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

$If numbers of moles n = constant P V = n R T \frac{P V}{T} = n R \frac{P V}{T} = constant$

So, let us say that initial conditions are given by $P_{1}$ , $V_{1}$ and $T_{1}$ . So $\frac{P _{1} V _{1}}{T _{1}}$ = $c o n s t a n t$

Later, the conditions are changed to $P_{2}$ , $V_{2}$ and $T_{2}$ . So $\frac{P _{2} V _{2}}{T _{2}}$ = $c o n s t a n t$

Equating these two, we get, $\frac{P _{1} V _{1}}{T _{1}} = \frac{P _{2} V _{2}}{T _{2}}$

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 $R$

$Let the Pressure, P = 1 bar Volume, V = 1 litre No. of molecules, n = 1 mole Temperature, T = 273.15 K$

Substituting these values in the equation for gas constant $R$

$R$ can also be found in the units $P a m^{3} m o l^{- 1} K^{- 1}$

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 $P a m^{3} m o l^{- 1} K^{- 1}$

The unit $P a m^{3}$ is equal to unit of energy $J$ . So

$R$ can also be found in the units $a t m L m o l^{- 1} K^{- 1}$ . For this we will have to substitute $1 b a r = \frac{1}{1 . 0 1 3 2 5} a t m$

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

$Boyle’s Law is P V = K Charles’ Law is \frac{V}{T} = K Avogadro’s Law is \frac{V}{n} = K$

Combining the above three laws we get the ideal gas law where $P V = n R T$

In combined gas law, $\frac{P _{1} V _{1}}{T _{1}} = \frac{P _{2} V _{2}}{T _{2}}$

$Gas constant R = 0.82 a t m L K^{- 1} m o l^{- 1} R = 8.314 J K^{- 1} m o l^{- 1} R = 0.0831 b a r L K^{- 1} m o l^{- 1}$

The End