Two diatomic molecules, X₂ and Y₂, exhibit the following potential-energy data (PE in kJ·mol⁻¹, r in nm; zero energy at infinite separation):
X₂: minimum PE = –520 at r = 0.132; PE at r = 0.112 is +480; PE at r = 0.152 is –200.
Y₂: minimum PE = –260 at r = 0.198; PE at r = 0.178 is +220; PE at r = 0.218 is –90.
(a) Determine the bond energy and equilibrium bond length for each molecule.
(b) Using the data provided, calculate the energy required to compress each bond by 0.020 nm from its equilibrium distance.
(c) Compute the ratio of the compression energies found in part (b) (X₂ : Y₂) and interpret what this reveals about the relative stiffness of the two bonds.
(d) Spectroscopic measurements give fundamental vibrational frequencies of 2.7×1013Hz for X₂ and 1.4×1013Hz for Y₂. Evaluate whether these data are consistent with your interpretation from part (c), citing specific numerical reasoning.
(e) Suppose X₂ and Y₂ consist of the same element but with different bond orders. Assign a probable bond order to each molecule and justify your assignments using all evidence from parts (a)–(d).