Which of the following relations are correct if `Delta H` represents only magnitude ?

Options

A. a. Exothermic reactions: `E_(a(f)) + Delta H = E_(a(b))`
B. b. Endothermic reactions: `E_(a(f)) = E_(a(b)) + Delta H`
C. c. Exothermic reactions: `Delta H gt E_(a)`
D. d. Exothermic reactions: `Delta H lt E_(a)`

Explanation

To determine which relations are correct when \( \Delta H \) represents only magnitude, we can analyze the relationships between the forward activation energy (\( E_f \)), backward activation energy (\( E_b \)), and the change in enthalpy (\( \Delta H \)) for both exothermic and endothermic reactions.

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- \( \Delta H \): Change in enthalpy.
- \( E_f \): Forward activation energy.
- \( E_b \): Backward activation energy.

2. **For Exothermic Reactions**:
- In exothermic reactions, the enthalpy change \( \Delta H \) is negative.
- The relationship can be expressed as:
\[ \Delta H = E_f - E_b \]
- Rearranging gives:
\[ E_b = E_f + \Delta H \]
- Since \( \Delta H \) is negative, this means:
\[ E_b = E_f - |\Delta H| \]
- This indicates that the backward activation energy is less than the forward activation energy.

3. **For Endothermic Reactions**:
- In endothermic reactions, the enthalpy change \( \Delta H \) is positive.
- Again, using the relationship:
\[ \Delta H = E_f - E_b \]
- Rearranging gives:
\[ E_f = \Delta H + E_b \]
- This indicates that the forward activation energy is greater than the backward activation energy.

4. **Comparing Activation Energies**:
- For exothermic reactions, we know that \( \Delta H < E_f \).
- For endothermic reactions, \( \Delta H > E_b \).

5. **Conclusion**:
- Based on the analysis, we find that:
- Option A: Correct (for exothermic reactions).
- Option B: Correct (for endothermic reactions).
- Option C: Correct (comparison of activation energies).
- Option D: Not applicable as it does not align with the established relationships.

### Final Answer:
The correct options are A, B, and C.

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