Contents
6-1
6-2
6-3
6-4
6-5
6-6
Properties of Gases
The Simple Gas Laws
Combining the Gas Laws:
The Ideal Gas Equation and
The General Gas Equation
Applications of the Ideal Gas Equation
Gases in Chemical Reactions
Mixtures of Gases
Slide 1 of 46
6-1 Properties of Gases:
• The gaseous states of three halogens.
• Most common gases are colorless
– H2, O2, N2, CO and CO2
Slide 2 of 46
General Chemistry: Chapter 6
Properties of Gases
• Gases assume the volume and shape of their
containers.
• Gases are the most compressible of the states
of matter.
• Gases diffuse into one another and mix evenly
and completely when confined to the same
container.
• Gases have much lower densities than liquids
and solids.
Four properties determine the
physical behavior of a gas
If we know three of these properties,
we can calculate the value of the
remaining using the equation of state
What keep this balloon
distended?
Pressure is defined as force per unit area;
• The pressure is
defined as a force
divided by the area
over which the force is
distributed.
Force (N)
P (Pa) =
Area (m2)
Liquid Pressure
• The pressure exerted
by a liquid depends on:
– The height of the
column of liquid.
– The density of the
column of liquid.
P = g ·h ·d
It is difficult to measure the total
force exerted by gas molecules so,
The pressure of a gas is measured
indirectly, by comparing it with a liquid
pressure.
What keeps the Hg(l) at a greater height inside the tube than outside?
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Slide 9 of 46
• A Barometer is an instrument for measuring
the pressure exerted by the atmosphere.
• The atmosphere exerts a force on the
surface of the Hg (l) in the outside
container.
• The column exerts a downward pressure
that depends on its height and the density
of Hg (l).
• When this downward P = the P of the
atmosphere, the column height is
maintained.
• The height of mercury in the barometer
provides a measure of barometric pressure.
Standard Atmospheric Pressure (1 atm) is
equal to the pressure that supports a column of
mercury exactly 760 mm (or 76 cm) high at 0°C
at sea level
1 torr = 760 mm Hg = 1 atm
1 atm = 101,325 Pa = 1.01325 x 105 Pa
A manometer is a device used to measure pressure of gases other than
the atmosphere: the pressure of the gas to be measured can be
compared to the barometric pressure by using a manometer.
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Slide 14 of 46
6-2 Simple Gas Laws
• Boyle’s Law: Pressure
of a fixed amount of
gas maintained at
constant temperature
is inversely
proportional to the
volume of the gas.
Slide 15 of 46
P
1
V
General Chemistry: Chapter 6
PV = constant
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Charles Law:
The volume of a fixed amount of gas maintained at a constant
pressure is directly proportional to the Kelvin (absolute)
temperature of the gas.
V T
V=bT
Temperature at which the volume of a hypothetical gas
becomes 0 is the absolute zero of temperature.
• The volume of gas
increases as the
temperature is raised.
• The relationship is linear.
• One point is common to
the four lines is their
intersection with the
temperature axis.
• The gas volumes all reach
the value of zero at the
same temperature.
• This temperature is the
absolute zero of
temperature: - 273.15 ⁰C
or 0 K
Charles Law
Standard conditions of Temperature and Pressure
STP
• Gas properties depend on T and P, so it is
useful to have a set of standard conditions of
temperature and pressure.
• STP: 0 ⁰C and 1 bar = 105 Pa
Avogadro's law
• At constant pressure and temperature, the
volume of a gas is directly proportional to the
number of moles of the gas present.
V α n or V = c × n
The constant c, c = V/n , is the volume per mole
of a gas and is called the molar volume of the
gas.
Molar volume of gases vary with T and P.
Avogadro’s Law
At a fixed temperature and pressure:
V
n
At STP
1 mol gas = 22.4 L gas
or
V=cn
The molar volume of a gas is approximately 22.414 L at 0⁰C and
1 atm.
Law of Combining Volumes
The volume ratio of the gases consumed and produced in a
chemical reaction is the same as the mole ratio, provided the
volumes are measured at the same temperature and pressure.
