Transcript Document

Gases
Chapter 10
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Elements that exist as gases at 250C and 1 atmosphere
5.1
5.1
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.
•
Gases have much lower densities than liquids and solids.
5.1
Chemistry in Action:
Scuba Diving and the Gas Laws
P
Depth (ft)
Pressure
(atm)
0
1
33
2
66
3
V
5.6
Chemistry in Action: Super Cold Atoms
Gaseous Rb Atoms
1.7 x 10-7 K
Bose-Einstein Condensate
Pressure
• Pressure is the amount
of force applied to an
area.
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Force
Pressure = Area
(force = mass x acceleration)
Units of Pressure
Barometer
5.2
Manometers Used to Measure Gas Pressures
5.2
Kinetic Molecular Theory of Gases
KE = ½ mu2
5.7
Kinetic Molecular Theory of Gases and
the Particulate Nature of Matter
• What is the relationship between pressure and
volume?
• As the volume decreases the pressure ___
• Mathematically:
• Experimentally
5.7
P a 1/V
P x V = constant
P1 x V1 = P2 x V2
Constant temperature
Constant amount of gas
5.3
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?
5.3
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?
5.3
Kinetic Molecular Theory of Gases and
the Particulate Nature of Matter
• What is the relationship between temperature and
volume?
• As the temperature decreases the volume ___
• Mathematically: V a T
• Experimentally
5.7
• The volume of a fixed
amount of gas at constant
pressure is directly
proportional to its absolute
temperature.
• i.e.,
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Variation of gas volume with temperature
at constant pressure.
VaT
V = constant x T
V1/T1 = V2 /T2
Temperature must be
in Kelvin
T (K) = t (0C) + 273.15
5.3
A sample of carbon monoxide gas occupies 3.20 L at
125 0C. At what temperature will the gas occupy a
volume of 1.54 L if the pressure remains constant?
5.3
Kinetic Molecular Theory of Gases and
the Particulate Nature of Matter
• What is the relationship between the number of
moles of gas and the volume?
• As the number of moles of gas increases the
volume ___
• Mathematically:
• Experimentally
5.7
Avogadro’s Law
Va
V=
Constant temperature
Constant pressure
5.3
Avogadro's Hypothesis
Gay -Lussac's Law of Combining Gas Volumes
5.3
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?
5.3
Ideal Gas Equation
Boyle’s law:
Charles’ law:
Avogadro’s law:
Va
V=
R is the gas constant
5.4
Ideal-Gas Equation
The constant of
proportionality is
known as R, the gas
constant.
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Calculate the volume of a 0.500 mole
sample of Helium gas at 1.00 atm pressure
and 298 K
5.4
Argon is an inert gas used in lightbulbs to retard the
vaporization of the filament. A certain lightbulb
containing argon at 1.20 atm and 18 0C is heated to
85 0C at constant volume. What is the final pressure of
argon in the lightbulb (in atm)?
5.4
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.3
5.3
The conditions 0 0C and 1 atm are called standard
temperature and pressure (STP).
Experiments show that at STP, 1 mole of an ideal
gas occupies 22.414 L.
PV = nRT
(1 atm)(22.414L)
PV
R=
=
nT
(1 mol)(273.15 K)
R=
5.4
What is the volume (in liters) occupied by 49.8 g of HCl
at STP?
T = 0 0C = 273.15 K
5.4
Density (d) Calculations
PM
m
d=
=
V
RT
m is the mass of the gas in g
M is the molar mass of the gas
Molar Mass (M ) of a Gaseous Substance
dRT
M=
P
d is the density of the gas in g/L
5.4
A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm
and 27.0 0C. What is the molar mass of the gas?
M=
M=
5.4
Gas Stoichiometry
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
6CO2 (g) + 6H2O (l)
mol CO2
V CO2
Dalton’s Law of Partial Pressures
V and T
are
constant
P1
P2
Ptotal = P1 + P2
5.6
Consider a case in which two gases, A and B, are in a
container of volume V.
nART
PA =
V
nA is the number of moles of A
nBRT
PB =
V
nB is the number of moles of B
PT = PA + PB
PA = XA PT
nA
XA =
nA + nB
nB
XB =
nA + nB
PB = XB PT
Pi = Xi PT
mole fraction (Xi) =
ni
nT
5.6
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
0.116
Xpropane =
8.24 + 0.421 + 0.116
= 0.0132
Ppropane = 0.0132 x 1.37 atm = 0.0181 atm
5.6
Densities of Gases
If we divide both sides of the ideal-gas
equation by V and by RT, we get
n
P
=
V
RT
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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
NH4Cl
NH3
17 g/mol
HCl
36 g/mol
5.7
Densities of Gases
• Mass  volume = density
• So,
m P
d=
=
V RT
Note: One only needs to know the
molecular mass, the pressure, and the
temperature to calculate the density of
a gas.
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Molecular Mass
We can manipulate the density equation to
enable us to find the molecular mass of a
gas:
P
d=
RT
Becomes
dRT
= P
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Partial Pressures
• When one collects a gas over water, there is water
vapor mixed in with the gas.
• To find only the pressure of the desired gas,
one must subtract the vapor pressure of
water from
the total pressure.
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Bottle full of oxygen
gas and water vapor
2KClO3 (s)
2KCl (s) + 3O2 (g)
PT = PO2 + PH2 O
5.6
Dalton’s Law of
Partial Pressures
• The total pressure of a mixture of gases
equals the sum of the pressures that each
would exert if it were present alone.
• In other words,
Ptotal = P1 + P2 + P3 + …
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5.6
Densities of Gases
• We know that
– moles  molecular mass = mass
n=m
• So multiplying both sides by the
molecular mass ( ) gives
m P
=
V RT
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Effusion
Effusion is the
escape of gas
molecules
through a tiny
hole into an
evacuated space.
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Effusion
The difference in the
rates of effusion for
helium and nitrogen,
for example, explains
a helium balloon
would deflate faster.
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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
=

