GAS LAWS AND
THE MOLE
The difference between solids, liquids and gases is the
arrangement and freedom of movement of particles
Take a Closer Look at Gases
•Gases move very rapidly in a
disordered fashion colliding
with each other and the walls
of the container (Brownian
Motion)
•Particles separated by
relatively large distances
and are easily compressed
•The more energy (heat /
light) you give the particles
the more rapidly the move
Diffusion
Diffusion is the spreading out of a substance, and is
due the natural movement of the particles
Specified Demonstration 1
Ammonia and hydrogen chloride gases
diffuse from opposite ends of the tube.
When the two gases combine a cloud of
ammonium chloride (NH4Cl) is formed
Examples:
Diffusion of gas in air / Diffusion of ink in water
• Gases obey certain laws we need to
study what is meant by Temperature,
Pressure and Volume before looking at
the laws more closely
Temperature
• This is a measure of the degree of
hotness of an object
• Two scales are used
1. The Celsius scale(also called the
centigrade scale)
2. The Kelvin scale (also called the
absolute scale)
• The celsius scale was developed in 1742
and uses the freezing point of water as
0 and the boiling point of water as 100
• These are 2 fixed points on the scale
• The kelvin scale was developed in 1848
and states 0 is the point where a gas
would occupy no volume if cooled
indefinitely without becoming a liquid or
a solid It is called absolute 0 or 0 K
Converting from Celsius to Kelvin
• Temperature can be
converted from celsius
to kelvin by adding 273
Pressure
• The is the force that the gas exerts
per unit area of its container
• It is measured in Newtons per meter
squared N/m2 also called the Pascal (Pa)
• Normal atmospheric pressure is
1 x 105Pa
• As Pascals are very small Kilopascal
(KPa) are also used
• 1KPa = 1000Pa
Volume
• Volume describes the amount of space
taken up by a gas
• SI units for volume are m3 This is too
large for laboratory scale work so we
use litres (l) or cm3
• Litres are also called cubic decimetres
(dm3)
• 1 litre = 1000cm3 = 1 cubic decimetre
Standard Temperature and
Pressure
• As the volume of a gas varies with
temperature and pressure we need to use
standard temperature and pressure (s.t.p.)
when we are comparing two gases
• The standards that have been chosen are
Standard temperature = 273K (0⁰C)
Standard Pressure = 1 x 105Pa or 100KPa
• There are many different gases that
behave in many different ways, some
are flammable, some are coloured, some
are poisonous, some are vital for life
etc.
• Even though gases have different
chemical properties they all obey
certain laws
• We shall study 5 of these
Gas Laws
BOYLES LAW
At constant temperature (T), the volume of a
given mass of any gas is inversely proportional to
the pressure (P) of the gas
P
V
• This means V
1
P
• Therefore if k is a constant of
proportionality V = K 1
P
Or pV = K
See table 10.1 p 111
CHARLES LAW
At constant pressure the volume of a given
mass of any gas is directly proportional to the
temperature
V=k
T
• Remember T is measured in Kelvin
• This law essentially states that as
temperature increases volume increases
as long as pressure stays the same
The Combined Gas Law
(General Gas Law)
• Boyles law states pV=k
• If the temperature stays the same and the
volume changes to V2 then the pressure will
change to p2 as they are inversely proportional
• Thus it is true to say p1V1 = p2V2
• Similarly from Charles’ Law V1 = V2
T1 T2
These combine to form
• These combine to form
p1 V1 = p2V2
T1
T2
• To use this combined law see example 10.1
page 113
• Remember all temperature values must be on
the K scale and the units must be the same for
pressure and volume on both sides eg. If Kpa
are used on the left they must also be on the
right
Gay-Lussac
Law of combining volumes: When gases react the
volumes consumed in the reaction bear a simple
whole number ratio to each other, and to the
volumes of any gaseous product of the reaction, all
volumes being measured under the same conditions of
temperature and pressure
He found for example that two
volumes of hydrogen combine with
one volume of oxygen to give
water
2H + 1O → 1H2O
Avogadro’s Law
Equal volumes of gases, under the same conditions
of temperature and pressure, contain equal
number of molecules
So lets say at 300K (temp) and 100,000Nm-2
(Pressure) we have two containers one with (He) and
another with carbon-dioxide (CO2). They will have
the same number of molecules
He
CO2
So what can we take from GayLussac (GL) and Avogadro………
• Consider the reaction of Hydrogen and
chlorine according to the GL law
1 H2 + 1Cl2 → 2HCl
1 volume + 1 volume → 2 volumes
• Instead of volume lets do it in terms of
number of molecules (N) (Avogadro)
1 H2 + 1Cl2 → 2HCl
1 molecule + 1 molecule → 2 molecules
Reading Chemical Equations
H2 – means hydrogen gas molecule H-H
2H – mean 2 hydrogen atoms H + H
2H2 -means 2 hydrogen gas molecules
H-H + H-H
Some More Examples……
H2O is 2 x H and 1 x O
but 2H2O is 2 molecules of H2O
CH4 is 1 x C and 4 x H
But 2CH4 is 2 molecules of CH4
• Sulphur dioxide reacts with hydrogen sulphide
according to the equation
SO2 + 2H2S → 3S + 2H2O
• What volume of sulphur dioxide would
completely react with 140cm3 of hydrogen
sulphide, all volumes being measured under
the same conditions of temperature and
pressure?
