An exothermic reaction X `to` Y has an activation energy 30 KJ `"mol"^(-1)` . If energy change `DeltaE` during the reaction is -20 KJ, then the activation energy for the reverse reaction in KJ is __________ . (Integer answer)

Answer

To solve the problem, we need to determine the activation energy for the reverse reaction of an exothermic reaction given the activation energy for the forward reaction and the energy change (ΔE) during the reaction.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Activation energy for the forward reaction (Ea_forward) = 30 kJ/mol
- Energy change during the reaction (ΔE) = -20 kJ

2. **Understand the Concept:**
- In an exothermic reaction, the products have lower energy than the reactants. The energy change (ΔE) is negative, indicating that energy is released.
- The relationship between the activation energies of the forward and reverse reactions can be expressed as:
\[ \Delta E = E_a^{forward} - E_a^{reverse} \]
- Rearranging this gives:
\[ E_a^{reverse} = E_a^{forward} - \Delta E \]

3. **Substitute the Values:**
- Substitute the known values into the equation:
\[ E_a^{reverse} = 30 \, \text{kJ/mol} - (-20 \, \text{kJ}) \]
- This simplifies to:
\[ E_a^{reverse} = 30 \, \text{kJ/mol} + 20 \, \text{kJ} \]

4. **Calculate the Activation Energy for the Reverse Reaction:**
- Therefore:
\[ E_a^{reverse} = 50 \, \text{kJ/mol} \]

### Final Answer:
The activation energy for the reverse reaction is **50 kJ/mol**.

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