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Chapter 21 - Physical Properties of Gases

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Week 1, Lesson 1
Chapter 21 – Physical Properties
of Gases
Behaviour of Gases
• Here are some everyday illustrations of the behaviour of gases.
These examples tell us a great deal about their physical properties.
– Air is used to inflate tyres. Generally a maximum air pressure is
recommended for tyres.
– Aerosol cans carry a warning not to expose them to high
temperatures.
– Helium balloons that are used to carry instruments into the upper
atmosphere for scientific observation are only partially inflated when
they leave the ground.
– Balloons used for sight-seeing can use heated air.
– If a bottle of strong smelling liquid, such as perfume, is opened in a
room, it doesn’t take long for the smell to spread.
– Scuba divers need to be very careful when ascending from a dive.
– When going for a drive in the mountains or travelling in a plane, you
often experience a popping sensation in your ears.
Properties of Gas
•
•
•
•
Low Density
Spread to fill available space
Easily compressed
Mix together rapidly.
Properties of Gas in Detail
• Low density: suggests that the particles of gas
are more widely spread.
• Easily Compressed: as above.
• Fill Available Space: suggest particles move
independently of one another.
• Mix Rapidly: the wide spacing of particles
together with their movement.
Kinetic Molecular Theory
• The model used to explain gas behaviour is called the kinetic
molecular theory.
• According to this model:
– Gases are composed of small particles. The total volume of the
particles in sample is very much smaller than the volume of occupied
space. Most of the volume taken up is empty space.
– These particles move rapidly in a random, straight line motion.
Particles will collide with each other and walls of the container.
– The bonding forces between particles are extremely weak. It is
assumed the particles move independently.
– Collisions between particles are elastic, energy is conserved. Kinetic
energy (energy of movement) can be transferred from one particle to
another but total kinetic energy will remain constant.
– The average kinetic energy of the particles increases as the
temperature of the gas is increased.
Relationship between Molecular
Kinetic Energy and Temperature
• According to the kinetic molecular theory, the
average kinetic energy of gas particles is
proportional to the temperature of that gas
sample.
• At an given temperature however;
– The average kinetic energy of the gas is not dependent on
the particular gas
– Within each gas sample, there will be some particles of
low kinetic energy and some of high energy. The
temperature merely reflects the average kinetic energy
particles in the sample.
Relationship b/w molecular kinetic
energy and temperature cont…
• The graph below shows the relative number of oxygen
molecules with a given kinetic energy at three different
temperatures.
• From the figure, you can see that:
– Only a small proportion of molecules has very low or very
high kinetic energy.
– At all three temperatures, there are some molecules with
very low kinetic energy
– The proportion of molecules with high kinetic energy
increases with temperature
– The average kinetic energy of the sample increases with
temperature
– The area under each graph represents the total number of
oxygen molecules. As the amount of gas is the same at all
three temperatures, the area under each graph must be
the same.
Average Kinetic Energy = ½ mv2
• The average kinetic energy of particles in
gases is related to their average speed of
movement by the relationship:
• m = mass of gas particles
• v = average velocity of the particles
• Therefore the lighter the gas atoms or
molecules in the sample, the greater their
average velocity.
Diffusion
• Is the term used to describe the way each gas in a
mixture of gases spreads itself evenly to fill the
total volume available.
• The rate at which gases diffuse depends on the
average velocity of their particles.
• Therefore gases of lower relative molecular mass
will diffuse more rapidly than gases of higher
relative molecular mass at the same temperature.
• Diffusion occurs more rapidly at higher
temperatures than lower temperatures.
Using the Kinetic Molecular Theory
• The model of gases helps to explain why
strong smells spread quickly.
• The particles that make up the gas are in
constant motion and continue to move in all
directions.
• Because there is so much space between
these particles and all other gas particles in
the air, all the gas particles rapidly mix with
each other.
Using the Kinetic Molecular Theory
cont…
• The model also explains why gases expand to
fill any container.
• The gas particles continue to move outwards
until stopped by walls of the container.
• This means that the amount of space a fixed
mass of gas takes up can be altered by
changing the size of its container.
Using the Kinetic Molecular Theory
cont…
• A gas can be compressed by reducing the volume
of its container because there is so much space
between the gas particles.
• The more a gas is compressed, the greater the
number of collisions the gas particles will have with
each other and the wall of its container.
• These collisions produce a force on the walls of the
container, such as the inside of a tyre, which can be
measured.
