Three diatomic molecules, Q₂, R₂, and S₂, are studied spectroscopically. The following experimental data are obtained:
• Q₂: equilibrium bond length = 110 pm; bond energy = 430 kJ mol⁻¹
• R₂: equilibrium bond length = 125 pm; bond energy = 360 kJ mol⁻¹
• S₂: equilibrium bond length = 115 pm; bond energy unknown (not directly measured)
It is determined that S₂ contains the same two atoms as Q₂ and R₂, but its bond order lies between that of Q₂ and R₂. Using the information provided, construct and analyze potential-energy curves for these molecules.
(a) On one set of appropriately labeled axes, draw qualitative potential-energy curves for Q₂ and R₂ that are consistent with the numerical data above. Clearly label the equilibrium bond length and bond energy for each molecule on your diagram.
(b) Using the relationship between bond order, bond length, and bond energy, sketch a qualitative potential-energy curve for S₂ on the same axes. Place its minimum at an internuclear distance consistent with its intermediate bond order and justify your placement.
(c) From your sketch, estimate a reasonable numerical range for the bond energy of S₂ and justify your range using the relative depths of the wells you have drawn.
(d) Discuss how uncertainties in experimental determination of bond length could affect the precision of the bond-energy estimate for S₂ and propose one additional measurement that could reduce this uncertainty.