Question

Which is the value of R?
(A) $1.99cal{{\deg }^{-1}}mo{{l}^{-1}}$
(B) $0.0821litre-atm{{\deg }^{-1}}mo{{l}^{-1}}$
(C) $9.8kcal{{\deg }^{-1}}mo{{l}^{-1}}$
(D) $8.3joule{{\deg }^{-1}}mo{{l}^{-1}}$

Answer 1

Hint: The question is asking us to find out the correct values of R. Recollect what R is. Think about universal gas constant and try to recollect what is its value and units. The question has given four options in four different units. Convert the value of R in the given units to get the answer.

Complete answer:
- R is the universal gas constant. It is equivalent to the Boltzmann constant.
- Universal gas constant is expressed in terms of energy per temperature per mole.
- The value of R is $8.314J{{K}^{-1}}mo{{l}^{-1}}$.
- Now, let’s take a look at all the options given in the question. There are four units namely, $cal{{\deg }^{-1}}mo{{l}^{-1}}$, $litre-atm{{\deg }^{-1}}mo{{l}^{-1}}$, $kcal{{\deg }^{-1}}mo{{l}^{-1}}$ and $joule{{\deg }^{-1}}mo{{l}^{-1}}$.
- We know the value of R in joule per kelvin per mole. Now, we need to get the value of R in terms of litre-atm, kcal and cal.
- The conversion factors are as follows,
\[1litre-atm=101.325joule\]
\[1kcal=4184joule\]
\[1cal=4.184joule\]
- Therefore, the value of R in terms of calories per kelvin per mole is given as, $R=\dfrac{8.314}{4.184}=1.987cal{{K}^{-1}}mo{{l}^{-1}}$.
- Similarly, the value of R in terms of kilocalories per kelvin per mole is given as, $R=\dfrac{8.314}{4184}=0.001987kcal{{K}^{-1}}mo{{l}^{-1}}$.
- Similarly, the value of R in terms of kilocalories per kelvin per mole is given as, $R=\dfrac{8.314}{101.325}=0.0821litre-atm{{K}^{-1}}mo{{l}^{-1}}$.

Therefore, the correct answers are options (A), (B) and (D).

Note:
Remember the value of universal gas constant, R in joule per kelvin per mole. Also, memorize some conversion factors like litre-atm to joule, cal to joule so that the value of R can be easily calculated in numerical problems where energy is given in terms of cal instead of joule.