• The force on the wall area is measured as pressure.
Pressure
• In terms of the kinetic theory of gases, pressure is
defined as the force exerted in a unit area of a
surface by the particles of a gas as they collide
with each other and the walls of a container.
• The gas pressure exerted depends on the number
of collisions between the molecules and the walls
of the container.
• The pressure of a fixed amount of gas is
independent of the actual gas being considered.
Partial Pressure
• The pressure exerted by the individual gases in a mixture is
known as partial pressure.
• In a sample of air in a container, the partial pressure of the
nitrogen is the pressure that amount of nitrogen would exert
if it were the only gas in the container.
• When two gases are mixed together, the molecules of each
move independently and collide with the walls as though the
other gas were not there.
• The total pressure of a gas mixture is the sum of the individual
partial pressures of the gases in the mixture.
• The pressure will increase if the amount of gas or
temperature is increased or if the volume is decreased.
Measuring Pressure and Volume
• Since pressure is the force exerted on a unit of
area of a surface, we can write the
relationship:
Pressure = force/area = F/A
• The units of pressure will depend on the units
used to measure the force and area.
• Over the years, scientists have used different
units to measure force and area, so there are
a number of different units of pressure.
Week 1, Lesson 2
Units of Pressure
• The SI unit for force is the newton and for area is square
metre. So pressure for SI units is newtons per square metre or
N m-2.
• One N m-2 is equivalent to the pressure of one pascal (1 Pa)
• In 1982, IUPAC, adopted a standard for pressure equivalent to
100000Pa or 100kPa.
• This gave rise to a new unit of pressure, the bar, where 1 bar
equals 100kPa.
• Mercury barometers resulted in atmospheric pressure being
measured in millimetres of mercury or mmHg.
• Another unit is the standard atmosphere (atm).
• 1 standard atm is the pressure required to support 760mmHg.
• This is the average atmospheric pressure at sea level.
Four Units of Pressure
•
•
•
•
Millimetres of Mercury (mmHg)
Atmospheres (atm)
Pascals (Pa or N m-2)
Bars (bar)
1atm = 760mmHg = 1.013 x 105Pa = 101.3kPa = 1.013bar
Volume
• There are also a number of different units
used for volume.
• The common units are litre (L), millilitre (mL),
cubic metre (m3), cubic decimetre (dm3) and
cubic centrimetre (cm3).
1 mL
=
1cm3
1L
1L
=
1 x 103mL
1m3
1m3
=
1 x 103L
=
1x106mL
=
=
1dm3
1 x 103dm3
=
1x 106cm3
Week 1, Lesson 3
The Gas Laws
• It is possible to establish some rules or laws
that quantify the relationship between
volume, temperature, pressure and number of
particles of gas.
• These are known as the gas laws.
• They are used to describe the behaviour of all
gases, regardless of chemical components.
Boyle’s Law
• Robert Boyle showed that for a given amount of gas
at constant temperature, the volume of the gas is
inversely proportional to its pressure.
• Or, if the volume of a fixed amount of gas is halved,
the pressure will be doubled (at constant temp).
• PV = k – this relationship is useful because it allows
the calculation of a fixed amount of gas at a constant
temperature if the pressure is changed, OR
• P1V1 = P2V2
Charles’ Law
• To work with Charles’ Law we first need to
look at temperature.
• In this case, we do not use the celsius scale,
rather the kelvin scale or absolute
temperature scale.
• The relationship between temperature on the
Celsius scale (t) and temperature on the Kelvin
scale (T) is: T = t + 273
• Absolute zero is 0K or -273°C
Charles’ Law cont…
• Charles’ law states that the volume of a fixed
amount of gas is directly proportional to the
kelvin temperature, provided the pressure
remains constant.
• This law can be expressed using the
relationship, V/T = k, and then:
• V1/T1 = V2/T2
Amount of Gas
• The volume occupied by a gas depends
directly on the amount of gas (in mol) present,
provided the temperature and pressure
remain constant.
• The relationship between volume and amount
of gas is represented by the equation:
V1/n1 = V2/n2
Molar Volume of Gas
• If we take 1 mole of any gas, the volume it occupies
will depend on the temperature and pressure only.
• This volume is known as the molar volume (Vm) of a
gas.
• The volume of 1 mole of gas is equal to its total
volume divided by the amount, in mol, of gas
present.
