bond length

Examples of bond length in the following topics:

• Bond Lengths

  • The distance between two atoms participating in a bond, known as the bond length, can be determined experimentally.
  • The bond length is the average distance between the nuclei of two bonded atoms in a molecule.
  • Bonds lengths are typically in the range of 1-2 Å, or 100-200 pm.
  • Even though the bond vibrates, equilibrium bond lengths can be determined experimentally to within ±1 pm.
  • For example, the bond length of $C - C$ is 154 pm; the bond length of $C = C$ is 133 pm; and finally, the bond length of $C \equiv C$ is 120 pm.

• Physical Properties of Covalent Molecules

  • The Lewis bonding theory can explain many properties of compounds.
  • Lewis theory also accounts for bond length; the stronger the bond and the more electrons shared, the shorter the bond length is.
  • According to the theory, triple bonds are stronger than double bonds, and double bonds are stronger than single bonds.
  • However, the theory implies that the bond strength of double bonds is twice that of single bonds, which is not true.
  • Discuss the qualitative predictions of covalent bond theory on the boiling and melting points, bond length and strength, and conductivity of molecules

• Bond Energy

  • The higher the bond energy, the 'stronger' we say the bond is between the two atoms, and the distance between them (bond length) is smaller.
  • Similarly, the C-H bond length can vary by as much as 4% between different molecules.
  • For this reason, the values listed in tables of bond energy and bond length are usually averages taken over a variety of compounds that contain a specific atom pair.
  • The internuclear distance at which the energy minimum occurs defines the equilibrium bond length.
  • In general, the stronger the bond between two atoms, the lower the energy minimum is and the smaller the bond length.

• Steric Effects

  • If a covalent bond forms between the atoms, the energy versus distance curve displays a distinct minimum, representing a bond energy of Eb, at a distance (req) equal to the average bond length.

• Reactions of Fused Benzene Rings

  • The two structures on the left have one discrete benzene ring each, but may also be viewed as 10-pi-electron annulenes having a bridging single bond.
  • The structure on the right has two benzene rings which share a common double bond.
  • As expected from an average of the three resonance contributors, the carbon-carbon bonds in naphthalene show variation in length, suggesting some localization of the double bonds.
  • The C1–C2 bond is 1.36 Å long, whereas the C2–C3 bond length is 1.42 Å.
  • This contrasts with the structure of benzene, in which all the C–C bonds have a common length, 1.39 Å.

• Bond Polarity

  • Bond polarity: when atoms from different elements are covalently bonded, the shared pair of electrons will be attracted more strongly to the atom with the higher electronegativity.
  • Such bonds are said to be 'polar' and possess partial ionic character.
  • The dipole moment is calculated by evaluating the product of the magnitude of separated charge, q, and the bond length, r:
  • If two charges of magnitude +1 and -1 are separated by a typical bond length of 100 pm, then:
  • In molecules containing more than one polar bond, the molecular dipole moment is just the vector addition of the individual bond dipole moments.

• Double and Triple Covalent Bonds

  • The double bond between the two carbon atoms consists of a sigma bond and a π bond.
  • A triple bond involves the sharing of six electrons, with a sigma bond and two $\pi$ bonds.
  • Experiments have shown that double bonds are stronger than single bonds, and triple bonds are stronger than double bonds.
  • Double bonds have shorter distances than single bonds, and triple bonds are shorter than double bonds.
  • The bond lengths and angles (indicative of the molecular geometry) are indicated.

• Explanation of Valence Bond Theory

  • Valence bond theory states that overlap between two atomic orbitals forms a covalent bond between two atoms.
  • In chemistry, valence bond (VB) theory is one of two basic theories—along with molecular orbital (MO) theory—that use quantum mechanics to explain chemical bonding.
  • Single bonds have one sigma bond.
  • Double bonds consist of one $\sigma$ and one $\pi$ bond, while triple bonds contain one $\sigma$ and two $\pi$ bonds.
  • Since the nature of the overlapping orbitals is different in H2 and F2 molecules, bond strength and bond lengths differ between H2 and F2 molecules.

• sp3 Hybridization

  • In a tetravalent molecule, four outer atoms are bonded to a central atom.
  • Perhaps the most common and important example of this bond type is methane, CH4.
  • To form four bonds, the atom must have four unpaired electrons; this requires that carbon's valence 2s and 2p orbitals each contain an electron for bonding.
  • This would indicate that one of the four bonds differs from the other three, but scientific tests have proven that all four bonds have equal length and energy; this is due to the hybridization of carbon's 2s and 2p valence orbitals.
  • The observed H-O-H bond angle in water (104.5°) is less than the tetrahedral angle (109.5°); one explanation for this is that the non-bonding electrons tend to remain closer to the central atom and thus exert greater repulsion on the other orbitals, pushing the two bonding orbitals closer together.

• Hybridization in Molecules Containing Double and Triple Bonds

  • sp2, sp hybridizations, and pi-bonding can be used to describe the chemical bonding in molecules with double and triple bonds.
  • Ethene (C2H4) has a double bond between the carbons.
  • The hydrogen-carbon bonds are all of equal strength and length, which agrees with experimental data.
  • The chemical bonding in acetylene (ethyne) (C2H2) consists of sp-sp overlap between the two carbon atoms forming a sigma bond, as well as two additional pi bonds formed by p-p overlap.
  • In ethene, carbon sp2 hybridizes, because one π (pi) bond is required for the double bond between the carbons, and only three σ bonds form per carbon atom.