Chapter 12
Gases
1
Overview
 Gas Laws
–
–
–
–
–
Gas pressure and its measurement
Empirical gas laws
Ideal gas laws
Stoichiometry and gases
Gas Mixtures; Law of Partial Pressures
 Kinetic and Molecular Theory
– Kinetic Theory of an Ideal Gas
– Molecular speeds: diffusion and effusion
– Real gases
2
Measurements on Gases
 The most readily measured properties of a
gas are:
 Temperature
 Volume
 Pressure
3
Measuring Pressure
 Pressure (P) is the force (F) that acts on a given area
(A)
 One of the most important of the measured quantities
for gases
 Pressure has traditionally been measured in units
relating to the height of the Hg and is thus expressed
as mm Hg = 1 Torr.
4
Atmospheric Pressure and the
Barometer
 Due to gravity, the atmosphere exerts a downward force
and therefore a pressure upon the earth's surface
 Force = (mass*acceleration) or F=ma
 The earth's gravity exerts an acceleration of 9.8 m/s2
 A column of air 1 m2 in cross section, extending through
the atmosphere, has a mass of roughly 10,000 kg
5
 Atmospheric pressure can be measured by using a barometer
 A glass tube with a length somewhat longer than 760 mm is
closed at one end and filled with mercury
 The filled tube is inverted over a dish of mercury such that no air
enters the tube
 Some of the mercury flows out of the tube, but a column of
mercury remains in the tube. The space at the top of the tube is
essentially a vacuum
 The dish is open to the atmosphere, and the fluctuating
pressure of the atmosphere will change the height of the
mercury in the tube
6
The mercury is pushed up the tube until the
pressure due to the mass of the mercury in the
column balances the atmospheric pressure
7
Standard Atmospheric Pressure
 Standard atmospheric pressure corresponds
to typical atmospheric pressure at sea level
 It is the pressure needed to support a
column of mercury 760 mm in height
 In SI units it equals 1.01325 x 105 Pa
8
 Relationship to other common units of
pressure:
 (Note that 1 torr = 1 mm Hg)
9
 A manometer is used to measure the
pressure of an enclosed gas. Their
operation is similar to the barometer, and
they usually contain mercury.
 It consists of a tube of liquid connected to
enclosed container which makes it possible
to measure pressure inside the container.
10
 A closed tube manometer is used to measure
pressures below atmospheric
 An open tube manometer is used to measure
pressures slightly above or below atmospheric
 In a closed tube manometer the pressure is just
the difference between the two levels (in mm of
mercury)
11
 In an open tube manometer the difference in
mercury levels indicates the pressure
difference in reference to atmospheric
pressure
12
Manometer
13
14
 Other liquids can be employed in a manometer
besides mercury.
 The difference in height of the liquid levels is
inversely proportional to the density of the liquid
i.e. the greater the density of the liquid, the smaller
the difference in height of the liquid
 The high density of mercury (13.6 g/ml) allows
relatively small manometers to be built
15
The Gas Laws
 Boyle's Law: For a fixed amount of
gas and constant temperature, PV =
constant.
16
 The volume of some amount of a gas was
1.00 L when the pressure was 10.0 atm;
what would the volume be if the pressure
decreased to 1.00 atm?
17
The Gas Laws
 Charles's Law: at constant pressure
the volume is linearly proportional to
temperature. V/T = constant
18
A gas occupied a volume of 6.54 L at 25°C
what would its volume be at 100°C?
19
The Gas Laws
 Avagadro’s law for a fixed pressure and
temperature, the volume of a gas is directly
proportional to the number of moles of that
gas. V/n = k = constant.
20
The volume of 0.555 mol of some gas was
100.0 L; what would be the volume of 15.0
mol of the same gas at the same T and P?
21
 The three historically important gas laws
derived relationships between two
physical properties of a gas, while
keeping other properties constant:
22
 These different relationships can be
combined into a single relationship to make
a more general gas law:
23
 If the proportionality constant is called "R",
then we have:
24
 Rearranging to a more familiar form:
 This equation is known as the ideal-gas
equation
25
 Values for R are determined by the values
used for volume and pressure. The value
that we will use is
0.0821 l atm/mole K
26
 When any of the other three quantities in the
ideal gas law have been determined the last
one can be calculated.
27
28
 Calculate the pressure inside a TV picture
tube, if it's volume is 5.00 liters, it's
temperature is 23.0C and it contains
0.0100 mg of nitrogen.
29
Further Applications of Ideal-Gas
Equation
 The density of a gas the density of a
gas can be related to the pressure from
the ideal gas law using the definition of
density: d = mass/vol.
30
Estimate the density of air at 20.0C and
1.00 atm by supposing that air is
predominantly N2.
31
 Rearrangement permits the determination of
molecular mass of a gas from a measure of
the density at a known temperature and
pressure.
32
A certain gas was found to have a density of
0.480 g/L at 260C and 103 Torr. Determine
the MM of the compound.
33
Partial Pressure and Dalton’s
Law
 Dalton's Law = the sum of the partial
pressures of the gases in a mixture =
the total pressure or P = PA + PB + PC +
...where Pi = the partial pressure of
component i.
34
 Dalton found that gases obeying the ideal gas
law in the pure form will continue to act
ideally when mixed together with other ideal
gases.
 The individual partial pressures are used to
determine the amount of that gas in the
mixture, not the total pressure, PA = nART/V.
 Since they are in the same container T and V
will be the same for all gases.
35
1.00 g of air consists of approximately 0.76 g
nitrogen and 0.24 g oxygen. Calculate the
partial pressures and the total pressure
when this sample occupies a 1.00 L vessel
at 20.0C.
36
Partial Pressure and Dalton’s
Law2
 Mole fraction another quantity commonly determined
for gas mixtures. It is defined the number of moles of
one substance relative to the total number of moles in
the mixture or
nA
PA
XA 

