Transcript The Empirical Gas Laws

Lesson 2
Kinetic Molecular Theory states that all substances
are made of tiny particles that are in constant
motion.
 Gases have the most amount of movement in the
three states of matter. The movement of the
particles is independent of each other as each
particle travels in a straight line until it bumps
into another particle or wall of its container.

The movement of the particle is referred to as
kinetic energy. As the energy increases so
does the movement of the particles.

Quantitative measurements on gases were
first made by the English chemist Robert
Boyle (1627 - 1691). Boyle used two
instruments to measure pressure: the
manometer, which measures differences in
pressure, and the barometer, which measures
the total pressure of the atmosphere
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Units of pressure were originally all based on
the length of the column of liquid, usually
mercury, supported in a manometer or
barometer.
By far the most common of these units was
the mm Hg.
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However, the modern SI unit of pressure is
derived from the fundamental units of the SI.
Pressure is force per unit area, and force is
the product of mass times acceleration, so
the SI unit of pressure is the kg m s2/m2 or
newton/m2,
which is called the pascal (Pa).
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The standard temperature and pressure that
gas experiments are done at is referred to as
SATP.
Standard Ambient Temperature and Pressure
is 25° C and 100kPa.
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All of the older units of pressure have now been
redefined in terms of the pascal.
One standard atmosphere, the pressure of the
atmosphere at sea level, is by definition exactly
101,325 Pa.
The torr, named in honour of Torricelli, is
defined as 1/760 of a standard atmosphere or
as 101,325/760 Pa.
The mmHg can be considered identical to the
torr. The term bar is used for 100,000 Pa, which
is slightly below one standard atmosphere.
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Boyle used the manometer and barometer to
study the pressures and volumes of different
samples of different gases. The results of his
studies can be summarized in a simple
statement which has come to be known as
Boyle's law:
At any constant temperature, the product of
the pressure and the volume of any size
sample of any gas is a constant.

For a particular sample of any gas, Boyle's law
can be shown graphically as done in the
Figure below. It is more common to express it
mathematically as
P1V1 =P2V2

