IDEAL GASES
DEFINITION: An ideal gas is one which obeys the gas laws under all
conditions of temperature and pressure
Ideal gases do not actually exist but gases like helium with small non-polar molecules
behave ideally under conditions of high temperature and low pressure.
An Ideal Gas is modelled on the Kinetic Theory of Gases which has some basic
postulates:
a.
Gases consist of small particles (molecules) which
are in continuous random motion and thus possess
kinetic energy
b.
The volume of the particles present is negligible
compared to the total volume occupied by the gas
c.
Intermolecular forces are negligible – i.e no forces
of attraction or repulsion
d.
The moving particles constantly collide with
themselves and the side of the container. Pressure
exerted by the gas is due to these collisions
e.
All collisions between atoms or molecules are
perfectly elastic – no kinetic energy is lost
f.
At any given instant the particles do not all move at
the same speed, and therefore do not all have the
same kinetic energy. Temperature is a measure of
the average kinetic energy of the molecules of a
gas.
One can visualize it as a collection of perfectly hard spheres which collide but which
otherwise do not interact with each other.
The GAS LAWS:
Gay-Lussac’s law
The pressure of a fixed mass of gas is directly proportional to its absolute
temperature provided the volume remains constant.
Explanation: The higher the
temperature the faster the average
speed of the molecules. This results in
both more collisions, and harder
collisions between the molecules and
the container. Therefore the pressure
rises.
Gay-Lussac continued:
p
p1 p2
=
T1 T2
p∝T
(v =
const.)
T (Kelvin)
Charles’ law
The volume of a fixed mass of gas is directly proportional to its absolute
temperature provided the pressure remains constant.
Explanation: The particles have more
kinetic energy and thus have harder
collisions with the sides of the container,
thereby increasing the volume.
V
V 1 V2
=
T1 T2
V∝T
(p=const.)
.
T (Kelvin)
Boyle’s law
The volume of a fixed mass of gas is inversely proportional to its pressure provided
the temperature remains constant.
Explanation: As the volume of the
gas is decreased the molecules are
forced into a smaller space and
therefore collide more often.
P ∝ 1/V
V
p1V1 = p2V2
1/V
P
P
Avogadro’s Law
The pressure of a gas is directly proportional to the number of moles of gas
provided the temperature and volume remains constant.
n∝P
Explanation: The more molecules there are in a fixed space the more often
collisions occur.
REAL GASES
Under ordinary conditions, deviations from Ideal Gas behaviour are so slight that
they can be neglected. A gas which deviates from Ideal Gas behaviour is called a
Non-Ideal Gas or a Real Gas.
IDEAL GAS
Have infinitely small particles
REAL GAS
Particles have a volume
There are two sets of conditions in which Real Gases deviate from ideal gas
behaviour:
a. at low temperatures
Explanation:...............................................
..................................................................
P
..................................................................
.................................................................
..................................................................
b. at high pressures
Temperature
Real
p
Volume
The general gas equation
Combining the above equations we get the following General Gas Equation:
p1 V1 p 2 V2
=
T1
T2
Example:
A fixed mass of gas was placed in a gas syringe at 10 oC and 101 kPa and
found to have a volume of 43 cm3. What would be its volume if the
pressure was increased to 120 kPa and the temperature to 80 oC ?
Ideal Gas Equation
pV = nRT
Example:
p in pascals (Pa)
V in cubic metres m3
1 m3 = 1000 dm3 = 106 cm3
n in mols (mol)
R is the gas constant 8,31 J.K-1mol-1
T in Kelvin (K)
What is the pressure of a 500 cm3 tube of methane (CH4) if 4,6 g of the
gas are present at a temperature of 45 OC ?
Example:
What mass of oxygen is in a 2 dm3 container at STP?