What will be the value of ΔH, if the forward and reverse reactions have the same energy of activation?

The correct option is ΔH = 0.

To understand why this is the correct answer, let us look at the relationship between the enthalpy change ($\Delta H$) of a reaction and the activation energies of its forward and reverse paths.

For any chemical reaction, the change in enthalpy ($\Delta H$) is defined as the difference between the activation energy of the forward reaction ($E_{\mathrm{a(forward)}}$) and the activation energy of the reverse reaction ($E_{\mathrm{a(reverse)}}$). This can be mathematically expressed as:

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

According to the question, the forward and reverse reactions have the same energy of activation. Therefore, we can write:

$E_{\mathrm{a(forward)}}=E_{\mathrm{a(reverse)}}$

Substituting this equality into the enthalpy change equation gives:

$\Delta H=E_{\mathrm{a(forward)}}-E_{\mathrm{a(forward)}}=0$

Consequently, the enthalpy change of the reaction is zero ($\Delta H=0$).