The figure below is the plot of potential energy versus internuclear distance (𝑑) of $$H_2$$ molecule in the electronic ground state. What is the value of the net potential energy 𝐸0 (as indicated in the figure) in kJ mol$$^{−1}$$, for $$𝑑 = 𝑑_0$$ at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent? As reference, the potential energy of H atom is taken as zero when its electron and the nucleus are infinitely far apart.
Use Avogadro constant as $$6.023 \times 10^{23}$$ mol$$^{−1}$$.

For a covalent bond, the minimum of the potential-energy curve corresponds to the energy required to break the bond and separate the bonded atoms to an infinite internuclear distance. This energy is called the bond-dissociation energy $$D_0$$.

For the ground-state $$H_2$$ molecule, accurate spectroscopic measurements give $$D_0 = 4.52 \text{ eV}$$ per molecule.

At the equilibrium distance $$d = d_0$$ (marked on the graph) the attractive electron-nucleus interactions dominate, while, as stated in the question, the electron-electron and nucleus-nucleus repulsions are absent. Hence the net potential energy $$E_0$$ of the molecule relative to the chosen zero (two non-interacting hydrogen atoms) is simply the negative of the bond-dissociation energy:

$$E_0 = -\,D_0 = -\,4.52 \text{ eV per molecule}$$

To express this in kJ mol$$^{-1}$$, first convert electron-volts to joules:

$$1\ \text{eV} = 1.602 \times 10^{-19}\ \text{J}$$

$$E_0 = -\,4.52 \times 1.602 \times 10^{-19}\ \text{J}$$

$$E_0 = -\,7.243 \times 10^{-19}\ \text{J per molecule}$$

Using Avogadro’s constant $$N_A = 6.023 \times 10^{23}\ \text{mol}^{-1}$$, convert to energy per mole:

$$E_0 = \bigl(-\,7.243 \times 10^{-19}\ \text{J}\bigr) \times \bigl(6.023 \times 10^{23}\ \text{mol}^{-1}\bigr)$$

$$E_0 = -\,4.36 \times 10^{5}\ \text{J mol}^{-1}$$

$$E_0 \approx -\,4.36 \times 10^{2}\ \text{kJ mol}^{-1}$$

Therefore, the net potential energy at the equilibrium internuclear distance is

$$E_0 \approx -\,4.36 \times 10^{2}\ \text{kJ mol}^{-1}$$.