The unit of entropy is:
a. \[J{{K}^{-1}}mo{{l}^{-1}}\]
b. \[k{{J}^{-1}}mo{{l}^{-1}}\]
c. \[kJmo{{l}^{-1}}\]
d. \[~{{J}^{-1}}{{K}^{-1}}mo{{l}^{-1}}\]

Hint: Start by using the mathematical expression for calculation of entropy. Entropy is calculated by taking into consideration the temperature and heat of the system.

Complete answer:
Entropy is commonly denoted as S. It is a thermodynamic property. Entropy is a measurement of the degree of randomness or disorder in the system. Greater the degree of disorder, higher is the entropy.
Entropy (like other thermodynamic properties – internal energy (U), enthalpy (H) is a state function, independent of path.
Addition of heat thus, increases randomness. Therefore, S is directly proportional to heat (q).
Also, temperature (T) is a measure of average chaotic motion of particles in the system. The randomness is more Heat added to a system at lower temperature causes more randomness than when it is heated at higher temperature. Therefore, we can say S is indirectly proportional to T.
Hence, the relation between S, q and T for a reversible reaction is given as
\[S={{q}_{rev}}/T\]
SI Unit of heat (q) = \[Jmo{{l}^{-1}}\]
SI Unit of temperature (T) = \[K\]
SI Unit of Entropy = \[Jmo{{l}^{-1}}/\text{ }K\text{ }=\text{ }J{{K}^{-1}}mo{{l}^{-1}}\]

Therefore, the answer is option (a).

Note: At absolute zero (\[0{}^\circ K\]/\[-273.15{}^\circ C\]/\[-460{}^\circ F\]), the value of entropy is zero.
The total entropy change (\[\Delta {{S}_{total}}\]) for the system and surroundings of a spontaneous process is given by
\[\Delta {{S}_{total}}~=\Delta {{S}_{system}}+\Delta {{S}_{surrounding}}~>\text{ }0\]
When a system is in equilibrium, the entropy is maximum, and the change in entropy is zero. Hence, we can say that S for a spontaneous process increases till it reaches a maximum and at equilibrium, the change in entropy is zero.