3H2 (g) + N2 (g) → 2 NH3 (g)
Formation of Water
Avogadro’s hypothesis identifies the relationship between
stoichiometry and gas volume.
Combining the Gas Laws:
The Ideal Gas Equation and the General Gas Equation
• Boyle’s law
V
1/P
• Charles’s law
V
T
• Avogadro’s law V
n
V
nT
P
PV = nRT
Any gas whose behavior conforms to the ideal gas equation is
called an ideal or perfect gas. R is the gas constant.
The Gas Constant
PV = nRT
PV
R=
nT
= 0.082057 L atm mol-1 K-1
= 8.3145 m3 Pa mol-1 K-1
= 8.3145 J mol-1 K-1
6-4 Applications of the Ideal Gas Equation
Molar Mass and Density Determinations
PV = nRT
and
n=
m
M
m
RT
PV =
M
m RT
M=
PV
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General Chemistry: Chapter 6
Slide 30 of 46
Example: A chemist has synthesized a
greenish yellow gaseous compound of
chlorine and oxygen and finds that its density
is 7.71 g/L at 36°C and 2.88 atm. Calculate
the molar mass of the compound and
determine its molecular formula.
What volume of oxygen (at STP) can be formed from
0.500 mol of potassium chlorate?
• Step 1 Write the balanced equation
• KClO3 → KCl + O2
• Step 2 The starting amount is 0.500 mol KClO3. The
conversion is
mol KClO3 → mol O2 → L O2
• Step 3 Calculate the moles of O2, using the moleratio method.
• Step 4. Convert moles of O2 to liters of O2
EXAMPLE 6-12
Using the Ideal gas Equation in Reaction Stoichiometry Calculations.
The decomposition of sodium azide, NaN3, at high temperatures produces
N2(g). Together with the necessary devices to initiate the reaction and trap the
sodium metal formed, this reaction is used in air-bag safety systems. What
volume of N2(g), measured at 735 mm Hg and 26 C, is produced when 70.0 g
NaN3 is decomposed?
NaN3(s) → Na(l) + N2(g)
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General Chemistry: Chapter 6
Slide 33 of 46
EXAMPLE 6-12
Determine moles of N2:
nN2 = 70 g NaN3
1 mol NaN3
65.01 g NaN3
3 mol N2
= 1.62 mol N2
2 mol NaN3
Determine volume of N2:
V=
nRT
P
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(1.62 mol)(0.08206 L atm mol-1 K-1)(299 K)
= 41.1 L
=
(735 mm Hg)
1.00 atm
760 mm Hg
General Chemistry: Chapter 6
Slide 34 of 46
Mixture of Gases
• The simple gas laws and the ideal gas equation apply
to a mixture of nonreactive gases as well just by
using ntot for the value of n.
John Dalton proposed that, in a mixture of gases,
each gas expands to fill the container and exerts the
same pressure ( called its partial pressure) as it
would if it were alone in the container.
Dalton’s Law of Partial Pressures: The total pressure of a
mixture of gases is the sum of the pressures that each gas would
exert if it were present alone. Ptot = PA + PB + …
The following equation applies in a
Gaseous Mixture
nA/ntot = PA/Ptot = XA
• XA is called the Mole Fraction: a dimensionless
quantity that expresses the ratio of the number of
moles of one component to the total number of
moles present.
If 250 mL of gas is collected at 760 mm Hg and 25°C
determine the number of grams of O2 produced by the reaction.
2 KClO3 → 2 KCl + 3 O2
Collecting gas over a liquid
Ptot = Pbar = Pgas + PH2O
Example 6-13
A sample of impure KClO3 weighing 0.713 g is heated
to drive off oxygen:
KClO3 (s) → KCl (s) + O2 (g) (unbalanced)
The volume of O2, collected over water at 26°C and
101.3 kPa was 126 ml. The vapour pressure of water
at this temperature is 3.4 kPa.
1.What is the mass of KCl formed?
2.What is the percent purity of the KClO3?
