equilibrium bond length

Examples of equilibrium bond length in the following topics:

• Bond Lengths

  • The bond length is the average distance between the nuclei of two bonded atoms in a molecule.
  • Measured bond lengths are the distance between those unperturbed, or equilibrium, positions of the balls, or atoms.
  • 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.
  • The minimum energy occurs at the equilibrium distance r0, which is where the bond length is measured.

• 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.
  • The internuclear distance at which the energy minimum occurs defines the equilibrium bond length.
  • This bond length represents an 'equilibrium' value because thermal motion causes the two atoms to vibrate about this distance, much like a spring vibrates back and forth around its unstretched, or equilibrium distance.
  • In general, the stronger the bond between two atoms, the lower the energy minimum is and the smaller the bond length.

• Polyatomic Molecules

  • A polyatomic molecule is a single entity composed of at least three covalently-bonded atoms.
  • Polyatomic molecules are electrically neutral groups of three or more atoms held together by covalent bonds.
  • Molecular chemistry deals with the laws governing the interaction between molecules resulting in the formation and breakage of chemical bonds; molecular physics deals with the laws governing their structure and properties.
  • Molecules have fixed equilibrium geometries—bond lengths and angles—about which they continuously oscillate through vibrational and rotational motions.

• Reactions of Fused Benzene Rings

  • 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.
  • Electrophilic substitution reactions take place more rapidly at C1, although the C2 product is more stable and predominates at equilibrium.

• 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

• 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.

• Complex Ion Equilibria and Solubility

  • A complex ion is an ion comprising one or more ligands attached to a central metal cation with a dative bond.
  • A ligand is a species which can use its lone pair of electrons to form a dative covalent bond with a transition metal.
  • The equilibrium constant (Kc) for the reaction relates the concentration of the reactants and products.
  • The equilibrium constant expression (Kc), according to the Law of Chemical Equilibrium, for this reaction is formulated as follows:
  • The Beer-Lambert Law relates the amount of light being absorbed to the concentration of the substance absorbing the light and the path length through which the light passes:

• Acidity of Carboxylic Acids

  • We know that an equilibrium favors the thermodynamically more stable side, and that the magnitude of the equilibrium constant reflects the energy difference between the components of each side.
  • In an acid base equilibrium the equilibrium always favors the weaker acid and base (these are the more stable components).
  • Water is the standard base used for pKa measurements; consequently, anything that stabilizes the conjugate base (A:(–)) of an acid will necessarily make that acid (H–A) stronger and shift the equilibrium to the right.
  • In the carboxylate anion the two contributing structures have equal weight in the hybrid, and the C–O bonds are of equal length (between a double and a single bond).
  • Water is less acidic than hydrogen peroxide because hydrogen is less electronegative than oxygen, and the covalent bond joining these atoms is polarized in the manner shown.

• 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.

• Chromium

  • Most important are the chromate (CrO42-) and dichromate (Cr2O72-) anions, which exist in equilibrium:
  • The change in equilibrium is visible by a change from yellow (chromate) to orange (dichromate), such as when an acid is added to a neutral solution of potassium chromate.
  • As verified by X-ray diffraction, a Cr-Cr quintuple bond (length 183.51(4) pm) has also been described.