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Gases: Properties and
Behaviour
Gas Laws
Partial Pressures
Kinetic Theory and Ideal Gases
Real Gases
Diffusion and Effusion
Learning objectives
Describe properties of gases and define ideal gas
Describe the physical basis for pressure
Identify units of pressure and convert between
units
Describe and apply the main gas laws
Apply gas laws to stoichiometric problems
Describe and apply law of partial pressures
Features of gases
Gases are always miscible
Gases are compressible
Gases exert pressure
Gases are mostly nothing: less than 0.1 % of the
volume is occupied by molecules (contrast 70 %
for solids and liquids)
The ideal gas law assumes molecules occupy
zero percent
Molecular interactions
Strength of interactions
between molecules
determines the state
Strong attractions make
for high melting point
(ionic solids)
Weaker interactions
between molecules
occur in liquids
(covalent molecules)
Molecular interactions in gases are
negligible
Air is more than one removed
from nothing
Gases are mostly empty space:
molecules occupy <0.1 %
volume
1,000 times less dense than
solids and liquids
Emptiness allows complete
mixing
The Ideal gas
The ideal gas is defined as follows
Interactions between molecules are nonexistent
Volume occupied by molecules is zero
Collisions
There are two types of
collision
Between the
molecules and the
container
Between molecules
In the ideal gas these
collisions are perfectly
elastic (no energy loss)
Collisions between billiard
balls mirrors the collisions
between the molecules of an
ideal gas
Origins of pressure
Pressure is force per unit area: F/A
Force is rate of change of momentum: F = ma = d(mv)/dt
Molecules colliding with the walls of the container
exchange momentum
Units of pressure
The S.I. unit of pressure is the pascal (Pa)
1 Pa = 1 N/m2, where N is the S.I. unit of force
1 N = 1 kgm/s2
The weight of the air exerts pressure –
atmospheric pressure
This pressure is about 100,000 Pa
Older is better
101 kPa is an inconvenient way of measuring pressure
Traditional units are still used in preference to the SI system
Atmospheres, cm (or mm) of Hg and torr are the most common
Bar is becoming more widespread (1 bar = 100 kPa)
How do I measure the atmosphere?
Let me count the ways
1 atmosphere =
760 mm Hg = 76.0 cm Hg
14.70 psi
760 torr
1.013 bar
29.9 in Hg
101.3 kPa
Standard temperature and pressure
(STP)
Standard conditions allow direct comparison of
properties of different substances
Standard temperature is 273 K (0ºC)
Standard pressure is 760 mm Hg
At STP, 1 mole of any ideal gas occupies 22.414 L
Balancing act
Weight of air supports equal weight of mercury (or other liquid)
Mercury being dense, column is 76 cm equivalent to same weight of atmosphere (several miles high)
76 cm (760 mm) Hg = 1 atm
Manometers measure pressure in a
container (A) If pressure inside bulb < atmospheric,
atmosphere pushes down more.
(B) If pressure inside bulb > atmospheric, column
is pushed towards open end.
Gas Laws
Physical properties of gases were among the first experiments performed in the “modern” scientific era, beginning in the 17th century
All gases exhibit similar physical properties even if their chemical properties differ widely
Properties can be summarized in a few simple laws
Variables are pressure, volume, temperature and quantity. Keep one (or two) constant and vary the others
Gas laws: experience in math form
The properties of gases can be described by a number of simple laws
The laws establish quantitative relationships between different variables
They are largely intuitively obvious and familiar
The four variables
Pressure (P)
Volume (V)
Temperature (T in Kelvin)
Number of molecules (n in moles)
Variables and constants
In the elementary gas laws two of the four
variables are kept constant
Each law describes how one variable reacts to
changes in another variable
All the simple laws can be integrated into one
combined gas law
The first experimental gas law
Pressure increases, volume
decreases (T, n constant)
Boyle’s law
1P
V
Mathematical form
The volume of a fixed amount of an ideal gas varies inversely with pressure at constant temperature
PV = constant
P α 1/V
0
20
40
60
80
100
120
0 1 2 3 4 5
Pre
ssu
re (a
tm)
1/Volume (1/L)
P vs 1/V
Getting some exercise An exercise ball at pressure (Pa) = 1000 mm Hg
has volume (Va) = 60 L
When sat on, new volume (Vb) = 40 L. What is
new pressure?
