Consider `A overset(F.R.) underset(B.R.)rarr B+` heat, If activation energy for forward reaction is 100 kJ/mole then activation energy for backward reaction and heat of reaction is :

Options

A. 100, 200
B. 80, 20
C. 120, 220
D. 140, 40

Answer

To solve the problem, we need to find the activation energy for the backward reaction and the heat of reaction (HOR) given the activation energy for the forward reaction.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Activation energy for the forward reaction (Ea, forward) = 100 kJ/mol

2. **Understand the Relationship:**
- The relationship between the activation energies and the heat of reaction is given by the equation:
\[ E_{a, \text{backward}} = E_{a, \text{forward}} + \Delta H \]
- Here, \(E_{a, \text{backward}}\) is the activation energy for the backward reaction, and \(\Delta H\) is the heat of reaction.

3. **Determine the Heat of Reaction:**
- Since the reaction is exothermic (as indicated by the "+ heat" in the equation), the heat of reaction will be negative:
\[ \Delta H < 0 \]
- We can express the heat of reaction as:
\[ \Delta H = E_{a, \text{backward}} - E_{a, \text{forward}} \]

4. **Assume Values for Backward Activation Energy:**
- Let's denote the backward activation energy as \(E_{a, \text{backward}}\).
- We can try different values for \(E_{a, \text{backward}}\) to find a consistent solution with the given forward activation energy.

5. **Check Possible Options:**
- If we assume \(E_{a, \text{backward}} = 140 \text{ kJ/mol}\):
\[ \Delta H = 140 - 100 = 40 \text{ kJ/mol} \quad (\text{not valid, as it should be negative}) \]
- If we assume \(E_{a, \text{backward}} = 120 \text{ kJ/mol}\):
\[ \Delta H = 120 - 100 = 20 \text{ kJ/mol} \quad (\text{not valid, as it should be negative}) \]
- If we assume \(E_{a, \text{backward}} = 80 \text{ kJ/mol}\):
\[ \Delta H = 80 - 100 = -20 \text{ kJ/mol} \quad (\text{valid, as it is negative}) \]
- If we assume \(E_{a, \text{backward}} = 140 \text{ kJ/mol}\):
\[ \Delta H = 140 - 100 = 40 \text{ kJ/mol} \quad (\text{not valid, as it should be negative}) \]

6. **Conclusion:**
- The only consistent values that satisfy the conditions are:
- Backward activation energy \(E_{a, \text{backward}} = 140 \text{ kJ/mol}\)
- Heat of reaction \(\Delta H = -40 \text{ kJ/mol}\)

### Final Answer:
- Activation energy for the backward reaction = 140 kJ/mol
- Heat of reaction = -40 kJ/mol