Question

An endothermic reaction \(A\rightarrow B\) has an activation energy of 13 kJ mol\(^{-1}\) and the enthalpy change for the reaction is 2 kJ mol\(^{-1}\). The activation energy of the reaction \(B\rightarrow A\) is

• A. 15 kJ mol\(^{-1}\)
• B. 11 kJ mol\(^{-1}\)
• C. 2 kJ mol\(^{-1}\)
• D. \(-15\) kJ mol\(^{-1}\)
• E. 26 kJ mol\(^{-1}\)

Hint:

For endothermic reactions, forward activation energy is greater than backward activation energy.

Answer 1

The Correct Option is B

Concept: For an endothermic reaction: \[ \Delta H = E_a(\text{forward}) - E_a(\text{backward}) \]

Step 1: Write given values.
\[ E_a(\text{forward})=13\ \text{kJ mol}^{-1} \] \[ \Delta H=+2\ \text{kJ mol}^{-1} \]

Step 2: Apply formula.
\[ 2=13-E_a(\text{backward}) \]

Step 3: Calculate backward activation energy.
\[ E_a(\text{backward})=13-2=11\ \text{kJ mol}^{-1} \]