Check: P increases as V decreases
Note: doesn’t matter what units provided they are
consistent
a a b bPV PV
(1000 )(60 )1500
40
a a
b
b
PV mmHg LP mmHg
V L
Example
Charles’ Law
Pressure and amount constant
As temperature increases, the volume increases
Mathematical form The volume of a fixed amount of an ideal gas varies
directly with absolute temperature at constant pressure
V α T
V/T = constant
NOTE: Temperature must be in Kelvin (ºC + 273)
At absolute zero there is no motion and the residual volume is that of the atoms – which is assumed to be zero
0
5
10
15
20
25
30
35
40
45
0 100 200 300 400 500 600
Vo
lum
e (L
)
Temperature (K)
V vs T
Example
Avogadro’s Law Pressure and temperature constant
Increase the amount, the volume increases
Summary of gas laws
Mathematical form
The volume of an ideal gas varies directly with its
molar amount at constant T and P
V α n
V/n = constant
Same volume of any gas contains same number
of moles at constant T,P
The standard molar volume at 273 K and 1 atm is
22.414 L
Comparison with reality Standard molar volume of 22.41 L compares with
experimental values of common real gases
Agreement shows that these ideal gas laws can
be widely applied for real gases
Less ideal gases (NH3) agree better than some
more ideal gases (Ar)
Putting them together: the ideal gas
law PV = nRT
R is the gas constant = 0.0821 L-atm/mol-K
Note units of R. R also appears in thermodynamic calculations, but with different units and numerical value (8.315 J/K-mol). Use the one appropriate to the calculation
• Units of pressure – atm
• Units of temperature – K
• Units of volume – L
Standard temperature and pressure: T = 0 ºC and P = 1 atm
Example
The combined gas law
Allows us to calculate change in one variable for
changes in the three other variables
PVR
nT Combined
Gas Law
AvogadroAmonton
CharlesBoyle
Applications A system at initial conditions Xa changes to new
conditions Xb
If we know three of the variables in state b, the
fourth can be obtained
In most of these problems na = nb
a a b b
a a b b
PV PV
n T n T
a a b b
a b
P V PV
T T
The “simple” laws are derived from
the combined law
In case variable does not change its value, a = b
Example: if T and n are unchanged,
Boyle’s law is obtained:
a a b b
a a a a
PV PV
n T n T
PV k
Example
Stoichiometry and gas reactions:
Mole relationships in different states
Solids: mass and molar mass
Solutions: volume and molarity
Gases: volume and ideal gas law
Calculate volume of gas produced (product) or
consumed (reactant) in a reaction at given
conditions of P and T
Calculate molar mass or density of a gas using
ideal gas law
Example
Mixtures of gases: partial pressures
Dalton’s law states that, in a mixture of gases,
each gas behaves independently of the others and
exerts the same pressure that it would by itself
The total pressure exerted is the sum of the
individual (partial) pressures of the components of
the mixture
P = P1 + P2 + P3 +…
Example
Partial pressure and the ideal gas law
In a mixture of gases, pressure exerted by
component i
Where ni is number of moles of component i
Total pressure is then:
V
RTnP i
i
V
RTnnnPP
i
itot
...)( 321
Mole fraction and the ideal gas law
Mole fraction (Xi) is ratio of moles of component i to total
number of moles ntot
But n = PV/RT
tot
i
tot
i
iP
P
RT
VP
RT
VP
X
i
i
i
tot
iii
n
n
n
n
nnn
nX
...)( 321
i
itot nn
Mole fractions and partial pressures
The partial pressure exerted by any gas is equal to
its mole fraction times the total pressure
What is the partial pressure of each component in
this mixture if total pressure is 600 mm Hg?
totalii PXP
Visual summary of the gas laws