Gas laws
Relationships between variables
in the behaviour of gases
Learning objectives
 Describe physical basis for pressure in a gas
 Describe the basic features of the kinetic theory
 Distinguish among and convert common units of
pressure
 Apply gas laws to simple problems in predicting
conditions of a gas
 Apply ideal gas law to simple stoichiometry
problems in gases
Gas: no interactions
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



Not rigid
Completely fills container
Compressible
Low density
Energetic molecules
Kinetic theory and car tires – a case
for atoms
 Molecules have energy
 Energy increases with T
 Pressure is caused by energetic molecules
striking tire wall
 Pumping up tire increases number of
molecules
 More molecules – higher pressure
 Higher temperature – higher pressure
Kinetic theory of gases
 Gases consist of small atoms or molecules
in constant random motion
 Volume occupied by molecules is negligible
 Molecules are independent of each other –
no interactions
 Collisions are perfectly elastic (no energy
loss)
 Average energy is proportional to the
temperature
Under pressure: the atmosphere
 Gases exert pressure by virtue of motion
 Gravity makes the air density higher near
the earth’s surface
 Pressure decreases with elevation
Atmospheric pressure
 Pressure is force per unit area
 The weight of the air supports a column of
mercury 760 mm high
 Barometer is used for measuring
atmospheric pressure
 Atmospheric pressure changes with the
weather
The atmosphere is layered
 Troposphere
 Where the weather happens
 Stratosphere
 Where the ozone is
 Mesosphere
 Ionosphere
 The brutal strength of solar radiation ionizes all
the components – permits transmission of radio
signals around the earth without need of mirrors
Units of pressure
 Atmosphere
 Atmospheric pressure = 1 atm
 mm (or cm, or in) of mercury
 Atmospheric pressure = 760 mm (76 cm/29.9 in) Hg
 Pascal is SI unit for pressure
 Atmospheric pressure = 101 000 Pa (N/m2)
 Pounds/square inch
 Atmospheric pressure = 14.7 lb/in2
 Torr
 Atmospheric pressure = 760 torr
 Bar
 Atmospheric pressure = 1.01 bar
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 or 1
atmosphere
 At STP, 1 mole of any ideal gas occupies
22.414 L
Pressure changes (units)
 Convert 0.50 atm into a) mm Hg b) Pa
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
Boyle’s law
 The first experimental gas
law
 Pressure increases, volume
decreases (T, n constant)
1
P
V
Boyle’s law problems
 Initial conditions: P1 and V1
 Final conditions: P2 and V2
PV
1 1  PV
2 2
 Four variables: three given, one unknown
 Rearrange equation:
PV
PV
1 1
P2 
;V2  1 1
V2
P2
 Units are not important provided same on both
sides
Tank contains 12 L of gas at 4,500 mm Hg. What is
volume when pressure = 750 mm Hg?
Charles’ Law
 As temperature increases,
volume increases (P, n
constant)
 Temperature must be
measured in Kelvin
V T
Absolute zero
 Gay-Lussac observed V changed by 1/273
of value at 0ºC
 Plotted as V = kT (T = ºC + 273):
 V = 0 at T = 0
 Does the gas actually occupy zero volume?
 No, at lower T the law is not followed
Do’s and don’ts with Charles’ law
V1 V2

T1 T2
Combined gas law
 Fold together Boyle and Charles:
PV
P2V2
1 1

T1
T2
 Given five of the variables, find the sixth
 Units must be consistent
 Temperature in Kelvin
Example of combined gas law
 Gas at 27ºC and 2 atm pressure occupies 2 L.
What is new volume if pressure becomes 4 atm
and temperature is raised to 127ºC?
Gay-Lussac and law of combining
volumes
 When gases react at constant temperature
and pressure, they combine in volumes that
are related to each other as ratios of small
whole numbers
 His experiments with hydrogen and oxygen
had implications for the understanding of the
atom and the structures of simple molecules
Avogadro’s Law
 As the number of moles of
gas increases, so does the
volume (P, T constant)
V n
V1 V2

n1 n2
Dalton’s law of partial pressures
 A mixture of gases exerts a pressure as if all
the gases were independent of one another
 Total pressure is the sum of the pressures
exerted by each one
 P = p1 + p2 + p3 + …
Calculations with partial pressures
Molar gas volume
 The molar volume of a gas is the volume
occupied by 1 mole. At STP (standard
temperature 273 K, and pressure 1 atm)
one mole of gas occupies 22.4 L
 Gas density is easily obtained from the
molar mass and molar volume – d = m/V
Ideal Gas Law
 The particles of an ideal gas have mass but no
volume - a fair approximation at low pressures
 Collisions between the gas molecules are perfectly
“elastic” – like superhard billiard balls.
Reasonable for smaller molecules or noble gases
PV  nRT
 R is the ideal gas constant = 0.0821 L-atmK-1mol-1
 Gases deviate from ideal behaviour as
 pressure increases – closer proximity of molecules
 molecules are more polar – stronger interactions
Calculations with the ideal gas law
Chemical equations with gases
 Reactions with solids involve masses
 Reactions with gases involve volumes
Volume A
n = PV/RT
Moles A
Mole:mole ratio
Moles B
V = nRT/P
Volume B
Stoichiometry with the ideal gas law
Gas laws and crash safety
 The airbag represents a
fascinating study of
chemistry applied in a very
practical area
 Airbags have reduced
serious injuries and
fatalities by a significant
margin compared with seat
belts only
 Chemistry plays a crucial
role in the performance of
the airbag
Timing is everything
 The airbag must deploy within about 40 ms
of the impact
 The airbag must not deploy unless there is
an impact
 Inflation depends upon a rapid chemical
reaction generating a quantity of gas
 The bag, once inflated, must then deflate at
the point of impact with the driver to prevent
injury
Chemistry is involved at many points
 Chemical reaction to produce gas (nitrogen)
 Strong N≡N bond provides driving force
 Reaction kinetics determine rate – must be
fast
 Gas laws provide inflation – P proportional
to T