# 4.2 explaining the properties of gases

```15. (a) T1 = (130 + 273) K = 403 K
T2 = (100 + 273) K = 373 K
PV
PV
1 1
= 2 2
T1
T2
PV T
V2 = 1 1 2
T1 P2
3.05 atm u 1.0 L u 373 K
403 K u 1.01 atm
= 2.8 L
373 K
3.05 atm
or V2 = 1.0 L u
u
403 K
1.01 atm
= 2.8 L
=
According to the combined gas law, the 1.0 L bubble of water vapour expands to 2.8 L
when it reaches the surface.
(b) A geyser erupts when the superheated water (that is steadily increasing in temperature) at
the bottom of the shaft exerts a vaporization pressure that is greater than the downward
pressure due to the height of the water “column” in the shaft. In a wider shaft, the time
required for the temperature to increase enough is much greater. If the shaft is too wide,
convection currents in the water may carry heat away from the bottom layer so quickly
that it will never get hot enough to vaporize.
16. Barometers and manometers both historically used a column of liquid (usually mercury)
where a height of mercury is measured and used as a unit of gas pressure, “mm Hg”.
Barometers measure atmospheric pressure while manometers measure pressure of a gas
sample. A Bourdon gauge measures the pressure of a gas sample by the movement of a coiled
tube. As the pressure increases, the coil tends to straighten out and this movement is
translated into the movement of a needle over a dial. Robert Boyle used a manometer and a
barometer to do his experiments, which eventually led to Boyle’s law.
Extension
17. Scientists have come very close to achieving absolute zero, to within a few billionths kelvin.
According to the quantum mechanics theory, molecules at absolute zero do not have zero
kinetic energy, but rather they have a minimum possible quantity called the “zero-point”
energy. According to quantum mechanics theory, it seems that molecular motion would not
cease altogether at absolute zero.
18. Some of the properties of mercury that make it useful in barometers are its higher density and
low vapour pressure, compared to water. Mercury also has high cohesion and low adhesion.
4.2 EXPLAINING THE PROPERTIES OF GASES
Practice
(Page 164)
1. (a) According to the kinetic molecular theory, as the temperature increases, the average
speed of the gas particles increases. If the volume is kept constant, then faster-moving
particles will collide more often with the sides of the container. More collisions mean a
greater pressure.
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(b) According to kinetic molecular theory, as the volume decreases, the particles are confined
to a smaller space and will collide more often with each other and the walls of the
container. More collisions mean a greater pressure.
(c) The intermolecular forces of attraction between gas particles are negligible and,
therefore, they are able to move rapidly and independently of each other. As a result,
gases mix quickly. In liquids, the intermolecular forces of attraction are far greater than
those in gases, and the individual molecules move much more slowly. Thus, the rate of
mixing for liquids is slower.
(d) According to the kinetic molecular theory, gases such as air are very compressible
because most of the volume is empty space. The fact that there is very little empty space
between the molecules of a liquid, such as oil, makes liquids not compressible. In a
hydraulic system, the pressure applied at one end (e.g., brake pedal) needs to be
transmitted to the other end (e.g., brakes). This will work only if the medium inside the
system is not compressible.
(e) A bullet moves in a straight line over a long distance before it hits its target. According to
the kinetic molecular theory, a gas molecule moves only a very short distance before
colliding with another gas molecule, and thus changing its direction.
2. Air fresheners, fragrances (natural and artificial), pheromones, and the dissolving of solids all
depend on the molecular motion described by the kinetic molecular theory. The motion of air
particles, for example, helps the molecules of air freshener, perfumes, or pheromones to
disperse. The motion of the water molecules in hot tea, for example, helps the sugar to
dissolve.
3. An accepted scientific theory must describe observations in terms of non-observable ideas,
explain existing evidence, predict results of future experiments, and be as simple as possible
in concept and application.
(Page 164)
1. Elsie MacGill was the first woman to:
Ɣ receive a Master’s degree in the field of aeronautics
Ɣ design an aircraft
Ɣ become a corporate member of the Engineering Institute of Canada
Ɣ become a technical advisor to the United Nations’ International Civil Aviation
Organization
2. Some gas properties that are important in aeronautics are density, pressure, temperature, and
gas velocity.
Practice
(Page 166)
4. (a) law of combining volumes
(c) Scientific laws and theories are similar in that they both provide descriptions, are used to
make predictions, and are as simple as possible. However, laws are empirical and based
on observable facts; theories are based on non-observable ideas. Only theories provide
explanations.
