Question

The S.I. unit of universal gas constant is:
A. \[Watt{K^{ - 1}}mo{l^{ - 1}}\]
B. \[N{K^{ - 1}}mo{l^{ - 1}}\]
C. \[J{K^{ - 1}}mo{l^{ - 1}}\]
D. \[erg{K^{ - 1}}mo{l^{ - 1}}\]

Answer 1

Hint:
The gas constant is a physical constant denoted by R and is expressed in terms of units of energy per temperature increment per mole. It is also known as Ideal gas constant or molar gas constant or universal gas constant.
The gas constant value is equivalent to Boltzmann constant as it is expressed as energy per increment of temperature per particle while Boltzmann constant is expressed as the pressure-volume product instead of energy per increment of temperature per particle.

 Complete step-by-step solution:
In an ideal gas equation-The four gas variables are: pressure (P), volume (V), number of mole of gas (n), and temperature (T). Lastly, the constant in the equation shown below is R, known as the gas constant:
\[PV = nRT\]
When it comes to the gas constant, R. Value of R will change when dealing with different units of pressure and volume (Temperature factor doesn't change like we always use temperature in Kelvin while using the Ideal gas equation). When the value of R is appropriate then only you get the correct answer to the problem. R is basically a constant, and the different values of R correlates accordingly with the different units given. While selecting the value of R, choose the one with the appropriate units of the given information (sometimes we need to convert the given units accordingly). Here are some commonly used values of R:
Values of R
\[0.082057{\text{ }}L{\text{ }}atm{K^{ - 1}}mo{l^{ - 1}}{\text{ }}\]
\[62.364{\text{ }}LTorr{K^{ - 1}}mo{l^{ - 1}}\]
\[8.3145{\text{ }}{m^3}Pa{K^{ - 1}}mo{l^{ - 1}}\]
\[8.314erg{K^{ - 1}}mo{l^{ - 1}}\]
\[8.3145{\text{ }}J{K^{ - 1}}mo{l^{ - 1}}\] (SI unit)
So \[J{K^{ - 1}}mo{l^{ - 1}}\] is the SI unit for the gas constant and hence, option C is correct.

Note:-
Since the 2019 redefinition of SI base units, which came into effect on 20 May 2019, both \[{N_A}\] and \[K\] are defined with exact numerical values when expressed in SI units. As a consequence, the value of the gas constant is also exactly defined, at precisely \[8.31446261815324\] \[J{K^{ - 1}}mo{l^{ - 1}}\].