The Mole
The mole is the unit we
use in chemistry for the
amount of a substance
We use moles because it
is impossible to measure
out molecules
A mole of a substance is the amount
of that substance that contains as
many particles (atoms/molecules/ions)
as there are atoms of 12C in 12g of
12C
• Therefore 1 mole of 12C weighs 12g
and contains 6 x 1023 carbon atoms
• 6 x 1023 is known as Avogadros
constant and is given the symbol L
Avogadro's constant (L)
602000000000000000000000
particles
How Big is a mole?
• One mole of
marbles would
cover the
entire Earth to
a depth of
fifty miles
How Big is a mole?
• One mole of rice
grains is more
than the number
of grains of all
crops grown
since the
beginning of
time.
So this means……
1 mole of sodium (Na) = 6 x 1023 Sodium atoms
1 mole of Iron (Fe) = 6 x 1023 Iron atoms
And….
1 mole of Chlorine gas (Cl2)= 6 x 1023 chlorine
molecules
1 mole of water (H20) = 6 x 1023 water
molecules
So lets look at an equation……
SO2 + 2H2S → 3S + 2H2O
1 mole + 2 moles → 3moles + 2 moles
(6 x 1023 ) Molecules of SO2 + (2 x 6 x 1023 ) molecules of
H2 → (3 x 6 x 1023 ) molecules of S + (2 x 6 x 1023 )
molecules of H2O
How many atoms are in 4 moles
of neon gas?
Neon gas – Ne
1 mole of neon gas = 6 x 1023 atoms
Therefore…
4 moles of neon gas = 4 x (6 x 1023)
= 2.4 x 1024 neon atoms
How many atoms are there in 0.15moles
of sulphur dioxide?
1 mole of SO2 = 6 x 1023 molecules
0.15 moles of SO2 = 0.15 x 6 x 1023 molecules
0.15 moles of SO2 = 0.9 x 1023 molecules
Every SO3 has 3 atoms (1xS and 2xO)
0.9 x 1023 molecules of SO2 = 3 x (0.9 x 1023) Atoms
= 2.7 x 1023 Atoms
A sample of oxygen contains 3 x 1022
molecules. How many moles is this?
6 x 1023 molecules = 1 mole
3 x 1022 molecules = 3 x 1022 moles
6 x 1023
= 0.05 moles
Molar Volume of Gases
• Avogadro said that under the same
conditions of temperature and pressure
(s.t.p.), equal volumes of gases have
equal numbers of molecules
(s.t.p.) standard temperature and pressure
pressure = 101 325 Nm-2 = 101 325 Pa
Temperature = 273 K
This means…..
At s.t.p.
1 mole of gas = molar volume = 22.4 l
= 22400cm3
= 2.24 x 10 -2 m3
So at s.t.p. 1 mole of nitrogen (N2) occupies 22.4 l
And 1 mole of CO2 occupies 22.4 l
What is the volume at
s.t.p. of 0.25 moles of chlorine
gas
1 mole = 22.4 l @ s.t.p.
Therefore….
0.25 moles = 0.25 x 22.4 l @ s.t.p.
= 5.6 l
How many moles are there in 280
cm3 of nitrogen gas at s.t.p.
@ s.t.p. 22 400 cm3 = 1 mole
@ s.t.p. 280 cm3
= 280 moles
22400
= 0.0125
Relative Molecular Mass (M)
Average mass of a molecule of a
substance relative to one twelfth of
the mass of an atom of 12C
For an element eg. C the molecular
mass is equal to the relative atomic
mass
For molecules it is the sum of the
relative atomic masses
Examples
The relative atomic mass of:
Carbon = 12
Iron = 55
Hydrogen gas (H2) = (2 x 1) = 2
Water (H2O) = (2 x H) + (1 x O)
= (2 x 1) + (1 x 16)
= 18
Measuring Relative Atomic Mass
• Measured using a mass spectrometer
(see chapter 2)
Molar Mass
The molar mass of a substance is the mass
in grams of one mole of the substance.
The units for molar mass are gmol-1
Examples
Substance
Iron (Fe)
Oxygen (O2)
Water (H2O)
Relative
Molecular Mass
55
32
18
Molar Mass
55 gmol-1
32 gmol-1
18 gmol-1
Calculations using moles
Moles of X = mass of X (in grams)
molar mass of X
Volume of X = (Moles of X) x (22.4L)
Number of particles of X = (Moles of X) x (L)
L = Avogadros Constant
REMEMBER YOU CAN REARRANGE THESE
EQUATIONS IF YOU NEED TO