Topic
13
Table of Contents
Topic
13
Topic 13: Gases
Basic Concepts
Additional Concepts
Gases: Basic Concepts
Topic
13
Defining Gas Pressure—
How are number of particles
and gas pressure related?
• The pressure of a gas is the force per unit
area that the particles in the gas exert on the
walls of their container.
• As you would
expect, more air
Click box to
particles inside the
view movie
clip.
ball mean more
mass inside.
Gases: Basic Concepts
Topic
13
Defining Gas Pressure—
How are number of particles
and gas pressure related?
• From similar observations and
measurements, scientists from as long ago
as the 18th century learned that the pressure
of a gas is directly proportional to its mass.
Gases: Basic Concepts
Topic
13
Defining Gas Pressure—
How are number of particles
and gas pressure related?
• According to the kinetic theory, all matter is
composed of particles in constant motion,
and pressure is caused by the force of gas
particles striking the walls of their container.
• The more often gas particles collide with the
walls of their container, the greater the
pressure.
Gases: Basic Concepts
Topic
13
Defining Gas Pressure—
How are number of particles
and gas pressure related?
• Therefore the pressure
is directly proportional
to the number of
particles.
• For example, doubling
the number of gas
particles in a basketball
doubles the pressure.
Gases: Basic Concepts
Topic
13
How are temperature
gas pressure related?
and
• At higher temperatures, the particles in a gas
have greater kinetic energy.
• They move faster and collide with the walls
of the container more often and with greater
force, so the pressure rises.
Gases: Basic Concepts
Topic
13
How are temperature
gas pressure related?
and
• If the volume of the container and the
number of particles of gas are not changed,
the pressure of a gas increases in direct
proportion to the Kelvin temperature.
• The volume of a gas at constant pressure
is directly proportional to the Kelvin
temperature.
Gases: Basic Concepts
Topic
13
Devices to Measure Pressure—
The Barometer
• One of the first instruments used to measure
gas pressure was designed by the Italian
scientist Evangelista Torricelli (1608-1647).
• He invented the barometer, an instrument
that measures the pressure exerted by the
atmosphere.
Gases: Basic Concepts
Topic
13
Devices to Measure Pressure—
The Barometer
• His barometer was so sensitive that it
showed the difference in atmospheric
pressure between the top and bottom
of a flight of stairs.
Gases: Basic Concepts
Topic
13
•
•
•
•
Devices to Measure Pressure—
The Barometer
The height of the mercury column measures
the pressure exerted by the atmosphere.
We live at the bottom of an ocean of air.
The highest pressures occur at the lowest
altitudes.
If you go up a mountain, atmospheric
pressure decreases because the depth of air
above you is less.
Gases: Basic Concepts
Topic
13
Devices to Measure Pressure—
The Barometer
• One unit used to measure
pressure is defined by using
Torricelli’s barometer.
• The standard atmosphere
(atm) is defined as the
pressure that supports a 760mm column of mercury.
Gases: Basic Concepts
Topic
13
Devices to Measure Pressure—
The Barometer
• This definition can be represented by the
following equation.
• Because atmospheric pressure is measured
with a barometer, it is often called
barometric pressure.
Gases: Basic Concepts
Topic
13
Devices to Measure Pressure—
The Barometer
• A barometer measures
absolute pressure; that is,
the total pressures exerted
by all gases, including the
atmosphere.
Gases: Basic Concepts
Topic
13
Pressure Units
• Atmospheric pressure is the force per unit
area that the gases in the atmosphere exert
on the surface of Earth.
• The SI unit for
measuring pressure
is the pascal (Pa),
named after the
French physicist
Blaise Pascal
(1623-1662).
Gases: Basic Concepts
Topic
13
Pressure Units
• Because the pascal is a small pressure unit,
it is more convenient to use the kilopascal.
1 kilopascal (kPa) is equivalent to 1000
pascals.
• One standard
atmosphere is
equivalent to
101.3 kilopascals.
Gases: Basic Concepts
Topic
13
Pressure Units
• Because there are so many different
pressure units, the international
community of scientists recommends that
all pressure measurements be made using
SI units, but pounds per square inch
continues to be widely used in
engineering and almost all nonscientific
applications in the United States.
Gases: Basic Concepts
Topic
13
Pressure Conversions
• You can use the table to convert pressure
measurements to other units.
• For example, you can now find the absolute
pressure of the air in a bicycle tire.
Gases: Basic Concepts
Topic
13
•
•
•
•
Pressure Conversions
Suppose the gauge pressure is 44 psi.
To find the absolute pressure, add the
atmospheric pressure to the gauge pressure.
Because the gauge pressure is given in
pounds per square inch, use the value of the
standard atmosphere that is expressed in
pounds per square inch.
One standard atmosphere equals 14.7 psi.
