Bond Lengths and Energies

Skills to develop

Define bondlength and bond energy and note relationship between the two

Define bond order explain its relationship to bondlength or bond energy

Evaluate enthalpies of reactions using bond energies

Recognize covalent substances and characterize ionic character as difference in electonegativity

Describe trends in bondlengths of a series of related compounds

Bondlengths and Bond Energies

Distances between centers of bonded atoms are called bondlengths, or bond distances. Bondlengths vary depending on many factors, but in general, they are very consistent. Of course the bond orders affect bondlength, but bondlengths of the same order for the same pair of atoms in various molecules are very consistent. Thus, there are tables of interatomic distances or bondlengths in some standard handbooks.

Bondlength (pm) and bond energy (kJ/mol)
Bond Length Energy Bond Length Energy
H--H 74 436 H--C 109 413
C--C 154 348 H--N 101 391
N--N 145 170 H--O 96 366
O--O 148 145 H--F 92 568
F--F 142 158 H--Cl 127 432
Cl-Cl 199 243 H--Br 141 366
Br-Br 228 193 H--I 161 298
I--I 267 151
C--C 154 348
C--C 154 348 C=C 134 614
C--N 147 308 CºC 120 839
C--O 143 360
C--S 182 272 O--O 148 145
C--F 135 488 O=O 121 498
C--Cl 177 330
C--Br 194 288 N--N 145 170
C--I 214 216 NºN 110 945
Bondlengths are determined by X-ray diffraction of solids, by electron diffraction, and by spectroscopic methods (study the light absorbed or emitted by molecules).

Bondlength (pm) and bond energy (kJ/mol)
Bond	Length	Energy	Bond	Length	Energy
H--H	74	436	H--C	109	413
C--C	154	348	H--N	101	391
N--N	145	170	H--O	96	366
O--O	148	145	H--F	92	568
F--F	142	158	H--Cl	127	432
Cl-Cl	199	243	H--Br	141	366
Br-Br	228	193	H--I	161	298
I--I	267	151
			C--C	154	348
C--C	154	348	C=C	134	614
C--N	147	308	CºC	120	839
C--O	143	360
C--S	182	272	O--O	148	145
C--F	135	488	O=O	121	498
C--Cl	177	330
C--Br	194	288	N--N	145	170
C--I	214	216	NºN	110	945

The bondlengths ranges from the shortest of 74 pm for H-H to some 200 pm for large atoms, and the bond energies depends on bond order and lengths. sHalf of the bondlength of a single bond of two similar atoms is called covalent radius. The sum of two covalent radii of two atoms is usually the single bondlength. For example, the covalent radii of H and C are 37 and 77 pm respectively. The C-H bond is thus (37+77) 114 pm. Note that 77 pm = 154/2 pm.

The bond order is the number of electron pairs shared between two atoms in the formation of the bond. Bond order for C=C and O=O is 2. The amount of energy required to break a bond is called bond dissociation energy or simply bond energy. Since bondlengths are consistent, bond energies of similar bonds are also consistent. Thus, tables of bond energies are also of common occurence in handbooks. Some typical bondlengths in picometers (1 pm = 10^-12 and bond energies in kJ/mol are given here to illustrate a general trend so that you are familiar with these quantities.

The bond energy is essentially the average enthalpy change for a gas reaction to break all the similar bonds. For the methane molecule, C(-H)₄, 435 kJ is required to break a single C-H bond for a mole of methane, but breaking all four C-H bonds for a mole requires 1662 kJ. Thus the average bond energy is (1662/4) 416 (not 436) kJ/mol.

Bond energy is a measure of the strength of a chemical bond. The larger the bond energy, the stronger the bond.

Covalent Bonds

Bonds between the same type of atom are covalent bonds, and bonds between atoms when their electronegativity differs by a little (say 0.7) are also predominant covalent in character. There is also some covalent character between ions of what we usually call ionic solids. For example, bonds in the following substances are predominantly covalent:

Elements: H₂, Li₂, B₂, C₂, N₂, O₂, F₂, Cl₂, S₈, P₄, I₂, diamond, graphite, silicon etc
Covalent compounds: H₂O, NH₂, CH₄, H₃C-CH₃, H₂C=CH₂, SiO₂, CO₂, N₂O₄, NO₂, SO₂, SO₂ etc.

Theoretically, even ionic bonds have some covalent character. Thus, the boundary between ionic and covalent bonds is a vague one.

For covalent bonds, bond energies and bondlengths depend on many factors: electron afinities, sizes of atoms involved in the bond, differences in their electronegativity, and the overall structure of the molecule. There is a general trend in that the shorter the bondlength, the higher the bond energy. However, there is no formula to show this relationship, because the variation is widespread. From a table of values, we can not grasp the trend easily. The best method to see the trend is to plot the data on a graph.

In a discussion of bond energies, this link has shown how energy varies as two H atoms approach each other in the formation of a H-H covalent bond:

Covalent bonds such as H-Cl, H-I etc are polar, because the bonding electrons are attracted to the more electronegative atoms, Cl and I in these cases. In general, the higher the electronegativity difference, the more polar are the bonds. In particular, H-F, and H-O bonds are very polar.

Example 1.

Use the table of bond energies to find the DH^o for the reaction: H₂(g) + Br₂(g) ® 2 HBr(g)

Solution

From the Table of bondlength and bond energy given above, a table below is obvious:

Changes	DH^o
H-H ® H + H	436
Br-Br ® Br + Br	193
H + H + Br + Br ® 2 H-Br	2*(-366) = -732
Overall (add up)
H-H + Br-Br ® 2 H-Br	-103

Discussion

Another approach is shown below. Write the bond energy below the formula, and then apply the principle of conservation of energy.

	Bonds broken	Bonds formed
	H-H + Br-Br	2 H-Br
DH^o	436 + 193	-2*366 energy released
DH^o = 436 + 193 - 2*366 = -103

Exercise

Evaluate the energy changes for the following reactions

   H     H            H H
    \   /             | |
     C=C   + H-H -> H-C-C-H
    /   \             | |
   H     H            H H

Ans: - 124 kJ

     H                Cl
     |                |
   H-C-H + Cl-Cl -> H-C-Cl + H-H
     |                |
     H                H

Confidence Building Questions

Which bond in the list has the highest bond energy,
H-H, H-O, H-F, H-I or I-I?

Discussion: Describe the trends in bondlength and bond energy from the Table above.
Which bond of the following list has the lowest bond energy, H-H, C-C, N-N, O-O, Cl-Cl, Br-Br, I-I? Note that all these are single bonds.

Discussion: The bondlengths and energies of two possible ones are compared here. I-I, 267 pm, 153 kJ/mol; O-O, 148 pm, 145 kJ/mol.
For carbon-carbon bonds, which one has the highest bond energy, single bond, double bond, or triple bond.

Discussion: Bond energies: single, 348; double, 614; triple, 839 kJ/mol. The higher the bond order, the more the bond energy.
Define bond energy

Discussion: Energy is always required to break a chemical bond. Chemical bonds store energy.