Choose the reaction, for which the standard enthalpy of reaction is equal to the standard enthalpy of formation:

Options

A. `2C_((g))+3H_(2(g))toC_(2)H_(6(g))`
B. `3/2 O_(2(g))to O_(3(g))`
C. `1/8 S_(8)(s)+O_(2(g))to SO_(2(g))`
D. `2H_(2(g))+O_(2(g))to 2H_(2)O(l)`

Explanation

To determine the reaction for which the standard enthalpy of reaction is equal to the standard enthalpy of formation, we need to analyze each option based on the definition of standard enthalpy of formation.

### Step-by-Step Solution:

1. **Understand the Definition**:
- The standard enthalpy of formation (ΔH_f°) is defined as the change in enthalpy when one mole of a compound is formed from its elements in their standard states.

2. **Analyze Each Option**:
- **Option A**: Formation of C2H6 from H2 and carbon.
- Reaction: C(s) + 3H2(g) → C2H6(g)
- Carbon's stable state is solid (graphite), but in this reaction, carbon is in gaseous form. Therefore, this option does not meet the criteria for standard enthalpy of formation.
- **Conclusion**: Reject Option A.

- **Option B**: Formation of O3 from O2.
- Reaction: 3/2 O2(g) → O3(g)
- O2 is in its stable state (gas). This reaction forms one mole of O3 from O2, so it meets the criteria.
- **Conclusion**: Accept Option B.

- **Option C**: Formation of SO2 from S8 and O2.
- Reaction: S8(s) + 8O2(g) → 8SO2(g)
- Both S8 and O2 are in their stable states. However, this reaction produces 8 moles of SO2, not 1 mole. Therefore, it does not qualify as the standard enthalpy of formation.
- **Conclusion**: Reject Option C.

- **Option D**: Formation of H2O from H2 and O2.
- Reaction: 2H2(g) + O2(g) → 2H2O(l)
- This reaction produces 2 moles of H2O, not 1 mole. Thus, it does not meet the criteria for standard enthalpy of formation.
- **Conclusion**: Reject Option D.

3. **Final Conclusion**:
- The reactions for which the standard enthalpy of reaction is equal to the standard enthalpy of formation are Options B and C, but only Option B meets the criteria for producing one mole of the compound from its elements in their standard states.