Gases: Basic Concepts
Topic
13
Converting Barometric Pressure Units
• In weather reports, barometric pressure is
often expressed in inches of mercury.
• What is one standard atmosphere expressed
in inches of mercury?
• You know that one standard atmosphere is
equivalent to 760 mm of Hg. What is that
height expressed in inches?
• A length of 1.00 inch measures 25.4 mm on
a meterstick.
Gases: Basic Concepts
Topic
13
Converting Barometric Pressure Units
• Select the appropriate equivalent values and
units given.
• Multiply 760 mm by the number of inches in
each millimeter to express the measurement
in inches.
Gases: Basic Concepts
Topic
13
Converting Barometric Pressure Units
• The factor on the right of the expression
above is the conversion factor.
• Notice that the units are arranged so that
the unit mm will cancel properly and the
answer will be in inches.
Gases: Basic Concepts
Topic
13
Converting Pressure Units
• The reading of a tire-pressure gauge is
35 psi. What is the equivalent pressure in
kilopascals?
• The given unit is pounds per square inch
(psi), and the desired unit is kilopascals (kPa).
• The relationship between these two units is
14.7 = 101.3 kPa.
Gases: Basic Concepts
Topic
13
Converting Pressure Units
Gases: Basic Concepts
Topic
13
Converting Pressure Units
• Multiply and divide the values and units.
• Notice that the given units (psi) will cancel
properly and the quantity will be expressed
in the desired unit (kPa) in the answer.
Gases: Basic Concepts
Topic
13
The Gas Laws
• The gas laws apply to ideal gases, which
are described by the kinetic theory in the
following five statements.
• Gas particles do not attract or repel
each other.
• Gas particles are much smaller than
the spaces between them.
Gases: Basic Concepts
Topic
13
The Gas Laws
• Gas particles are in constant, random
motion.
• No kinetic energy is lost when gas particles
collide with each other or with the walls of
their container.
• All gases have the same kinetic energy at
a given temperature.
Gases: Basic Concepts
Topic
13
Boyle’s Law: Pressure and Volume
• Robert Boyle
(1627-1691), an
English scientist,
used a simple
apparatus pictured
to compress gases.
Gases: Basic Concepts
Topic
13
Boyle’s Law: Pressure and Volume
• After performing many experiments with
gases at constant temperatures, Boyle had
four findings.
a) If the pressure of a gas increases, its
volume decreases proportionately.
b) If the pressure of a gas decreases, its
volume increases proportionately.
Gases: Basic Concepts
Topic
13
Boyle’s Law: Pressure and Volume
c) If the volume of a gas increases, its
pressure decreases proportionately.
d) If the volume of a gas decreases, its
pressure increases proportionately.
• By using inverse proportions, all four
findings can be included in one statement
called Boyle’s law.
Gases: Basic Concepts
Topic
13
Boyle’s Law: Pressure and Volume
• Boyle’s law states that the pressure and
volume of a gas at constant temperature
are inversely proportional.
Click box to view movie clip.
Gases: Basic Concepts
Topic
13
Boyle’s Law
• At a constant temperature, the pressure
exerted by a gas depends on the frequency
of collisions between gas particles and the
container.
• If the same number of particles is squeezed
into a smaller space, the frequency of
collisions increases, thereby increasing the
pressure.
Gases: Basic Concepts
Topic
13
Boyle’s Law
• Thus, Boyle’s law states that at constant
temperature, the pressure and volume of a
gas are inversely related.
• In mathematical terms, this law is expressed
as follows.
Gases: Basic Concepts
Topic
13
Applying Boyle’s Law
• A sample of compressed methane has a
volume of 648 mL at a pressure of 503 kPa.
• To what pressure would the methane have to
be compressed in order to have a volume of
216 mL?
• Examine the Boyle’s law equation. You need
to find P2, the new pressure, so solve the
equation for P2.
Gases: Basic Concepts
Topic
13
Applying Boyle’s Law
• Substitute known values and solve.
Gases: Basic Concepts
Topic
13
Charles’s Law
• When the temperature of a sample of gas is
increased and the volume is free to change,
the pressure of the gas does not increase.
Instead, the volume of the gas increases in
proportion to the increase in Kelvin
temperature. This observation is Charles’s
law, which can be stated mathematically as
follows.
Gases: Basic Concepts
Topic
13
Charles’s Law
Click box to view movie clip.
Gases: Basic Concepts
Topic
13
Applying Charles’s Law
• A weather balloon contains 5.30 kL of
helium gas when the temperature is 12°C.
• At what temperature will the balloon’s
volume have increased to 6.00 kL?
• Start by converting the given temperature
to kelvins.
Gases: Basic Concepts
Topic
13
Applying Charles’s Law
• Next, solve the Charles’s law equation for
the new temperature, T2.
