Calculate the enthalpy of allotropic transformation from monoclinic to rhombic sulphur from the following data:
`S("rhombic") + O_(2)(g) to SO_(2)(g) Delta_(r)H^(@) = -294.1 kJ`
`S("monoclinic") + O_(2)(g) to SO_(2)(g) Delta_(r)H^(@) = -295.4 kJ`

Explanation

To calculate the enthalpy of allotropic transformation from monoclinic to rhombic sulfur, we can use the provided enthalpy changes for the reactions involving both forms of sulfur.

### Step-by-Step Solution:

1. **Write the reactions with their enthalpy changes**:
- For rhombic sulfur:
\[ S(\text{rhombic}) + O_2(g) \rightarrow SO_2(g) \quad \Delta_rH^\circ = -294.1 \, \text{kJ} \]
- For monoclinic sulfur:
\[ S(\text{monoclinic}) + O_2(g) \rightarrow SO_2(g) \quad \Delta_rH^\circ = -295.4 \, \text{kJ} \]

2. **Reverse the reaction for rhombic sulfur**:
- When we reverse the reaction for rhombic sulfur, we get:
\[ SO_2(g) \rightarrow S(\text{rhombic}) + O_2(g) \quad \Delta_rH^\circ = +294.1 \, \text{kJ} \]

3. **Combine the reactions**:
- Now, we can add the two reactions together:
\[ S(\text{monoclinic}) + O_2(g) \rightarrow SO_2(g) \quad \Delta_rH^\circ = -295.4 \, \text{kJ} \]
\[ SO_2(g) \rightarrow S(\text{rhombic}) + O_2(g) \quad \Delta_rH^\circ = +294.1 \, \text{kJ} \]

4. **Cancel out common species**:
- The \(SO_2(g)\) and \(O_2(g)\) on both sides cancel out:
\[ S(\text{monoclinic}) \rightarrow S(\text{rhombic}) \]

5. **Calculate the overall enthalpy change**:
- Now, we can find the overall enthalpy change for the transformation from monoclinic to rhombic sulfur:
\[ \Delta H = (-295.4 \, \text{kJ}) + (+294.1 \, \text{kJ}) = -1.3 \, \text{kJ} \]

### Final Answer:
The enthalpy of allotropic transformation from monoclinic to rhombic sulfur is \(-1.3 \, \text{kJ}\).

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