous compound of the formula Ni(CO) x What
is the value of x given that under the same conditions methane
(CH4) effuses 3.3 times faster than the compound?
r1 2
x M1 = (3.3)2 x 16 = 174.2
r1 = 3.3 x r2
M2 =
r2
x = 4.1 ~ 4 35
M1 = 16 g/mol
58.7 + x • 28 = 174.2
( )
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Deviations from Ideal Behavior
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1 mole of ideal gas
PV = nRT
PV = 1.0
n=
RT
Repulsive Forces
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Attractive Forces
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Effect of intermolecular forces on the pressure exerted by a gas.
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Van der Waals equation
nonideal gas
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2
(V – nb) = nRT
( P + an
V2 )
}
}
corrected
pressure
corrected
volume
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CH-5
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Questions and Problems
Page 168 - 172
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5.14, 5.18, 5.20, 5.22, 5.24, 5.32, 5.34, 5.36, 5.38,
5.40, 5.42, 5.44, 5.46, 5.50, 5.82.
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