A gaseous compound containing only carbon,
hydrogen and fluorine is 36.4% C and 6.10% H
by mass.
The density of this gas at 1.50 atmospheres
and 27°C was found to be 4.025 g/L. Find the
molecular formulae of the gas.
Combustion of propane in the presence of
oxygen yields carbon dioxide and water. The
unbalanced equation is:
C3H8(g) + O2(g) → CO2(g) + H2O(g)
If 1.00 g of propane and 3.00 g of oxygen are
reacted in a 1.00 litre container at 227°C,
determine the limiting reagent and the total
pressure of the gases at the completion of the
reaction.
Kinetic-Molecular Theory of Gases:
A theory to explain the behavior of gases
Assumptions:
• Gas is composed of molecules, separated
by distances far greater than their own
dimensions. Molecules are considered
"points" with mass and negligible
volumes.
• Gas molecules are in constant random
motion, and they frequently collide.
• Collisions among molecules are perfectly
elastic, with the total energy of all the
molecules in a system remains the
same.
• Gas molecules exert neither attractive
nor repulsive forces on one another.
Distribution of Molecular Speeds
Not all molecules in a gas travel at the same speed; because of the large number
of molecules, we cannot know the speed of each molecule, but we can make a
statistical prediction of how many molecules have a particular speed.
Urms
u2
Is of particular interest to us…as
we can use it to calculate the
average Kinetic Energy
% of molecules with a certain speed
Distribution of Molecular Speeds
changes with molar mass and temperature
u rms
3RT
M
Effusion and Diffusion:
• Diffusion is the term used to describe the mixing of
gases. The rate of diffusion is the rate of the mixing
of gases.
• Effusion is the term used to describe the passage of
a gas through a tiny orifice into an evacuated
chamber.
• The rate of effusion measures the rate at which the
gas is transferred into the chamber.
• Thomas Graham found experimentally that the rate
of effusion of a gas is inversely proportional to the
square root of the mass of its particles.
Gas Properties Relating to the Kinetic-Molecular Theory
General Chemistry: Chapter 6
Graham’s Law
rateof effusionof A
rateof effusionof B
(u rms ) A
(u rms ) B
3RT/M A
3RT/MB
MB
MA
• Only for gases at low pressure (natural escape, not a jet).
• Tiny orifice (no collisions)
• Does not apply to diffusion.
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General Chemistry: Chapter 6
Slide 50 of 46
A 1.00 litre tank is filled with an equal mass of F2, O2
and N2 gas.
a) Arrange the molecules in order of increasing
average speed.
b) Calculate the mole fraction of F2.
c) What is the partial pressure of N2 if the pressure in
the container is 1.00 atm?
• An ideal gas obeys the gas laws.
• The volume the molecules of an
ideal gas occupy is negligible compared to the
volume of the gas.
This is true at all temperatures and pressures.
• The intermolecular attractions between the
molecules of an ideal gas are negligible at all
temperatures and pressures.
6-9 Nonideal (Real) Gases
• Compressibility factor PV/nRT = 1
• Deviations occur for real gases.
– PV/nRT > 1 - molecular volume is significant; high P
– PV/nRT < 1 – intermolecular forces of attraction; e.g.
NH3: 0.88.
Slide 53 of 46
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Real Gases
Gases behave ideally
at high T and low P
And,
non-ideally at low T and high P
Deviations from the gas laws occur at high
pressures and low temperatures.
At high pressures, the volumes of the real gas
molecules are not negligible compared to the
volume of the gas.
At low temperatures, the kinetic energy of the gas
molecules cannot completely overcome the
intermolecular attractive forces between the
molecules.
Van der Waals Equation
P+
n2a
V2
V – nb
= nRT
nb is the volume of the molecules themselves; so,
V – nb is the volume available for molecular motion.
The decrease in P has also been taken into account.
a and b increase as the size of the molecules increase,
and therefore, deviation from ideality increases.
Slide 56 of 46
A 1.00 L flask contains 20.0 mole of CO2 gas at 25°C.
