An endothermic reaction has a forward activation energy of 75\text{ kJ mol}^{-1} and an en… — JAMB UTME

An endothermic reaction has a forward activation energy of $75\text{ kJ mol}^{-1}$ and an enthalpy change ( $\Delta H$ ) of $+30\text{ kJ mol}^{-1}$ . What is the activation energy of the reverse reaction?

$45\text{ kJ mol}^{-1}$ Answer
B
$105\text{ kJ mol}^{-1}$
C
$30\text{ kJ mol}^{-1}$
D
$75\text{ kJ mol}^{-1}$

Answer

The activation energy of the reverse reaction is

45\text{ kJ mol}^{-1}

For an endothermic reaction, the products have higher potential energy than the reactants by an amount equal to

\Delta H

. The energy barrier to go from products to the transition state (reverse activation energy) is therefore smaller than the barrier from reactants to the transition state (forward activation energy). Using

\Delta H = E_{a(\text{forward})} - E_{a(\text{reverse})}

, we get

30 = 75 - E_{a(\text{reverse})}

, giving

E_{a(\text{reverse})} = 45\text{ kJ mol}^{-1}

Step-by-Step Solution

Identify the given thermodynamic parameters for the endothermic reaction.

Forward activation energy

E_{a(\text{forward})} = 75\text{ kJ mol}^{-1}

and enthalpy change

\Delta H = +30\text{ kJ mol}^{-1}

Establishing the known energy levels from the problem stem.

Apply the relationship between forward activation energy, reverse activation energy, and enthalpy change.

\Delta H = E_{a(\text{forward})} - E_{a(\text{reverse})}

The difference between the energy barrier of the forward reaction and reverse reaction determines the net heat content change.

Substitute the values and solve for

E_{a(\text{reverse})}

E_{a(\text{reverse})} = 75\text{ kJ mol}^{-1} - 30\text{ kJ mol}^{-1} = 45\text{ kJ mol}^{-1}

Rearranging the equation yields the activation energy needed for the reverse process.

Key Concept

Relationship between forward activation energy, reverse activation energy, and enthalpy change in energy profile diagrams.

Estimated Time:45s

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