Gases: Properties and
Behaviour
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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
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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
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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
Boyle’s law
 The first experimental gas law
 Pressure increases, volume
decreases (T, n constant)
1
P
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
120
P vs 1/V
Pressure (atm)
100
80
60
40
20
0
0
1
2
3
1/Volume (1/L)
4
5
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? P V  PV
a a
b b
PaVa (1000mmHg )(60 L)
Pb 

 1500mmHg
Vb
40 L
 Check: P increases as V decreases
 Note: doesn’t matter what units provided they are
consistent
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
VαT
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
45
V vs T
40
35
Volume (L)
30
25
20
15
10
5
0
0
100
200
300
Temperature (K)
400
500
600
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
Vαn
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
PV
R
nT
Boyle
Charles
Combined
Gas Law
Amonton
Avogadro
Applications
 A system at initial conditions Xa changes to new
conditions Xb
PV
PV
a a
 b b
naTa nbTb
 If we know three of the variables in state b, the
fourth can be obtained
 In most of these problems na = nb
PaVa PbVb

Ta
Tb
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,
PV
PV
a a
b b

naTa naTa
 Boyle’s law is obtained:
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
ni RT
Pi 
V
 Where ni is number of moles of component i
 Total pressure is then:
(n1  n2  n3  ...) RT
Ptot   Pi 
V
i
Mole fraction and the ideal gas law
 Mole fraction (Xi) is ratio of moles of component i to total
number of moles ntot
ni
ni
ni
Xi 


(n1  n2  n3  ...) ntot  ni
i
 But n = PV/RT
 V 
Pi 

Pi
RT 

Xi 

 V  Ptot
Ptot 

 RT 
ntot   ni
i
Mole fractions and partial pressures
 The partial pressure exerted by any gas is equal to
its mole fraction times the total pressure
Pi  X i Ptotal
 What is the partial pressure of each component in
this mixture if total pressure is 600 mm Hg?
Visual summary of the gas laws