Calculation of Total Entropy Change for the Transition of Sulphur

Given:
- Temperature of the transition: 368 K
- Number of moles of sulphur: 1 mol
- Change in enthalpy: -401.7 J/mol

Step 1: Calculation of Entropy Change
The total entropy change for the transition can be calculated using the equation:

ΔS = ΔH / T

Where:
- ΔS is the total entropy change
- ΔH is the change in enthalpy
- T is the temperature in Kelvin

Substituting the given values:
ΔS = -401.7 J/mol / 368 K

Step 2: Conversion of Units
The given enthalpy change is in joules per mole, and the temperature is in Kelvin. However, the entropy change should be in J/mol·K. Therefore, we need to convert the units.

Since the given enthalpy change is per mole, we don't need to make any changes. However, the temperature needs to be converted from Celsius to Kelvin.

T(K) = T(°C) + 273.15
T(K) = 0°C + 273.15
T(K) = 273.15 K

Substituting the converted temperature into the equation:
ΔS = -401.7 J/mol / 273.15 K

Step 3: Calculation of Total Entropy Change
Now, we can calculate the total entropy change:
ΔS = -401.7 J/mol / 273.15 K
ΔS ≈ -1.470 J/(mol·K)

Step 4: Explanation
The total entropy change for the transition of 1 mol of sulphur from the monoclinic to the rhombic solid state at 368 K is approximately -1.470 J/(mol·K).

At a molecular level, the transition involves a rearrangement of the sulphur atoms from the monoclinic crystal structure to the rhombic crystal structure. This rearrangement leads to a change in the arrangement and disorder of the atoms, resulting in an increase in entropy.

The negative value of the entropy change indicates that the transition is not favorable in terms of entropy. However, the transition is driven by the decrease in enthalpy, as indicated by the given change in enthalpy (-401.7 J/mol).

The surrounding is assumed to be an ice-water bath at 0°C (273.15 K). This assumption allows us to calculate the entropy change at a specific temperature. The ice-water bath acts as a heat sink, absorbing any heat released or absorbed during the transition.

Overall, the transition of sulphur from the monoclinic to the rhombic solid state at 368 K results in a decrease in entropy, indicating a decrease in disorder.

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