Calculate the total entropy change for the transition at 368K of 1mol of sulphur from the monoclinic to the rhombic solid state, if `DeltaH=-401.7J ,mol^(-1)` "for the transition". Assume the surroundings tio be an ice-water bath at `0^(@)C`:

Options

A. `-1.09 JK^(-1)`
B. `1.477 Jk^(-1)`
C. `0.38 JK^(-1)`
D. None of these

Explanation

To calculate the total entropy change for the transition of 1 mole of sulfur from the monoclinic to the rhombic solid state at 368 K, we will follow these steps:

### Step 1: Identify the given data
- Change in enthalpy (ΔH) = -401.7 J/mol
- Temperature of the system (T_system) = 368 K
- Temperature of the surroundings (T_surroundings) = 0 °C = 273 K

### Step 2: Calculate the entropy change for the system (ΔS_system)
The formula for the entropy change of the system is given by:
\[ \Delta S_{system} = \frac{\Delta H}{T_{system}} \]
Substituting the values:
\[ \Delta S_{system} = \frac{-401.7 \, \text{J/mol}}{368 \, \text{K}} \approx -1.09 \, \text{J/K} \]

### Step 3: Calculate the entropy change for the surroundings (ΔS_surroundings)
The formula for the entropy change of the surroundings is given by:
\[ \Delta S_{surroundings} = \frac{-\Delta H}{T_{surroundings}} \]
Substituting the values:
\[ \Delta S_{surroundings} = \frac{-(-401.7 \, \text{J/mol})}{273 \, \text{K}} \approx 1.47 \, \text{J/K} \]

### Step 4: Calculate the total entropy change (ΔS_total)
The total entropy change is the sum of the entropy changes of the system and the surroundings:
\[ \Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings} \]
Substituting the values:
\[ \Delta S_{total} = -1.09 \, \text{J/K} + 1.47 \, \text{J/K} \approx 0.38 \, \text{J/K} \]

### Final Answer
The total entropy change for the transition is approximately:
\[ \Delta S_{total} \approx 0.38 \, \text{J/K} \]