Gases (Chapter 10)
• Rather than considering the atomic
nature of matter we can classify it
based on the bulk property:
gaseous, liquid or solid.
• Gases are the most easily
understood form of matter (we
shall see why).
Component
Symbol
Volume
Nitrogen
N2
78.084%
Oxygen
O2
20.947%
Argon
Ar
0.934%
Carbon Dioxide
CO2
0.033%
Neon
Ne
18.2 parts per million
Helium
He
5.2 parts per million
Krypton
Kr
1.1 parts per million
Sulfur dioxide
SO2
1.0 parts per million
Air is an example of a complex mixture of gases:
gases form homogeneous mixtures regardless
of identities or proportions (unlike liquids and
solids).
Gases expand to fill any container, and are highly
compressible (unlike liquids and solids)
Methane
CH4
2.0 parts per million
Hydrogen
H2
0.5 parts per million
N2O
0.5 parts per million
These characteristics arise because
the molecules of gas are very far
apart and don’t (mostly) interact.
Different gases thus behave
similarly.
Iodine
Nitrous Oxide
99.998%
Xenon
Xe
0.09 parts per million
Ozone
O3
0.07 parts per million
NO2
0.02 parts per million
I2
0.01 parts per million
Nitrogen dioxide
Carbon monoxide
CO
trace
Ammonia
NH3
trace
Pressure
• Pressure is the force that acts on a given area (P=F/A).
• Gravity on earth exerts a pressure on the atmosphere:
atmospheric pressure.
• We can evaluate this by calculating the force due to
acceleration (by gravity) of a 1m2 column of air extending
through the atmosphere (this has a mass of ~10,000kg).
F  m.a
F  10,000kg  9.8m / s 2  100,000kgm / s 2
This unit is a Newton (N)
1  105 N
5
2
P  F/A

1

10
N
/
m
1m 2
This unit is a Pascal (Pa)
Units of Pressure
S.I. unit of pressure is the N/m2, given the name Pascal (Pa).
A related unit is the bar (1x105 Pa) used because atmospheric
pressure is ~ 1x105 Pa (100 kPa, or 1bar).
Torricelli (a student of Galileo) was the first to recognise that the
atmosphere had weight, and measured pressure using a barometer
Standard atmospheric pressure was thus defined
as the pressure sufficient to support a mercury
column of 760mm (units of mmHg, or torr).
Another popular unit was thus introduced to
simplify things, the atmosphere (atm =
760mmHg).
Pressure
• Atmospheric pressure and relationship between units
1 atm = 760 mmHg = 760 torr = 101.325kPa = 1.01325 bar)
Measuring Pressure: the manometer
Exercise:
On a certain day a barometer gives the atmospheric pressure as 764.7 torr. If a
metre stick is used to measure a height of 136.4mm in the open arm, and
103.8mm in the gas arm of a manometer, what is the pressure of the gas sample?
(give in torr, atm, kPa and bar).
Result
Difference in height is 32.6 mm. Gas inside
has greater pressure than prevailing
atmospheric pressure: 764.7 + 32.6 mmHg =
797.3 mmHg (Torr)
Convert to atm: divide by 760 = 1.049 atm
Convert to kPa: multiply by 101.325 = 106.3
kPa
Convert to bar: divide by 100 = 1.063 bar
Gas Laws
• A large number of experiments have determined that 4
variables are sufficient to define the physical condition (or
state) of a gas: the gas laws.
Boyle’s Law, Charles’ Law, Avogadro’s hypothesis
Robert Boyle: (1627-1691) the first modern chemist, known as
the father of chemistry.
His 1661 book The Sceptical Chymist marks the introduction of
the scientific method, a definition of elements and compounds
and a refutation of alchemy and magic potions.
Boyle biography
Boyle’s Law
• Boyle investigated the variation of the volume occupied by a
gas as the pressure exerted upon it was altered and noted that
the volume of a fixed quantity of gas, at constant temperature
is inversely proportional to the pressure
1
V  constant  or PV  constant
p
Charles’ Law
• A century later, a French scientist, Jacques Charles discovered that the
volume of a fixed amount of gas, as constant pressure, is proportional
to the absolute temperature. Cool a balloon, or a sealed plastic bottle, to
verify this!
V
V  constant  T or  constant
T
It was recognised (by William
Thomson, Lord Kelvin, a Belfast
born physicist) that if the graph was
extrapolated to zero volume, an
absolute zero of -273.15 oC is
obtained.
Avogadro’s Law
• Relationship between quantity of gas and volume established by
Gay-Lussac (balloon science!) and Avogadro in the 19th Century.
Result was Avogadro’s hypothesis: equal volumes of gases at the
same temperature and pressure contain equal numbers of
molecules
Experiments show that 22.4L of gas at 0oC and 1atm
(STP), or 24.8L of gas at 298.15 K and 1 bar (SATP),
contains 6.022 x 1023 molecules (Avogadro’s number, NA)
Avogadro’s law: volume of gas at constant temperature and
pressure is proportional to the number of moles of gas (n)
V  constant  n
Remember:
1 mole = Avogadro’s
number of objects
Putting it all together
1
V  , V  T, V  n
P
nT
V
P
 nT 
V  R

