Hint: R is Universal gas constant of an ideal gas. We can calculate the value of R using the ideal gas equation, PV=nRT. The units and the values of the gas constant ‘R’ depends on the units of pressure, volume and temperature. To calculate the value of R in SI units, the values of P, V, T also have to be taken in SI units.
Complete step by step solution:
Firstly SI units mean International system of measuring the quantities.
We are going to calculate the value of R using the ideal gas equation formula.
So let us consider the basic SI units for all the constituents of the equation by taking unit measurements for one mole of a gas at standard temperature and pressure conditions.
So, one mole of a gas has the value of pressure is $101.3\times {{10}^{3}}pa$.
One mole of a gas occupies $22.4lt$ or $22.4\times {{10}^{-3}}{{m}^{3}}$
The temperature of an ideal gas at STP is ${{0}^{0}}Cor273.15k$
Let us substitute the above values in the ideal gas equation, PV=nRT
Where P is pressure of the gas, V is Volume, n- no. Of moles, R is a universal gas constant which has constant value and T represents temperature of the given conditions.
So, PV= nRT can be written in the following manner
\[\begin{align}
& PV=nRT \\
& R=\dfrac{PV}{nT} \\
& =\dfrac{101.3\times {{10}^{3}}\times 22.4\times {{10}^{-3}}}{1\times 273} \\
& =8.314N{{m}^{2}}{{m}^{3}}{{K}^{-1}}mo{{l}^{-1}}or8.314J{{K}^{-1}}mo{{l}^{-1}} \\
\end{align}\]
The value of R in SI units is $8.314J{{K}^{-1}}mo{{l}^{-1}}$.
Additional information:
The value of R depends upon the units of the variables in the equation PV= nRT. Upon substituting the variables in the mentioned system of units of measurement, considering, 1mole of an ideal gas, the value of ‘R’ changes. But the obtained value remains constant for the given system of units.
The value of ‘R’ in different units is $\implies8.314$$J{K^{ - 1}}mo{l^{ - 1}}$ ,
$\implies 0.0820 Latm$${K^{ - 1}}mo{l^{ - 1}}$
$\implies1.985 cal$${K^{ - 1}}mo{l^{ - 1}}$
Formulae for conversions:-
Celsius to Kelvin scale of temperature - ${t^ \circ }$C + 273K
Atm to Pascal scale of pressure - $1atm =$ 101.3 $ \times $ 10$^3$kilopascal
Liters to cubic meter - $1litre =$ 10$^{ - 3}$m$^3$
Note: Converting the values of pressure, volume and temperature are important from atm to Pascal, liters to cubic meter; Celsius to kelvin respectively which are their units in S.I system i.e. International system of units. The above mentioned formulae are used for the conversions of all the parameters from one scale to the other.