This means that the pressure and the volume
vary inversely; as the pressure increases the
volume of the sample gas must decrease and
vice versa.
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A sample of gas occupies a volume of 47.3
cm3 at 25°C with a pressure of 30 mm of
mercury. If the pressure is increased to 75
mm of mercury, what will the volume be at
the new pressure?
G
P1 = 30 mm Hg
V1 = 47.3 cm3
P2 = 75 mm Hg
S
V2 = (30 mm x 47.3 cm )
75 cm Hg
3
V2 = 18.9 cm3
R
V2 = ?
A
P1V1 = P2V2
V2 = P1V1 / P2
P
Therefore, When the
pressure increased from
30 mm Hg to 75 mm Hg
the volume decreased
from 47.5 cm3 to 18.9
cm3
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A student is trying to compress the gas in a
cylinder that has an initial volume of 1000
cm3 and a pressure of 100 kPa. The student
decreases the volume by 500 cm3. What is the
pressure of the gas in the cylinder?
G
P1 = 100 kPa
V1 = 1000 cm3
V2 = 500 cm3
S
P2
= (100 kPa x1,000 cm3)
500 cm3
P2 = 200 kPa
R
P2 = ?
P
A
P1V1 = P2V2
P2= P1V1 / V2
Therefore, When the
student compressed the
cylinder to half of its
original volume the
pressure doubled to 200
kPa.
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Questions: Page 335 # 1-5
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In SI Metric the temperature scale is defined
as Kelvin temperature scale.
The degree unit is the Kelvin (K). The symbol
for the unit is K, not o K.
Kelvin temperatures must be used in many
gas law equations in which temperature
enters directly into the calculations.
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The Celsius and Kelvin scale are related unit
for unit. One degree unit on the Celsius scale
is equivalent to one degree unit on the Kelvin
scale. The only difference between these two
scales is the zero point.
The zero point on the Celsius scale was
defined as the freezing point of water, which
means that there are higher and lower
temperatures around it.
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The zero point on the Kelvin
scale - called absolute
zero – it corresponds to the
lowest temperature that is
possible. It is 273.15 units
lower than the zero point on
the Celsius scale.
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So this means that 0 K equals -273.15 oC and
0oC equals 273.15 K. Thermometers are
never marked in the Kelvin scale.
If we need degrees in Kelvin the following
relationships are to be used.
TK = tc + 273.15
or
tc = TK - 273.15
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Liquid nitrogen (sometimes abbreviated LOX)
is used in liquid-fuel rockets. Its boiling point
is -183oC. What is this temperature in
Kelvin’s?
A substance is heated from 300 K to 315 K.
What is the change in temperature expressed
in °C.
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Perform the following conversions
a)24°C to K
a)50 K to °C
a)30 °C to K
a)215. 15 K to °C
a)-37.89 °C to K
a)333. 67 K to °C.
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A clinical thermometer registers a patient's
temperature to be 37.13oC. What is this in
Kelvin’s?
The coldest permanently inhabited place on
earth is the Siberian village of Oymyakon in
Russia. In 1964 the temperature reached a
shivering -71.11oC. What is this temperature
in Kelvin’s?
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Helium has the lowest boiling point of any
liquid. It boils at 4 K. What is this in oC?
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The direct relationship between the volume of
a gas and the temperature of the gas (on the
Kelvin temperature scale) is known as Charles
Law. According to this law,
as the temperature of a gas increases, the
volume increases proportionally, provided
that the pressure and the amount of gas
remains the same.
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However, as the graph above shows, the
volume extrapolates to zero at a temperature
of -273.15oC. If this temperature were taken
as the zero of a temperature scale then all
negative temperatures could be eliminated.
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Such a temperature scale is now the
fundamental scale of temperature in the SI. It
is called the absolute scale, the
thermodynamic scale, and the Kelvin scale.
Temperature on the Kelvin scale, and only on
the Kelvin scale, is symbolized by T.
Charles’s Law can be written as
V 1 T 2= V 2 T 1
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The volume of a sample of gas is 23.2 cm3 at
20oC. If the gas is ideal and the pressure
remains unchanged what is its volume at
80oC?
G
V1 = 23.2 cm3
T1 = 20oC = 293.15 K
T2 = 80oC = 353.15K
S
V2 = (23.2 cm3 x 353.15K)
293.15 K
= 27.95 cm3
R
V2 = ?
P
A
V1T2= V2T1
Therefore, when the
temperature increased by 60
K it increased the volume
from 23.2 cm3 to 27.95 cm3
V2 = V1T2 / T1
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Compressed oxygen is widely used in
hospitals and retirement homes. To make it
easier to transport, the oxygen is cooled.
How many degrees Celsius would the gas be
if 200 L’s at 23 degrees Celsius is
compressed to 40 L?
G
V1 = 200 L
T1 = 23oC = 296.15 K
V2 = 40 L
R
A
V1T2= V2T1
T2 = V2T1 / V1
S
T2 = (40 L x 296.15 K )
200 L
= 59. 23 K = -213. 9 oC
P
Therefore, when the gas
is compressed for
transport it is cooled to 213. 9 oC.
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Questions: page 338 # 6-9
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When Dalton was conducting his studies,
which led him to the atomic-molecular theory
of matter, he also included studies of the
behaviour of gases. These led him to
propose, in 1803, what is now called Dalton's
law of partial pressures:
◦ Partial Pressures - The pressure, p, that a gas in a
mixture would exert if it were the only gas in the
same volume, at the same temperature.
Dalton law states that
the total pressure of a mixture of non-reacting
gases is equal to the sum of the partial
pressures of the individual gases.
The laws equation is expressed as:
Ptotal = P1 + P2 + P3 + ...
Where Ptotal is the total pressure of the mixture
and P1, P2, and P3 are the partial pressures of
each has in the mixture.
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This law can be explained by the molecular
kinetic theory, the type of gas particle doesn’t
matter because they are all behaving in the
same manner. They are all consistently
moving, and colliding with each other and
with the walls of the container.
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The air that we are breathing right now is
primarily composed of nitrogen, oxygen and
carbon dioxide. What is the air pressure in
this room if the following pressures occur?
N2 = 79.03 kPa, O2 = 21.28 kPa and CO2 =
1.01 kPa.
G
N2 = 79.03 kPa
O2 = 21.28 kPa
CO2 = 1.01 kPa
S
Ptotal = 79.03 kPa +
21.28 kPa + 1.01 kPa
= 101. 32 kPa
R
Ptotal = ?
A
Ptotal = P1 + P2 + P3 + ...
P
Therefore, the air
pressure in the room is
101.32 kPa.
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Questions page 339 # 10, 11, 12.