`A+B rarr C, DeltaH = +60` kJ/mol
`E_(a_f)` is 150 kJ. What is the activation energy for the backward reaction ?

Options

A. 210 kJ
B. 105 kJ
C. 90 kJ
D. 145 kJ

Answer

To solve the problem of finding the activation energy for the backward reaction, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The reaction is: \( A + B \rightarrow C \)
- The enthalpy change (\( \Delta H \)) for the reaction is given as \( +60 \, \text{kJ/mol} \).
- The activation energy for the forward reaction (\( E_{a_f} \)) is given as \( 150 \, \text{kJ} \).

2. **Understand the Relationship Between Activation Energies and Enthalpy Change:**
- The relationship between the activation energy of the forward reaction, the activation energy of the backward reaction, and the enthalpy change is given by the equation:
\[ \Delta H = E_{a_f} - E_{a_b} \]
- Here, \( E_{a_b} \) is the activation energy for the backward reaction.

3. **Rearrange the Equation to Solve for \( E_{a_b} \):**
- We can rearrange the equation to find the activation energy for the backward reaction:
\[ E_{a_b} = E_{a_f} - \Delta H \]

4. **Substitute the Known Values:**
- Now, substitute the known values into the rearranged equation:
\[ E_{a_b} = 150 \, \text{kJ} - 60 \, \text{kJ} \]

5. **Calculate the Activation Energy for the Backward Reaction:**
- Performing the calculation gives:
\[ E_{a_b} = 150 \, \text{kJ} - 60 \, \text{kJ} = 90 \, \text{kJ} \]

6. **Conclusion:**
- The activation energy for the backward reaction is \( 90 \, \text{kJ} \).

### Final Answer:
The activation energy for the backward reaction is \( 90 \, \text{kJ} \).

---