CHAPTER 12
„
Gases and the
Kinetic-Molecular Theory
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Gases vs. Liquids & Solids
Gases
„
Weak interactions
between molecules
Liquids & Solids
„
Strong interactions
between molecules
„
Molecules move rapidly
„
Molecules move slowly
„
Fast diffusion rates
„
Slow diffusion rates
„
Low densities
„
High densities
„
Easy to compress
„
Hard to compress
2
Pressure
„
Force per unit area
„
Units of pressure:
pounds per square inch (psi)
mm Hg = torr
atmospheres (atm)
pascals (Pa)
„
Normal atmospheric pressure – the pressure of air
at the sea level at 0°C (=32 F)
1 atm = 760 mm Hg = 760 torr = 101,325 Pa ≈ 101.3 kPa
(Evangelista Torricelli – 1608-1647)
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Kinetic-Molecular Theory
„
„
Explains the behavior of gases in terms of
molecular motion
The kinetic energy of gas molecules depends
on their velocities:
E =
„
mv 2
2
The gas exerts pressure due to the molecular
motion: many molecules have to strike the
surface to produce this macroscopic effect
4
Boyle’s Law
„
p ×V = const = k
p – pressure
V – volume
(at constant temperature and amount of gas)
p1 ×V1 = p2 ×V2
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Boyle’s Law – Molecular Picture
p1 ×V1 = p2 ×V2
„
„
„
„
The amount of gas (the number of gas
molecules) remains constant
The temperature is constant and therefore
the kinetic energy of gas molecules remains
about the same
If the volume is decreased, then higher
number of gas molecules strike a unit area,
therefore the pressure increases
If the volume is increased, the reverse
effect takes place – the pressure decreases
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Boyle’s Law – Example
„
A 1.00 L sample of gas at 760 mm Hg is
compressed to 0.800 L at constant temperature.
Calculate the final pressure of the gas.
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Charles’ Law
„
V ∝T
or
V = kT
(at constant pressure and amount of gas)
„
„
This equation defines a straight line
Extrapolating this line to V =0 results in
the absolute zero of temperature on
the Kelvin temperature scale
V1 V2
=
T1 T2
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Charles’ Law – Molecular Picture
„
„
„
„
The amount of gas (the number of gas
molecules) remains constant
V1 V2
=
T1 T2
As the temperature increases, the thermal
energy is converted into the kinetic energy
and gas molecules move faster
The gas molecules strike the surface more
vigorously and, if the pressure is to be kept
constant, the gas has to expand
If the temperature is decreased,
the volume also decreases
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Charles’ Law – Example
„
A sample of gas at 1.20 atm and 27°C is heated
at constant pressure to 57°C. Its final volume
is 4.75 L. What was its original volume?
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Combined Gas Law
„
For a constant amount of gas
p1V1 p2V2
=
T1
T2
„
„
Both Boyle’s Law and Charles’ Law can
be derived from the Combined Gas Law
The reverse is not true !
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Combined Gas Law – Example
ƒ A 4.00 L sample of gas at 30°C and 1.00 atm
is changed to 0°C and 800 mm Hg.
What is its new volume?
12
Ideal Gas Equation
pV = nRT
„
p – pressure
„
V – volume
„
n – # of moles of the gas
„
T – temperature
„
R – universal gas constant
R = 8.3144 J/(mol·K) = 0.08206 (L·atm)/(mol·K)
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Ideal Gas Equation
pV = nRT
„
Let’s calculate the volume of 1 mole
of some gas at 0°C and 1 atm:
14
Standard Molar Volume
„
„
The standard molar volume of an ideal
gas is equal to 22.414 liters per mole
at standard temperature and pressure
Standard temperature and pressure (STP)
T = 273.15 K = 0°C = 32 F
p = 760 torr = 1 atm = 101,325 Pa
„
„
1 mole of an ideal gas occupies 22.414 L
volume ONLY at standard temperature and
pressure
To find the volume of 1 mole at different
conditions we have to use other gas laws
15
Avogadro’s Law
„
„
At the same temperature and pressure,
equal volumes of all gases contain the
same number of molecules
At constant T and p, the volume V
occupied by a sample of gas is directly
proportional to the number of moles n
V ∝n
or
V = kn
V1 V2
=
n1 n2
16
Standard Molar Volume – Example
ƒ What volume will be occupied by 32.0 g of
oxygen at STP? How will this volume change
if the pressure is increased to 3 atm and
the temperature is raised to 100°C?
17
Ideal Gas Equation – Example
ƒ At 750 torr and 27°C, 0.60 g of a certain gas
occupies 0.50 L. Calculate its molecular weight.
18
Ideal Gas Equation – Example
ƒ A gas is composed of 30.4% N and 69.6% O.
Its density is 11.1 g/L at -20°C and 2.50 atm.
What is the molecular formula of the gas?
19
Ideal Gas Equation – Example
ƒ What volume of hydrogen will be produced in
the reaction of 3 g of zinc with the excess
of diluted hydrochloric acid, if the reaction
is carried out at room temperature (25°C)
and standard atmospheric pressure (1 atm)?
20
Dalton’s Law
„
„
Mixture of gases: A, B, C, …
Partial pressure – pressure that a gas
would exert if it alone occupied all the
volume occupied by the mixture of gases
21
Dalton’s Law – Example
„
Calculate the pressure of the mixture of
0.25 mol of H2 and 0.75 mol of N2 if at
25°C it occupies the volume of 12 L.
22
Mole Fraction
„
Mixture of gases: A, B, C, …
„
Mole fraction of gas A:
nA
nA
XA =
=
nA + nB + nC + ... ntot
23
Mole Fraction
„
Mixture of gases: A, B, C, …
„
Mole fraction of gas A:
nA
nA
XA =
=
nA + nB + nC + ... ntot
pA
pA
XA =
=
pA + pB + pC + ... ptot
24
Dalton’s Law – Example
„
Into a 5.00 L container at 18°C are placed
2.00 g H2, 44.0 g CO2, and 16.0 g O2. Calculate
the total pressure in the container, the partial
pressure and the mole fraction of each gas.
25
Assignments & Reminders
„
Read Sections 12-1 through 12-13
„
Homework #8 is now accessible on OWL
„
HAPPY THANKSGIVING !
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