M2
M1
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 = 3.3 x r2
5.7
Diffusion
Diffusion is the spread
of one substance
throughout a space or
throughout a second
substance.
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Graham's Law
KE1 = KE2
1/2 m1v12 =
m1
m2
=
1/2
2
m
v
v 22 2
2
v 12
2
v
 =
2
2
v
m

1
1
m2
=
v2
v1
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Apparatus for studying molecular speed distribution
5.7
Main Tenets of KineticMolecular Theory
Energy can be transferred
between molecules during
collisions, but the average
kinetic energy of the
molecules does not change
with time, as long as the
temperature of the gas
remains constant.
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Main Tenets of KineticMolecular Theory
The average kinetic
energy of the
molecules is
proportional to the
absolute temperature.
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The distribution of speeds
of three different gases
at the same temperature
The distribution of speeds
for nitrogen gas molecules
at three different temperatures
urms =
M
3RT
5.7
Deviations from Ideal Behavior
The assumptions made in the kinetic-molecular
model (negligible volume of gas molecules
themselves, no attractive forces between gas
molecules, etc.) break down at high pressure and/or
low temperature.  2009, Prentice-Hall, Inc.
Corrections for Nonideal
Behavior
• The ideal-gas equation can be adjusted to
take these deviations from ideal behavior
into account.
• The corrected ideal-gas equation is
known as the van der Waals equation.
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Effect of intermolecular forces on the pressure exerted by a gas.
5.8
Van der Waals equation
nonideal gas
2
an
( P + V2 ) (V – nb) = nRT
}
}
corrected
pressure
corrected
volume
5.8
Real Gases
In the real world, the
behavior of gases only
conforms to the idealgas equation at
relatively high
temperature and low
pressure.
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Real Gases
Even the same gas will
show wildly different
behavior under high
pressure at different
temperatures.
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Deviations from Ideal Behavior
1 mole of ideal gas
PV = nRT
PV = 1.0
n=
RT
Repulsive Forces
Attractive Forces
5.8