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$(A)$ The enthalpy change of a reaction $(\Delta H)$ is defined as the difference between the activation energy of the forward reaction $(E_{af})$ and

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$-20$

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$(A)$ The enthalpy change of a reaction $(\Delta H)$ is defined as the difference between the activation energy of the forward reaction $(E_{af})$ and the activation energy of the reverse reaction $(E_{ab})$.$\Delta H = E_{af} - E_{ab} = 180 \, kJ \, mol^{-1} - 200 \, kJ \, mol^{-1} = -20 \, kJ \, mol^{-1}$.$A$ catalyst provides an alternative reaction pathway with lower activation energy, but it does not change the energy of the reactants or the products.Since $\Delta H$ is a state function, it depends only on the initial and final states of the system.Therefore, the enthalpy change of the reaction remains unchanged in the presence of a catalyst, which is $-20 \, kJ \, mol^{-1}$.

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