Values of Gas Constant and Numerical Expressions
An ideal gas follows gas laws
There are three main gas laws
Boyle’s Law states that volume
$V$
of a gas is inversely proportional to pressure
$P$
when temperature
$T$
and number of moles
$n$
are constant
Charles's law states that the volume
$V$
of a gas is directly proportional to temperature
$T$
when pressure
$P$
and number of moles
$n$
are constant
Avogadro’s Law states that a gas contains equal no. of molecules
$n$
in equal volumes
$V$
of gases at the constant temperature and pressure
Combining these 3 laws, we get the ideal gas equation
Let's see what happens if we keep the number of moles of gas constant in ideal gas equation
$If numbers of molesn=constantPV=nRTTPV =nRTPV =constant$
So, let us say that initial conditions are given by
$P_{1}$
,
$V_{1}$
and
$T_{1}$
. So
$T_{1}P_{1}V_{1} $
=
$constant$
Later, the conditions are changed to
$P_{2}$
,
$V_{2}$
and
$T_{2}$
. So
$T_{2}P_{2}V_{2} $
=
$constant$
Equating these two, we get,
$T_{1}P_{1}V_{1} =T_{2}P_{2}V_{2} $
This is another form of the ideal gas equation when the number of moles of gas is not changed
We can also find the gas constant R using the combined gas law
Here
$P$
is the pressure
$V$
is the volume,
$n$
is the no. of molecules and
$T$
is the temperature
Let us take the standard conditions for an ideal gas and find
$R$
$Let the Pressure,P=1barVolume,V=1litreNo. of molecules,n=1moleTemperature,T=273.15K$
Substituting these values in the equation for gas constant
$R$
$R$
can also be found in the units
$Pam_{3}mol_{−1}K_{−1}$
For this unit of pressure should be changed from bar to Pascals
Unit of volume should be changed from
$L$
to
$m_{3}$
By substituting the above values, we get the value of
$R$
in
$Pam_{3}mol_{−1}K_{−1}$
The unit
$Pam_{3}$
is equal to unit of energy
$J$
. So
$R$
can also be found in the units
$atmLmol_{−1}K_{−1}$
. For this we will have to substitute
$1bar=1.013251 atm$
So the value of
$R$
Revision
A gas that follows the gas rules is an ideal gas
There are three main gas laws - Boyle’s, Charles's and Avogadro’s Laws
$Boyle’s Law isPV=KCharles’ Law isTV =KAvogadro’s Law isnV =K$
Combining the above three laws we get the ideal gas law where
$PV=nRT$
In combined gas law,
$T_{1}P_{1}V_{1} =T_{2}P_{2}V_{2} $
$Gas constantR=0.82atmLK_{−1}mol_{−1}R=8.314JK_{−1}mol_{−1}R=0.0831barLK_{−1}mol_{−1}$
The End