• This can be represented by the rearranged equation:
n = V/Vm
STP and SLC
• It is convenient to know the molar volume of a gas
under the conditions that normally exist in a
laboratory.
• The temperature of 25°C (298K) and a pressure of
101.3kPa approximate to lab conditions. These
conditions are known as standard laboratory
conditions (SLC).
• STP, or standard temperature and pressure refers to
a temperature of 0°C (273K) and a pressure of
101.3kPa.
• The molar volume of a gas at SLC is 24.5L mol-1 and
at STP is 22.4L mol-1
Week 2, Lesson 1
Combined Gas Equation
• In most experiments with gases it is convenient to
hold variables such as temperature and pressure
constant, however, this is unrealistic.
• It is more common for amount of gas, temperature,
pressure and volume to all change in the one
process.
• To deal with such cases, the gas laws can be
combined to give:
V = knT/P, where k is the proportionality
constant.
Combined Gas Equation cont…
• P1V1/n1T1 = P2V2/n2T2
• This is the combined gas equation. It allows
the calculation of any one of these variables, if
the other variables have known values.
• It the amount of gas is fixed (n1 = n2), this
relationship becomes:
P1V1/T1 = P2V2/T2
Week 2, Lesson 2
General Gas Equation
• The general gas equation is developed from the combined gas
equation by determining a value for the constant k in the
expression: V = knT/P
• In the general gas equation, the proportionality constant is
given the symbol R.
• So the equation becomes: PV = nRT
• Where R is called the general gas constant and is given the
value 8.31J K-1 mol-1
• P = measured in kPa
• V = measured in L
• n = measured in moles
• T = measured in K
General Gas Equation cont…
• A gas that behaves according to the general
gas equation is said to be an ideal gas.
• In practice, most gases can be considered to
obey the general gas equation at low
pressures and high temperatures.
Week 2, Lesson 3
Reacting Quantities
• The molar volume under standard conditions
or the general gas equation can be used to
calculate the volume of any gas produced or
consumed in a reaction.
Mass-Volume Stoichiometry
• Standard Conditions
When standard conditions apply (SLC or STP),
once the amount of gas, in mol, has been
determined, the molar volume can be used to
calculate the required volume of gas.
Standard Conditions example
A sample of calcium carbonate, mass 1.0g, is heated until it has decomposed completely.
Calculate:
a) The mass of carbon dioxide produced
b) The volume of carbon dioxide at SLC
c) The volume of carbon dioxide at STP
a.
Step 1: Write a balanced equation for the reaction
Step 2: Calculate the amount (in mol) of the substance with the known mass
Step 3: Use the mole ratio to calculate the amount of the required substance
Step 4: Calculate the mass required
b.
Step 1: Calculate the amount of carbon dioxide.
Step 2: Calculate the volume of carbon dioxide at SLC
c.
Step 1: Find volume of carbon dioxide at STP
Non-Standard Conditions
• Calculations become more complex if the gas
is not at standard conditions. In such cases,
once the amount of gas, in mol, has been
calculated, the general gas equation can be
used to calculate the volume of gas.
Non-Standard Conditions Example
Hydrogen peroxide decomposes according to the following
equation:
2H2O2(aq)  2H2O(l) + O2(g)
What volume of oxygen, collected at 30°C and 91kPa, is
produced when 10.0g of hydrogen peroxide decomposes.
Step 1: Write a balanced equation.
Step 2: Calculate the amount (in mol) of the substance with the
known mass.
Step 3: Use the mole ratio to calculate the amount of the
required substance.
Step 4: Calculate the volume of O2
Volume-Volume Stoichiometry
• We can use ratios in a balanced equation to
calculate the volumes of gaseous reactants or
products.
• At constant temperature and pressure, the
mole ratio will be equal to the ratio of gas
volumes.
Volume-Volume Stoichiometry
Example
Methane is burnt in a gas stove. If 50mL of methane, measured at a pressure of 1atm, is burnt in
air at 500°C, calculate:
a) The volume of O2, measured at 1atm and 500°C, required for complete combustion of the
methane.
b) The volumes of CO2 and H2O vapour produced at 1atm and 500°C
Solution:
CH4(g) + 2O2(g)  CO2(g) + 2H2O(l)
Mole Ratio 1mol 2mol
1mol
2mol
At constant temp and pressure, the mole ratio will equal the ratio of the gas volumes.
Volume Ratio 1vol
2vol
1vol
2vol
Therfore;
50mL
100mL 50mL
100mL
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