Page 187 - Chemistry ICSE Class IX

Study of Gas Laws 175
temperature and pressure on the volume of a given amount of any gas, is
called ideal gas equation.
How is the ideal gas equation derived

There are two methods by which the ideal gas equation can be derived.
These are given below:

Method 1
The volume of certain amount of a gas depends upon its temperature and
pressure. From the Boyle’s law,
V v 1/P (under constant temperature)
and from the Charles’ law
V v T (under constant pressure)
If the temperature and pressure of a gas are simultaneously changed,
then
T
V v
P
or PV = Constant × T (7.12)
The value of the constant in Eq. 7.12 is found to depend upon the
number of moles (n) and also on the units in which P and V are expressed.
Therefore, Eq. 7.12 may be written as,
PV = n × Constant × T (7.13)
The new constant in Eq. 7.13 is found to be independent of the nature of
gas and for this reason, it is called the universal gas constant, denoted by R.
The combined gas law or the gas equation for an ideal gas is,
PV = n RT (7.14)
For one mole of the gas, one may write
PV = RT (7.15)
m
where, V is called the molar volume of the gas.
m
Under standard temperature and pressure, molar volume of all gases
have a value equal to 22414 mL/mol or 22.414 L/mol. In general use, a
value of 22400 mL/mol or 22.4 L/mol is employed.

Method 2
Let a given amount of a gas has a volume V when the pressure is P and
1
1
temperature is T . If the pressure is changed to P , temperature being held
1
2
constant at T , let the volume change from V to v. Then, from the Boyle’s
1
1
law.
P V = P v
1
2
1
P V
or v = 1 1 (7.16)
P 2
Now, if pressure is maintained at P and temperature is changed from
2
T to T , let the volume change from v to V . Then, according to the Charles’
2
2
1
law,
v = V 2
T 1 T 2
V
or v = 2 × T
T 2 1