Question

What is the value of universal gas constant?

Answer 1

Hint: The universal gas constant is denoted by R. It is a proportionality constant equivalent to Boltzmann constant, but expressed in units of energy per temperature increment per mole.

Complete step-by-step answer:
The universal gas constant (R) is a proportionality constant in the equation of an ideal gas i.e. $PV=nRT$, where P is the pressure of the ideal gas, V is the volume occupied by the gas, n is the number of moles of the gas and T is the given temperature. We can rewrite the above equation as $R=\dfrac{PV}{nT}$. Therefore, the unit of R will be $\dfrac{\text{joule}}{\text{mole}\text{.Kelvin}}$ (the unit of the product of pressure and volume is joule)
The value of the universal gas constant in these units is $8.314J{{K}^{-1}}mo{{l}^{-1}}$.
Other units of universal gas constant are $Pa.{{m}^{3}}{{K}^{-1}}mo{{l}^{-1}}$ and $cal.{{K}^{-1}}mo{{l}^{-1}}$

Additional Information:
Physically, the gas constant is the constant of proportionality that relates the energy scale in physics to the temperature scale, when a mole of particles at the stated temperature is being considered. Thus, the value of the gas constant ultimately derives from historical decisions and accidents in the setting of the energy and temperature scales, plus a similar historical setting of the value of the molar scale used for the counting of particles. The last factor is not a consideration in the value of the Boltzmann constant, which does a similar job of equating linear energy and temperature scales.
The gas constant R is defined as the Avogadro constant NA multiplied by the Boltzmann constant (k) i.e. $R={{N}_{A}}k$

Note: When converting the units, for example from S.I. to C.G.S, the value of the constant will also change. Like in this case when write the value of R i.e. $8.314J{{K}^{-1}}mo{{l}^{-1}}$, in the units of $cal.{{K}^{-1}}mo{{l}^{-1}}$ then the value becomes $8.314.(\dfrac{1}{4.18}cal){{K}^{-1}}mo{{l}^{-1}}=1.987cal.{{K}^{-1}}mo{{l}^{-1}}$.
Because, one calorie of energy is almost equal to 4.18 joules of energy.