+
5 O2(g) &AElig;
3 CO2(g) +
4 H2O(g)
5. C3H8(g)
5.00 L
V
5
VO2 = 5.00 L u = 25.0 L
1
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or
VO2 = 5.00 L C3 H8 u
5 L O2
1 L C3 H 8
= 25.0 L
According to the law of combining volumes, the volume of oxygen required is 25.0 L.
6. 2 NO(g)
1.2 L
+
2 H2(g) &AElig;
VN 2 = 1.2 L u
N2(g)
V
+
2 H2O(g)
1
2
= 0.60 L
or
VN 2 = 1.2 L NO u
1 L N2
2 L NO
= 0.60 L
According to the law of combining volumes, the volume of nitrogen gas produced is 0.60 L.
7. (a) N2(g)
+
3 H2(g) &AElig;
V
3
VH2 = 1.0 ML u
2
= 1.5 ML
2 NH3(g)
1.0 ML
or
VH2 = 1.0 M L NH 3 u
3 L H2
2 L NH 3
= 1.5 ML
According to the law of combining volumes, the volume of hydrogen gas required is
1.5 ML.
(b) The gases are measured at the same temperature and pressure.
Web Activity: Web Quest—“Designer Air” for Tires
(Page 166)
[A typical conclusion could include the following.]
The difference in benefits between nitrogen and air are small. Little scientific evidence supports
clear benefits of nitrogen over air. We recommend that, unless the nitrogen company plans to
market pure nitrogen on the basis of it being a “dry” gas (containing no water vapour), they will
likely face opposition to the extra costs incurred by drivers.
The experimental design must assess the performance of tires filled with regular air
compared to those filled with nitrogen. Tires filled with air will be the control; all other variables
should be the same. There should be a clearly defined measure of performance, such as tire
longevity (perhaps measured as mass lost per 1000 km driven) or vehicle fuel consumption (in
km/10 L).
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Case Study: Weather Forecasts
(Page 167)
1. Initially, the pressure inside and outside the cave would be close to equal. If the low-pressure
system moves in quickly, the air in the cave will be at a higher pressure than the air outside.
According to Boyle’s law, as pressure on a gas (air) decreases, its volume increases and air
would, therefore, rush out of the cave. This situation is similar to gas rushing out of a pop
container that has just been opened.
2. Cloud patterns and formation, air rushing out of caves, the presence of sundogs, and the
behaviour of animals are some observations used by Aboriginal peoples to reveal information
3. The devices used to measure changes in atmospheric conditions have typically evolved to
become more precise and to incorporate sensitive probes that may use electricity. A modern
device used to measure temperature is the thermistor, which is composed of a treated metal
oxide in a ceramic matrix. The electrical resistance of the matrix changes in response to
temperature (and thus temperature itself) can be measured by determining changes in
electrical resistance. The range of temperatures that can be measured by thermistors is from
–80 qC (most common) to 250 qC (maximum). Their precision can vary to r 0.05 qC.
The mercury barometer is still among the most accurate and reliable tools for
measuring air pressure. Modern adaptations include the aneroid barometer, which contains a
sealed and partially evacuated tube whose walls flex with changes in atmospheric pressure.
The changes in the deflection of the walls are converted to level movements, which are then
converted to a reading of a moving needle against a gauge. Some other versions use a piece
of quartz that is made to vibrate using electricity. Since atmospheric pressure affects the
frequency of vibration, this variable can be determined. Some mercury barometers can
measure pressures at 500 m above sea level.
A sling psychrometer is used to find relative humidity. It is composed of two
thermometers—one covered with a cloth wick and kept wet, and the other kept dry. The
psychrometer is swung through the air on a chain. The drier the air, the more moisture will
evaporate from the surface of the wet thermometer, thereby lowering its temperature. The
readings on the two thermometers are compared, and reference charts can be used to convert
this temperature difference into relative humidity. A modern variant of this device uses a saltcovered probe that can absorb moisture from the air. Absorbing moisture causes the probe to
conduct electricity better and can be used to determine humidity. Precision for such devices
is r 2%.
Section 4.2 Questions
(Page 168)
1. (a) According to the kinetic molecular theory, the particles in the food colouring and the
water are in constant motion. The random collisions between the particles jostle the
particles and they slowly become mixed together. As this process continues, these
coloured particles become evenly distributed throughout the water.
