Gases: Properties and
Behaviour
Gas Laws
Partial Pressures
Kinetic Theory and Ideal Gases
Real Gases
Diffusion and Effusion
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
 The strength of the
interactions between
molecules determines
the state
 Strong attractions make
for high melting point
ionic solids
 Weaker interactions
between molecules
occur in liquids
Molecular interactions in gases are
negligible
 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 mass x acceleration F = ma
 Molecules colliding with the walls of the container
exchange momentum
Origins of pressure
 Pressure if force per unit area F/A
 Force is mass x acceleration F = ma
 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
How do I measure the atmosphere?
Let me count the ways
 1 atmosphere =
 760 mm Hg = 76 cm Hg
 14.7 psi
 760 torr
 1.01 bar
 29.9 in Hg
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
The barometer of pressure
 The weight of the air supports an equal weight of
mercury (or other liquid)
 Mercury being dense, the column is only 76 cm
compared to the height of the atmosphere
 76 cm (760 mm) Hg = 1 atm
Manometers measure pressure in a
container
 (a) If the pressure inside the bulb is less than
atmospheric, the atmosphere pushes down more.
 (b) If the pressure inside the bulb is above
atmospheric, the column is pushed towards the
open end.
Measuring pressure with a ruler
 The pressure in the container is given by
atmospheric pressure plus (minus) the difference
in levels for pressures greater (lower) than
atmospheric
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
The four variables
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
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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
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
Avogadro’s Law
 Pressure and temperature constant
 Increase the amount, the volume increases
 Summary of gas laws
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
Mathematical form
 The volume of an ideal gas varies directly with its
molar amount at constant T and P
 Vαn
 V/n = constant
 The same volume of any gas contains the 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
 The standard molar volume of 22.41 L can be
compared with the experimental values of
common real gases
 Agreement shows that these ideal gas laws can
be widely applied for real gases
Putting them together: the ideal gas
law
 P1V1/T1 = P2V2/T2
 PV = nRT
 R is the gas constant = 0.0821 L-atm/mol-K
 Note the units of R. This constant also appears in
thermodynamic calculations, but with different units and
numerical value (8.315 k/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
The combined gas law
 Allows us to calculate change in one variable for
changes in the three other variables
PV
k
nT
Boyle
Charles
Combined
Gas Law
Amonton
Avogadro
Applications
 A system under an initial set of conditions
represented by a changes to a new set of
conditions b
PaVa PV
b b

naTa nbTb
 If we know three of the conditions, the fourth can
be obtained
The “simple” laws are derived from
the combined law
 For any change of conditions where a variable
does not change its value, a = b
 Example: if T and n are unchanged,
PaVa PV
b b

naTa naTa
 Boyle’s law is regenerated:
PV  k
Getting some exercise
 An exercise ball is at a pressure of 1000 mm Hg
and has a volume of 60 L
 When sat on, the volume is only 40 L. What is the
new pressure?
PV
a a  PV
b b
PV
(1000mmHg )(60 L)
b b
Pa 

 1500mmHg
Va
40 L
 Check: P increases as V decreases
Stoichiometry and gas reactions
 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
 Also can calculate molar mass or density of a
gas using ideal gas law
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 +…
Mole fraction
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The pressure exerted by component i =
Pi = ni(RT/V)
Where ni is the number of moles of i
The total pressure is then:
P(total) = (n1 + n2 + n3 + …)RT/V
The mole fraction is the ratio of the moles of
component I to the total number of moles ntotal
ni
ni
Xi 

n1  n2  n3  ... ntotal
Mole fraction and the ideal gas law
 But n = PV/RT
 V 
Pi 

Pi
RT 

Xi 

 V  Ptotal
Ptotal 

 RT 
Xi 
ni
ntotal
Mole fractions and partial pressures
 The partial pressure exerted by any gas is equal to the
mole fraction x the total pressure
Pi  X i Ptotal
 What is the partial pressure of each component if the total
pressure is 600 mm Hg?
Visual summary of the gas laws