n A  nB     PA  PB    
 X can be calculated from
– moles of each gas in the mixture or
– the pressures of each gas
37
Gas Collection by Water
Displacement
 Certain experiments involve the
determination of the number of moles of a
gas produced in a chemical reaction
 Sometimes the gas can be collected over
water
 Potassium chlorate when heated gives off
oxygen:
 2KClO3(s) -> 2KCl(s) + 3O2(g)
 The oxygen can be collected in a bottle that is
initially filled with water
38
39
 The volume of gas collected is measured by
first adjusting the beaker so that the water
level in the beaker is the same as in the pan.
 When the levels are the same, the pressure
inside the beaker is the same as on the water
in the pan (i.e. 1 atm of pressure)
 The total pressure inside the beaker is equal
to the sum of the pressure of gas collected
and the pressure of water vapor in equilibrium
with liquid water
Pt = PO2 + PH2O
40
Suppose KClO3 was decomposed according
to
2 KClO3(s)+   2KCl(s) + 3O2(g).
PT = 755.2 Torr and 370.0 mL of gas was
collected over water at 20.0C. Determine
the number of moles of O2 if the vapor
pressure of water is 17.5 torr at this
temperature.
41
42
Stoichiometric Relationships with
Gases
 When gases are involved in a reaction,
gas properties must be combined with
stoichiometric relationships.
 Two types exist
– Volume of gas and volume of gas
– Condensed phase and volume of gas
43
 Determine the volume of oxygen gas
needed to react with 1.00 L of hydrogen gas
at the same temperature and pressure to
produce water.
44
45
Determine the volume of gas produced at
273.15 K and 1.00 atm if 1.00 kg of calcium
oxide reacts with a sufficent amount of
carbon. Assume complete reaction (i.e.
100% yield)
CaO(s) + 3C(s)  CaC2(s) + CO(g).
46
47
The Behavior of Real Gases
 The molar volume is not constant as is
expected for ideal gases.
 These deviations due to an attraction
between some molecules.
 Applicable at high pressures and low
temperatures.
48
 For compounds that deviate from ideality the
van der Waals equation is used:
 n2 a 
P +
(V - nb) = nRT

2
V constants
where a and
that are
 b are

characteristic of the gas.
49
The Kinetic Molecular Theory of
Gases
 Microscopic view of gases assumes that
– A gas is a collection of molecules (atoms)
in continuous random motion.
– The molecules are infinitely small pointlike particles that move in straight lines
until they collide with something.
50
KMT cont.
– Gas molecules do not influence each other
except during collision.
– All collisions are elastic; the total kinetic energy
is constant at constant T.
– Average kinetic energy is proportional to T.
51
The Kinetic Theory – Molecular
Theory of Gases
 Theory leads to a description of bulk
properties i.e. observable properties.
 The average kinetic energy of the
molecule is
3RT
Ek 
2N A
where NA = Avagadro’s number.
52
 Average kinetic energy of moving particles
can also be obtained from
1 2
E

mu
where u = average velocity
2
53
•Combine 1 & 2 to get a relationship between
the velocity, temperature and molecular mass.
3RT
Ek 
2N A
1 2
E  mu
2
54
3RT
u
M
55
Determine average velocity of He at 300 K.
56
Predict the ratio of the speeds of a gas if the
temperature is increased from 300 K to 450
K.
57
Graham’s Law: Diffusion and
Effusion of Gases
 Diffusion the process whereby a gas spreads out
through another gas to occupy the space with
uniform partial pressure.
 Effusion the process in which a gas flows through
a small hole in a container.
58
 Graham’s Law of Effusion the rate of
effusion of gas molecules through a hole is
inversely proportional to the square root of
the molecular mass of the gas at constant
temperature and pressure.
k
Rate 
MW
59
Graham’s Law for Two Gases
60
Determine the molecular mass of an
unknown compound if it effused through a
small orifice 3.55 times slower than CH4.
61
A compound with a molecular mass of 32.0
g/mol effused through a small opening in 35
s; determine the effusion time for the same
amount of a compound with a molecular
mass of 16.0.
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