Question

What is the numerical value of the gas constant R in $lit\text{ }atm\text{ }mo{{l}^{-1}}{{K}^{-1}}$ ?
A. $0.0821$
B. $8.314\times {{10}^{7}}$
C. $8.314$
D. $1.987$

Answer 1

Hint: Arrive at the answer by the process of elimination. Figure out the units of each of the give options and you will arrive at your answer. The value of the gas constant in base SI units should be known.

Complete step by step answer:
The letter R is the universal has constant which has many applications in equations like the ideal gas equation, Nernst equation, etc. It relates the energy or pressure-volume statistic to the temperature scale. It is known to be equivalent to the Boltzmann constant. The universal gas constant was noted as a product of the Boltzmann constant and the Avogadro’s number and is represented as:
\[R={{N}_{A}}{{k}_{b}}\]
Here, ${{N}_{A}}$ is Avogadro's number and ${{k}_{b}}$ is the Boltzmann constant.
The universal gas constant has different values according to the different units that it can take. The value for the SI units of the universal gas constant is $8.314J{{K}^{-1}}mo{{l}^{-1}}$. Here, you can see that the units are in joules, kelvins and the amount of substance i.e. moles. This also reinforces the fact that the constant relates energy and temperature. This value is the option C that is given, so this cannot be the answer.

If we convert joules to ergs, the universal gas constant will get the value of $8.314\times {{10}^{7}}erg{{K}^{-1}}mo{{l}^{-1}}$ since $1J={{10}^{7}}erg$.
The value that establishes a relation between energy and temperature yet again is $1.987\times {{10}^{-3}}kcal{{K}^{-1}}mo{{l}^{-1}}$. Here we can see that while the order of magnitude is not the same as that given, the base integer remains the same and if we convert the value, we can express it in calories and temperature. So, option D cannot be the answer.

Now, we still have not addressed the relation between temperature and the pressure volume graph. The value that relates these units is $0.0821\text{ }lit\text{ }atm\text{ }{{K}^{-1}}mo{{l}^{-1}}$. This is the value that we are concerned with.
Hence, the correct answer to this question is ‘A. $0.0821$’
So, the correct answer is “Option A”.

Note: Remember that you can always convert the value given in the SI units to arrive at the answer. Simply substitute the conversion values after converting joules to pascals and cubic meters.