(b) According to the kinetic molecular theory, a lower temperature means a lower average
kinetic energy or speed of the molecules. As the molecules slow down, they come closer
together. This results in more molecules per unit volume, and the density of the air
increases.
(c) According to the kinetic molecular theory, the added energy from the flame increases the
motion of both zinc and copper atoms. As this occurs, there are more collisions between
the zinc and copper atoms, resulting in some zinc atoms mixing in the top layer of copper
atoms.
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2. Twice the amount of gas in the same volume would produce twice as many collisions among
gas particles and between gas particles and the walls of the container. According to the
kinetic molecular theory, therefore, pressure would also double.
3. (a) When measured at the same temperature and pressure, volumes of gaseous reactants and
products of chemical reactions are always in simple ratios of whole numbers.
(b) N2(g) +
2 O2(g) &AElig;
2 NO2(g)
ratio of combining volumes = 1:2:2
(c)
There are entities on the left (reactants) for every two on the right (products). Because the
volume of a gas (at SATP) depends only on the number of entities present, the volume
will decrease after the reaction. The ratio of volumes will be 3:2.
4. (a) 2 H2S(g)
124 kL
3 O2(g) &AElig;
2 SO2(g)
V
3
VO2 = 124 kL u
186 kL
2
or
+
VO2 = 124 k L H 2S u
+
2 H2O(g)
3 L O2
3 L H 2S
= 186 kL
(b) 16 H2S(g)
248 kL
+
8 SO2 (g)
V
VSO2 = 248 kL u
&AElig;
3 S8(g)
+
16 H2O(g)
8
16
= 124 kL
or
VSO2 = 248 k L H 2S u
8 L SO 2
16 L H 2S
= 124 kL
[Note that the temperature and pressure given in this question do not have to be used
because all the gas volumes are measured at the same conditions.]
5. (a) 4 NH3(g)
100 L
or
+
5 O2(g) &AElig;
4 NO(g)
V
V
5
VO2 = 100 L u
= 125 L
4
4
VNO = 100 L u
= 100 L
4
VH2O = 100 L u 6 = 150 L
4
5 L O2
VO2 = 100 L NH 3 u
= 125 L
4 L NH 3
+
6 H2O(g)
V
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4 L NO
= 100 L
4 L NH 3
6 L H2O
VH2O = 100 L NH 3 u
= 150 L
4 L NH 3
According to the combined gas law, the volumes of oxygen, nitrogen monoxide and
water vapour are 125 L, 100 L, and 150 L respectively.
VNO = 100 L NH 3 u
(b) 2 NO(g)
+
O2(g)
V
VO2 = 750 L u
or
2 NO2(g)
750 L
&AElig;
1
2
= 375 L
VO2 = 750 L NO 2 u
1 L O2
2 L NO 2
= 375 L
According to the combined gas law, the volume of oxygen required is 375 L.
(c) 3 NO2(g)
+
100 L
H2O(l) &AElig;
VNO = 100 L u
1
3
2 HNO3(aq)
+
NO(g)
V
= 33.3 L
1 L NO
= 33.3 L
3 L NO 2
According to the law of combining volumes, the volume of nitrogen monoxide produced
is 33.3 L.
(d) No prediction can be made from the law of combining volumes because the nitric acid
and the ammonium nitrate are in aqueous solution, not in gaseous form.
6. The formation of dew and the boiling of water are two natural processes that can be explained
by the kinetic molecular theory. Dew forms as a result of the temperature falling, which
causes water vapour to condense due to the decrease in energy and motion of the water
molecules. During boiling, the reverse is true: molecules of liquid water continue to gain
energy and move faster until they escape the surface tension and cohesive forces of water.
The storage and transportation of heated and pressurized gases require technological
solutions that depend on the kinetic molecular theory. The storage containers and the
conduits through which such material must travel need to be strengthened with reinforced
material because the higher the temperature and pressure of a gas, the greater the frequency
and force of collisions among particles and between particles and the wall of a container.
Carrying out reactions at high temperatures and pressures causes the participating entities to
move faster and collide with greater force, which increases the rate at which the reactions
occur. Such reactions include the formation of ammonia and the production of sulfuric acid.
or
VNO = 100 L NO 2 u
Extension
7. Avogadro’s theory satisfies the stated criteria. His theory provides a logical and simple
explanation for Gay-Lussac’s observations. Avogadro’s theory is also consistent with
molecular formulas, covalent bonding theories, and atomic theory in terms of balancing
chemical equations.
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