Gases: Basic Concepts
Topic
13
Applying Charles’s Law
• Then, substitute the known values and
compute the result.
• Finally, convert the Kelvin temperature
back to Celsius.
New Temperature = 323 – 273 = 50oC
Gases: Basic Concepts
Topic
13
The Combined Gas Law
• The gas laws may be combined into a single
law, called the combined gas law, that relates
two sets of conditions of pressure, volume,
and temperature by the following equation.
• With this equation, you can find the value of
any one of the variables if you know the
other five.
Gases: Basic Concepts
Topic
13
Applying the Combined Gas Law
• A sample of nitrogen monoxide has a volume
of 72.6 mL at a temperature of 16°C and a
pressure of 104.1 kPa.
• What volume will the sample occupy at 24°C
and 99.3 kPa?
• Start by converting the temperatures to
kelvins.
Gases: Basic Concepts
Topic
13
Applying the Combined Gas Law
• Next, solve the combined gas law equation
for the quantity to be determined, the new
volume, V2.
Gases: Basic Concepts
Topic
13
Applying the Combined Gas Law
• Substitute the known quantities and
compute V2.
Gases: Basic Concepts
Topic
13
Avogadro’s Principle
• In the early nineteenth century, Avogadro
proposed the idea that equal volumes of all
gases at the same conditions of
temperature and pressure contain the same
number of particles.
• An extension of Avogadro’s principle is
that one mole (6.02 x 1023 particles) of any
gas at standard temperature and pressure
(0°C and 1.00 atm pressure, STP) occupies
a volume of 22.4 L.
Gases: Basic Concepts
Topic
13
Avogadro’s Principle
• Given that the mass of a mole of any gas is
the molecular mass of the gas expressed in
grams, Avogadro’s principle allows you to
interrelate mass, moles, pressure, volume,
and temperature for any sample of gas.
Gases: Basic Concepts
Topic
13
Applying Avogadro’s Principle
• What is the volume of 7.17 g of neon gas
at 24°C and 1.05 atm?
• Start by converting the mass of neon to moles.
• The periodic table tells you that the atomic
mass of neon is 20.18 amu. Therefore, the
molar mass of neon is 20.18 g.
Gases: Basic Concepts
Topic
13
Applying Avogadro’s Principle
• Next, determine the volume at STP of
0.355 mol Ne.
• If you needed only the volume at STP, you
could stop here.
• Finally, use the combined gas law equation
to determine the volume of the neon at
24°C and 1.05 atm pressure.
Gases: Basic Concepts
Topic
13
Applying Avogadro’s Principle
Gases: Basic Concepts
Topic
13
Question 1 – 3
Use the table and the equation 1.00 in. = 25.4
mm to convert the following measurements.
Round answers to the nearest tenth.
Basic Assessment Questions
Topic
13
Question 1
Use the table and the equation 1.00 in. = 25.4
mm to convert the following measurements.
Round answers to the nearest tenth.
59.8 in. Hg to psi
Basic Assessment Questions
Topic
13
Answer 1
29.4 psi
Basic Assessment Questions
Topic
13
Question 2
Use the table and the equation 1.00 in. = 25.4
mm to convert the following measurements.
Round answers to the nearest tenth.
7.35 psi to mm Hg
Basic Assessment Questions
Topic
13
Answer 2
380 mm Hg
Basic Assessment Questions
Topic
13
Question 3
Use the table and the equation 1.00 in. = 25.4
mm to convert the following measurements.
Round answers to the nearest tenth.
1140 mm Hg to kPa
Basic Assessment Questions
Topic
13
Answer 3
151.95 kPa
Basic Assessment Questions
Topic
13
Question 4
What pressure will be needed to reduce the
volume of 77.4 L of helium at 98.0 kPa to a
volume of 60.0 L?
Basic Assessment Questions
Topic
13
Answer
126 kPa
Basic Assessment Questions
Topic
13
Question 5
A sample of SO2 gas has a volume of 1.16 L at
a temperature of 23°C. At what temperature
will the gas have a volume of 1.25 L?
Basic Assessment Questions
Topic
13
Answer
46°C or 31.9 K
Gases: Additional Concepts
Topic
13
Additional Concepts
Gases: Additional Concepts
Topic
13
The Ideal Gas Law
• The pressure, volume, temperature, and
number of moles of gas can be related in a
simpler, more convenient way by using the
ideal gas law.
• The following is the law’s mathematical
expression, PV = nRT where n represents
the number of moles.
Gases: Additional Concepts
Topic
13
The Ideal Gas Law
• The ideal gas constant, R, already contains
the molar volume of a gas at STP along with
the standard temperature and pressure
conditions.
Gases: Additional Concepts
Topic
13
The Ideal Gas Law
• The constant R does the job of correcting
conditions to STP.
