A computer-generated plot of potential energy (PE) versus internuclear distance r for the hypothetical diatomic molecule A₂ is summarized verbally below. The PE axis is in kJ·mol⁻¹ and the zero of energy is defined at infinite separation of the atoms.
• Point P: r = 0.18 nm, PE = –150 kJ·mol⁻¹
• Point Q: r = 0.28 nm, PE = –430 kJ·mol⁻¹ (the curve’s minimum)
• Point R: r = 0.34 nm, PE = –250 kJ·mol⁻¹
For r > 0.45 nm, the PE approaches 0 kJ·mol⁻¹. For r < 0.12 nm, the PE rises steeply, reaching +800 kJ·mol⁻¹ at r = 0.10 nm.
(a) Determine the equilibrium bond length and the bond energy of A₂.
(b) Describe the physical significance of the negative potential-energy value at point Q relative to the zero-energy reference.
(c) Compare the sign and magnitude of the change in PE when the molecule is stretched from Q to R with the change when it is compressed from Q toward 0.18 nm. Explain the origin of each change in terms of attractive and repulsive interactions.
(d) Predict how both the equilibrium bond length and the bond energy would change if the molecule instead contained a double bond between the same two atoms. Justify your prediction.