 P 
PV  nRT
Boyle, Charles, Avogadro
Combine
Call proportionality constant R
(gas constant)
Ideal Gas Equation
A note on units and dimensional analysis
SI unit for R is J/mol.K or m3.Pa/mol.K (R=8.315 of these
units)
Need to use the units of Pa for pressure and m3(=1000L) for
volume in any calculation.
Alternatively you can use units of kPa and L.
If you wish to use atm and L (as in USA and Textbook)
R=0.0826 L.atm/mol/K.
Always use absolute temperature scale (K)
Exercises
• What is the volume of 1 mole of an ideal gas
under standard temperature and pressure (STP)?
• How many moles (g) of CO2 is liberated into a
250mL flask when a pressure of 1.3atm is found
upon heating calcium carbonate to 31oC?
• If a metal cylinder holds 50L of oxygen at 18.5atm
and 21oC, what volume will the gas occupy at
1atm and same T?
More Exercises
If the pressure of a gas in an aerosol can is 1.5atm at 21oC, what
would the pressure be if can is heated to 450oC?
What is the density of carbon tetrachloride vapour at 714torr
and 125oC?
Gases in chemical reactions
See student activities
If an air bag has a volume of 36L and is to be filled with nitrogen
gas at a pressure of 1.15atm and 26oC, how many grams of NaN3
must be decomposed?
Gas mixtures
• Dalton’s Law of partial pressures
The total pressure of a mixture of gases equals the
sum of the pressures that each would exert if it
were present alone
PT=P1+P2+P3+….Pn
Exercise:
A gaseous mixture is made from 6.00g oxygen and
9.00g methane placed in a 15L vessel at 0oC. What is the partial
pressure of each gas and the total pressure in the vessel?
Aside: A wronged chemist?
John Dalton, is credited with the formulation of the
atomic theory. This was disputed by William
Higgins, an Irish chemist from Colloney, Sligo,
who claimed to have been the first to postulate the
theory in his book Comparative view of the
phlogistic and anti-phlogistic theories (1789) a
work very critical of the Galway chemist Richard
Kirwan.
(Atkinson, E. R. The Atomic Hypothesis of William Higgins, J. Chem. Ed. 1940, 17(1), 3-11).
Mole Fractions
• The ratio n1/nT is called the mole fraction (denoted x1), a
dimensionless number between 0 and 1.
P1 n1RT / V
n1


PT nT RT / V nT
 n1 
P1    PT
 nT 
Mole fraction of N2 in air is 0.78, therefore if the total
barometric pressure is 760 torr, the partial pressure of N2 is
(0.78)(760) = 590 torr.
Kinetic –Molecular Theory
Theory describing why gas laws are obeyed (explains both pressure and
temperature of gases on a molecular level).
• Complete form of theory, developed over 100 years or so, published by
Clausius in 1857.
 Gases consist of large numbers of molecules that are in continuous,
random motion
 Volume of all molecules of the gas is negligible, as are
attractive/repulsive interactions
 Interactions are brief, through elastic collisions (average kinetic energy
does not change)
 Average kinetic energy of molecules is proportional to T, and all gases
have the same average kinetic energy at any given T.
Because each molecule of gas will have an individual kinetic energy, and thus
individual speed, the speed of molecules in the gas phase is usually characterised
by the root-mean-squared (rms) speed, u,(not the same though similar to the
average speed). Average kinetic energy є = ½mu2
Application to Gas Laws
• Increasing V at constant T:
Constant T means that u is unchanged.
But if V is increased the likelihood of
collision with the walls decreases,
thus the pressure decreases (Boyle’s
Law)
• Increasing T at constant V:
Increasing T increases u, increasing
collisional frequency with the walls,
thus the pressure increases (Ideal Gas
Equation).
Molecular speeds and mass
• The average kinetic energy of gases has a specific value at
a given temperature. The rms speed of gas composed of
light particles, He, is higher than that for heavier particles,
Ne, at the same temperature.
• Can derive an expression for the rms speed (from kinetic
theory)
3RT
u
M
M is the molar mass
See student activities
This gives rise to interesting consequences:
effusion
Effusion
• Thomas Graham (1846)
discovered that effusion is
inversely proportional to the
square root of molar mass.
r1

r2
M2
M1
Derived from comparison
of rms speeds
REAL GASES
Deviations from ideal gas law
WHY?
1. Molecules have volume
2. Molecules have attractive forces
(intermolecular)
1. V-nb
2. -a(n/V)2
Van der Waals Equation of State
nRT
n
P
 a 
V  nb
V 
2
Van der Waal’s constants
van der Waals Coefficients
a (Pa m3)
b(m3/mol)
Gas
Helium
3.46 x 10-3 23.71 x 10-6
Neon
2.12 x 10-2 17.10 x 10-6
Hydrogen
2.45 x 10-2 26.61 x 10-6
Carbon dioxide 3.96 x 10-1 42.69 x 10-6
Water vapor
5.47 x 10-1 30.52 x 10-6
a correlates with boiling point (see later)
b can be used to estimate molecular radii