• You do not have to correct STP in a
separate step.
Gases: Additional Concepts
Topic
13
The Ideal Gas Law
• The Value of R depends on the units in
which the pressure of the gas is measured,
as shown below.
• These values are all equivalent. Use the one
that matches the pressure units you are using.
Gases: Additional Concepts
Topic
13
Applying the Ideal Gas Law
• What pressure in atmospheres will 18.6 mol
of methane exert when it is compressed in a
12.00-L tank at a temperature of 45°C?
• As always, change the temperature to kelvins
before doing anything else.
Gases: Additional Concepts
Topic
13
Applying the Ideal Gas Law
• Next solve the ideal gas law equation for P.
• Substitute the known quantities and
calculate P.
Gases: Additional Concepts
Topic
13
Using Mass with the Ideal Gas Law
• Recall that it is possible to calculate the
number of moles of a sample of a substance
when you know the mass of the sample and
the formula of the substance.
Gases: Additional Concepts
Topic
13
Using Mass with the Ideal Gas Law
• You can substitute this expression into
the ideal gas law equation in place of n.
• Notice that this equation enables you to
determine the molar mass of a substance
if you know the values of the other four
variables.
Gases: Additional Concepts
Topic
13
Determining Molar Mass
• Determine the molar mass of an unknown
gas if a sample has a mass of 0.290 g and
occupies a volume of 148 mL at 13°C and
a pressure of 107.0 kPa.
• First, convert the temperature to kelvins.
Gases: Additional Concepts
Topic
13
Determining Molar Mass
• Next, solve the ideal gas law equation for M,
the molar mass.
• Finally, substitute values and calculate the
value of M.
• Notice that you must use the value of R that
uses kilopascals as pressure units and
express the volume in liters.
Gases: Additional Concepts
Topic
13
Determining Molar Mass
• Notice that the units cancel to leave grams per
mole, the appropriate units for molar mass.
Gases: Additional Concepts
Topic
13
Gas Stoichiometry
• Now that you know how to relate volumes,
masses, and moles for a gas, you can do
stoichiometric calculations for reactions
involving gases.
Gases: Additional Concepts
Topic
13
Gas Stoichiometry Using Mass
• Ammonium sulfate can be prepared by a
reaction between ammonia gas and sulfuric
acid as follows.
• What volume of NH3 gas, measured at 78°C
and a pressure of 1.66 atm, will be needed to
produce 5.00 x 103 g of (NH4)2SO4?
Gases: Additional Concepts
Topic
13
Gas Stoichiometry Using Mass
• First, you need to compute the number
of moles represented by 5.00 x 103 g of
(NH4)2SO4.
• Using atomic mass values from the
periodic table, you can compute the molar
mass of (NH4)2SO4 to be 132.14 g/mol.
Gases: Additional Concepts
Topic
13
Gas Stoichiometry Using Mass
• Next, determine the number of moles of
NH3 that must react to produce 37.84 mol
(NH4)2SO4.
Gases: Additional Concepts
Topic
13
Gas Stoichiometry Using Mass
• Finally, use the ideal gas law equation to
calculate the volume of 75.68 mol NH3 under
the stated conditions.
• Solve the equation for V, the volume to be
calculated.
• Convert the temperature to kelvins, substitute
known quantities into the equation, and
compute the volume.
Gases: Additional Concepts
Topic
13
Gas Stoichiometry Using Mass
• Notice that the values for the molar mass of
(NH4)2SO4 and the number of moles of NH3
have more than three significant figures,
whereas the calculated volume has only three.
Gases: Additional Concepts
Topic
13
Gas Stoichiometry Using Mass
• When you do a problem in a stepwise
way, you should maintain at least one
extra significant figure in the intermediate
values you calculate.
• Then, round off values only at the end of
the problem.
Additional Assessment Questions
Topic
13
Question 1
What is the pressure in atmospheres of 10.5
mol of acetylene in a 55.0-L cylinder at 37°C?
Answer
4.86 atm
Additional Assessment Questions
Topic
13
Question 2
What volume does 0.056 mol of H2 gas
occupy at 25°C and 1.11 atm pressure?
Answer
1.2L
Additional Assessment Questions
Topic
13
Question 3
A 250.0-mL sample of a noble gas collected at
88.1 kPa and 7°C has a mass of 0.378 g. What is
the molar mass of the gas? Identify the sample.
Answer
40.0g/mol; argon
Additional Assessment Questions
Topic
13
Question 4
When potassium chlorate is heated, it
decomposes to produce potassium chloride and
oxygen gas. Write a balanced equation for this
reaction, and calculate the mass of potassium
chlorate needed to produce 5.00 x 102 mL of
oxygen gas at 1.108 atm and 39°C.
Answer
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