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.

• Liquidity and Bond Prices

  • Liquidity causes bond prices and interest rates to differ.
  • We start the analysis with the same liquidity in both the government bond and corporate bond markets in Figure 2.
  • Thus, both bond markets have the identical equilibrium bond price, P*, and hence, the exact liquidity.
  • Thus, the government bond prices rise, which reduces the interest rate for government bonds.
  • On the other hand, the corporate bond prices decrease, raising the market interest rate for corporate bond.

• 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

• Information Costs and Bond Prices

  • Information costs influence the bond prices and interest rates.
  • We depict the bond markets in Figure 3.
  • The equilibrium bond prices are identical for both markets and equal P* and the interest rates would be equal.
  • High information cost bonds are not as attractive as an investment, so investors buy fewer bonds, reducing bond prices and raising interest rates.
  • Therefore, low-information-cost bonds pay a lower interest rate.

• 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.

• Time to Maturity

  • "Time to maturity" refers to the length of time before the par value of a bond must be returned to the bondholder.
  • "Time to maturity" refers to the length of time that can elapse before the par value (face value) for a bond must be returned to a bondholder.
  • The issuer of a bond has to repay the nominal amount for that bond on the maturity date.
  • The length of time until a bond's matures is referred to as its term, tenor, or maturity.
  • These dates can technically be any length of time, but debt securities with a term of less than one year are generally not designated as bonds.

• 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: