`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 find the activation energy for the backward reaction (E_AB), we can use the relationship between the change in enthalpy (ΔH), the activation energy of the forward reaction (E_AF), and the activation energy of the backward reaction (E_AB).

### Step-by-Step Solution:

1. **Write down the given information:**
- The reaction is: A + B → C
- ΔH = +60 kJ/mol (indicating that the reaction is endothermic)
- E_AF = 150 kJ (activation energy of the forward reaction)

2. **Use the relationship:**
The relationship between ΔH, E_AF, and E_AB is given by:
\[ \Delta H = E_{AF} - E_{AB} \]

3. **Rearranging the equation:**
To find E_AB, we can rearrange the equation:
\[ E_{AB} = E_{AF} - \Delta H \]

4. **Substituting the known values:**
Now, substitute the known values into the equation:
\[ E_{AB} = 150 \, \text{kJ} - 60 \, \text{kJ} \]

5. **Calculating E_AB:**
\[ E_{AB} = 90 \, \text{kJ} \]

6. **Conclusion:**
The activation energy for the backward reaction (E_AB) is 90 kJ.