The enthalpy change ($\Delta H$) of a reaction is related to the activation energies of the forward and reverse reactions by the equation: $\Delta H = E_{a,\text{forward}} - E_{a,\text{reverse}}$. When the activation energies for the forward and reverse reactions are equal ($E_{a,\text{forward}} = E_{a,\text{reverse}}$), their difference is zero, resulting in $\Delta H = 0$.