The plot below shows the energy of two hydrogen atoms as a function of their internuclear separation — Physical Chemistry Chemistry Question
Problem Context
The plot below shows the energy of two hydrogen atoms as a function of their internuclear separation r:
-500 0 500 1000 60 80 100 120 140 160 180 200 E , k J m o l-1 r, pm
r = 74 pm, E = –432 kJ mol -1
Explain why the potential energy decreases as the internuclear separation decreases from 120 pm to 80 pm.
Model Answer
The attraction of the electrons for the nucleus of the other atom causes the energy to decrease as the separation decreases, in this range.
Explain why the potential energy increases as the internuclear separation decreases from 70 pm to 60 pm.
Model Answer
As the nuclei get very close, the nuclear-nuclear repulsion overwhelms the electron-nucleus attraction, causing the energy to increase as the internuclear separation gets closer than the equilibrium distance.
Calculate the longest wavelength of light that has sufficient energy to break a H–H bond.
Model Answer
BDE = 432 kJ mol -1 = 7.17 10 -19 J/molecule
7.17 10 -19 J = hc/, so = (6.626 10 -34 J s)(2.998 10 8 m s -1 )/(7.17 10 -19 J)
= 2.77 10 -7 m = 277 nm
The vibrational frequency of H2(g) is 1.32 10 14 Hz. What percentage of the H–H bond dissociation energy is required to excite a molecular vibration of H2?
Model Answer
E = h = (6.626 10 -34 J s)(1.32 10 14 s -1 ) = 8.75 10 -20 J. This is {(8.75 10 -20 J)/(7.17 10 -19 J)}•100% = 12.2% of the BDE.
Will H2(g) absorb infrared radiation due to its molecular vibration? Explain why or why not.
Model Answer
While the frequency is in the infrared range, there will be no absorption of light because absorption of IR light requires a change in dipole moment of the molecule as it vibrates. H2 is symmetrical and always has a zero dipole moment, regardless of its vibrational excitation.