Calculate the pressure of the gas: (a) assuming
ideal behavior and (b) using the Van der Waals equation
and the following constants: a = 3.592 L2.atm.mol-2,
b = 0.04267 L.mol-1.
Repeat the question with 0.500 mol of CO2 (in a 1.00 L
flask at 25ºC). Compare your answers (i and ii).
Can you explain why the van dar Waals equation gives
a lower pressure than the ideal gas equation in (ii)
and a higher pressure than the ideal gas equation for
(i)?
At low pressures (0.5 mol/L) , the deviation is negative as
the effect of attractive forces overwhelms the effect
of molecular size and the attractive forces pull the
molecules together away from the container walls,
lowering the pressure.
At high pressures (20 mol/L), the deviation is positive as
the effect of molecular size overwhelms the effect of
attractive forces and the volume occupied by the
molecules means there is less volume between the
molecules, increasing the pressure.
Carbon dioxide switches from a negative to a
positive deviation at 600 atm (actual pressure not that
calculated from the ideal gas equation).
A sample of impure KClO3 weighing 0.713 g is
heated to drive off oxygen:
KClO3 (s) → KCl (s) + O2 (g) (unbalanced)
The volume of O2, collected over water at 26°C and
101.3 kPa was 126 ml. The vapour pressure of water
at this temperature is 3.4 kPa.
a What is the mass of KCl formed?
b What is the percent purity of the KClO3?
Pressure – Assessing Collision
Forces
• Translational kinetic energy,
ek
1
mu 2
2
• Frequency of collisions,
v
N
u
V
• Impulse or momentum
transfer,
I
mu
• Pressure proportional to
impulse times frequency
Slide 60 of 46
P
General Chemistry: Chapter 6
N
mu 2
V
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Derivation of Boyle’s Law:
PV = a, a depends on N and T.
• Let’s focus on a molecule travelling along the x
direction toward a perpendicular wall to its path with
the speed of ux.
The force exerted on the wall by the
molecule depends on:
1. The frequency of molecular collisions:
the # of collisions/ second
collision frequency α (molecular speed) × ( # of molecules per unit
volume)
2. The momentum transfer, or impulse. When a molecule hits
the wall of a vessel, momentum is transferred as the molecule
reverses direction. This momentum transfer is called impulse.
magnitude of impulse α (mass of particle) × (molecular speed)
the pressure of a gas is the product of impulse and collision
frequency
P α (mux) × ( ux )(N/V) α (N/V) mux2
m : mass of one molecule
Distribution of Molecular Speeds
u rms
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General Chemistry: Chapter 6
3RT
M
Slide 63 of 46
• At any moment, the molecules in a gas sample are travelling
at different speeds. So, we must consider the average of ux2 ,
we show it by, ux2
Thus:
P α (N/V) mux2
• One last thing, we should take into account ALL molecules,
not just those moving in the x direction.
• U2= ux2 + uy2+ uz2
P
1N
m u2
3V
P
1N
m u2
3V
Assume one mole:
PV=RT so:
NAm = M:
Rearrange:
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Pressure
PV
3RT
3RT
u rms
1
2
NAm u
3
NAm u
Mu
2
2
3RT
M
General Chemistry: Chapter 6
Slide 65 of 46
Temperature
Modify:
PV=RT so:
Solve for ek:
PV
1
N Am u 2
3
2
1
N A( m u2 )
3
2
2
RT
N A ek
3
3 R
ek
(T)
2 NA
Average kinetic energy is directly proportional to temperature!
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General Chemistry: Chapter 6
Slide 66 of 46
Pressure and Molecular Speed
• Three dimensional systems lead to:
P
1N
m u2
3V
um is the modal speed
uav is the simple average
Urms
u2
Is of particular interest to us…as
we can use it to calculate the
average Kinetic Energy
The average kinetic energy of the molecules is
proportional to the temperature in Kelvin’s.
Any two gases at the same temperature will
have the same average kinetic energy.
KE = 1/2 m u2
Where; KE is the average Kinetic Energy; u2 is
the mean square speed (ave. all molecules)