Question

Calculate the total entropy change for the transition at 368K for 1mol of sulphur from the monoclinic to the rhombic solid state, is $\Delta H=-401.7Jmo{{l}^{-1}}$ for the transition. Assume the surroundings to be an ice-water both at $0{}^\circ C$.
(A) $-1.09J{{K}^{-1}}$
(B) $-0.5J{{K}^{-1}}$
(C) $-0.385J{{K}^{-1}}$
(D) None of these

Answer 1

Hint: Think about the property of entropy of a thermodynamic process. We need to calculate the total entropy change for transition of sulphur from monoclinic form to rhombic form. The total entropy change is given as, $\Delta {{S}_{total}}=\Delta {{S}_{system}}+\Delta {{S}_{surroundings}}$. Just substitute the values and find out the answer.

Complete answer:
- According to the second law of thermodynamics, the total entropy change of the system and its surroundings increases in a spontaneous process. Mathematically, for a spontaneous process, $\Delta {{S}_{total}}=\Delta {{S}_{system}}+\Delta {{S}_{surroundings}}$
- Therefore, the total entropy change is the sum of entropy change of system and that of surroundings.
- The entropy change of a system is defined as the change in heat enthalpy per unit temperature in kelvin.
\[\Delta S=\dfrac{\Delta H}{T}\]
- The entropy change for a surrounding is given as,
\[\Delta {{S}_{surroundings}}=-\dfrac{\Delta H}{T}\]
- For the transition of sulphur from monoclinic form to rhombic form, $\Delta H=-401.7Jmo{{l}^{-1}}$.
- The temperature of the monoclinic system, ${{T}_{1}}$ is 368K and of rhombic form, ${{T}_{2}}$ is 273K.
- Therefore, the total change in entropy is given as,
\[\begin{align}
  & \Delta {{S}_{total}}=\Delta {{S}_{system}}+\Delta {{S}_{surroundings}} \\
 & =\dfrac{\Delta H}{{{T}_{2}}}-\dfrac{\Delta H}{{{T}_{1}}} \\
 & =\dfrac{-401.7}{273}-\dfrac{-401.7}{368} \\
 & =-1.471+1.092 \\
 & \Delta {{S}_{total}}=-0.38J{{K}^{-1}}
\end{align}\]
- Therefore, the total entropy change is -0.38J/K.

Therefore, the correct answer is option (C).

Note:
Remember entropy is a thermodynamic property which gives an idea about the degree of randomness in a system. Entropy depends on change in heat enthalpy and temperature. For spontaneous processes, total entropy change is greater than zero. At equilibrium, total entropy change is zero. For non-spontaneous processes, total entropy change is less than zero.