Some periodic trends in bond lengths and bond energies

Within a group of the periodic table, bond lengths tend to increase with increasing atomic number $Z$. Consider the group VII elements:

$${\bf F}_2\;\;\;\;\;\;\;\;\;\;d=1.417 {\rm\AA}$$

$${\bf Cl}_2\;\;\;\;\;\;\;\;\;d=1.991 {\rm\AA}$$

$${\bf Br}_2\;\;\;\;\;\;\;\;\;d=2.286 {\rm\AA}$$

$${\bf I}_2\;\;\;\;\;\;\;\;\;\;d=2.669 {\rm\AA}$$

which corresponds to an increased valence shell size, hence increased electron-electron repulsion.

An important result from experiment, which has been corroborated by theory, is that bond lengths tend not to vary much from molecule to molecule. Thus, a CH bond will have roughly the same value in methane, CH$_4$ as it will in aspirin, C$_9$H$_8$O$_4$.

Bond dissociation energies were discussed in the last lecture in the context of ionic bonds. There we used the symbol $\Delta E_d$ measured in kJ/mol. This measures the energy required to break a mole of a particular kind of bond. A similar periodic trend exists for bond dissociation energies. Consider the hydrogen halides:

$${\rm HF}\;\;\;\;\;\;\;\;\;\;\Delta E_d = 565 {\rm kJ/mol}\;\;\;\;\;\;\;\;\;\; d = 0.926 {\rm\AA}$$

$${\rm HCl}\;\;\;\;\;\;\;\;\;\Delta E_d = 429 {\rm kJ/mol}\;\;\;\;\;\;\;\;\;\; d = 1.284 {\rm\AA}$$

$${\rm HBr}\;\;\;\;\;\;\;\;\;\Delta E_d = 363 {\rm kJ/mol}\;\;\;\;\;\;\;\;\;\; d = 1.424 {\rm\AA}$$

$${\rm HI}\;\;\;\;\;\;\;\;\;\;\Delta E_d = 295 {\rm kJ/mol}\;\;\;\;\;\;\;\;\;\; d = 1.620 {\rm\AA}$$

Thus, as bond lengths increase with increasing $Z$, there is a corresponding decrease in the bond dissociation energy.

CC bonds are an exception to the the rule of constancy of bond lengths across different molecules. Because CC bonds can be single, double, or triple bonds, some differences can occur. For example, consider the CC bond in the molecules ethane (C$_2$H$_6$), ethylene (C$_2$H$_4$) and acetylene (C$_2$H$_2$):

$${\rm C}_2{\rm H}_6\;\;\;\;\;\;({\rm single})\;\;\;\;\;\; d=1.536 {\rm\AA}\;\;\;\;\;\;\;\;\;\;\Delta E_d = 345 {\rm kJ/mol}$$

$${\rm C}_2{\rm H}_4\;\;\;\;\;\;({\rm double})\;\;\;\;\;\; d=1.337 {\rm\AA}\;\;\;\;\;\;\;\;\;\;\Delta E_d = 612 {\rm kJ/mol}$$

$${\rm C}_2{\rm H}_2\;\;\;\;\;\;({\rm triple})\;\;\;\;\;\; d=1.264 {\rm\AA}\;\;\;\;\;\;\;\;\;\;\Delta E_d = 809 {\rm kJ/mol}$$

The greater the bond order, i.e., number of shared electron pairs, the greater the dissociation energy. The same will be true for any kind of bond that can come in such different ``flavors'', e.g., NN bonds, OO bonds, NO bonds, CO bonds, etc.