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Chapter 9: Problem 8

What are the relationships among bond order, bond energy, and bond length? Which of these quantities can be measured?

Short Answer

Expert verified
Bond order, bond energy, and bond length are related as follows: a higher bond order correlates with a shorter bond length and a higher bond energy, while bond energy is inversely proportional to bond length. Bond length can be measured experimentally using X-ray crystallography or spectroscopy, and bond energy can be measured as the change in energy during a chemical reaction. Bond order, however, cannot be directly measured and is a theoretical concept calculated based on electron configurations.

Step by step solution

01

Define bond order, bond energy, and bond length

Bond order is the number of chemical bonds between two atoms in a molecule, indicating the stability of the bond between them. Bond energy refers to the energy required to break a chemical bond between two atoms, while bond length refers to the distance between the nuclei of two bonded atoms.
02

Explain the relationship between bond order and bond length

A higher bond order generally correlates with a shorter bond length. This is because multiple bonds involve a greater number of electrons that participate in the bonding process between two atoms. The increased amount of electrons pulls the bonded atoms closer together, resulting in a shorter bond length.
03

Explain the relationship between bond order and bond energy

Bond order is directly proportional to bond energy. As the bond order increases, so does the bond energy. This is due to a stronger bond, involving more electrons holding the atoms together more tightly. As a consequence, more energy is required to break such bonds.
04

Explain the relationship between bond energy and bond length

Bond energy is inversely proportional to bond length. As the bond energy increases, the bond length decreases. A stronger bond with higher bond energy implies that the atoms are held more tightly and are closer together, leading to a shorter bond length. Conversely, a weaker bond with a lower bond energy will have a longer bond length.
05

Determine which of these quantities can be measured

Bond length can be measured experimentally, most commonly using X-ray crystallography or spectroscopy techniques. These methods allow us to measure the distance between the nuclei of bonded atoms with high precision. Bond energy can also be measured experimentally, usually as the change in energy (heat) released or absorbed during a chemical reaction involving bond breaking and forming. However, bond order cannot be directly measured like bond length and bond energy; it is a theoretical concept derived from molecular orbital theory and can be calculated based on the electron configuration of molecules.

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Most popular questions from this chapter

The atoms in a single bond can rotate about the internuclear axis without breaking the bond. The atoms in a double and triple bond cannot rotate about the internuclear axis unless the bond is broken. Why?

Compare and contrast bonding molecular orbitals with antibonding molecular orbitals.

The \(\mathrm{N}_{2} \mathrm{O}\) molecule is linear and polar. a. On the basis of this experimental evidence, which arrangement, NNO or NON, is correct? Explain your answer. b. On the basis of your answer to part a, write the Lewis structure of \(\mathrm{N}_{2} \mathrm{O}\) (including resonance forms). Give the formal charge on each atom and the hybridization of the central atom. c. How would the multiple bonding in \(\mathrm{N} \equiv \mathrm{N}-\ddot{\mathrm{O}}\) : be described in terms of orbitals?

For each of the following molecules or ions that contain sulfur, write the Lewis structure(s), predict the molecular structure (including bond angles), and give the expected hybrid orbitals for sulfur. a. \(\mathrm{SO}_{2}\) b. \(\mathrm{SO}_{3}\) c. d. e. \(\mathrm{SO}_{3}^{2-}\) i. \(\mathrm{SF}_{6}\) f. \(\mathrm{SO}_{4}^{2-}\) j. \(\mathrm{F}_{3} \mathrm{~S}-\mathrm{SF}\) g. \(\mathrm{SF}_{2}\) \(\mathbf{k} . \mathrm{SF}_{5}{ }^{+}\) h. \(\mathrm{SF}_{4}\)

As the head engineer of your starship in charge of the warp drive, you notice that the supply of dilithium is critically low. While searching for a replacement fuel, you discover some diboron, \(\mathrm{B}_{2}\). a. What is the bond order in \(\mathrm{Li}_{2}\) and \(\mathrm{B}_{2}\) ? b. How many electrons must be removed from \(\mathrm{B}_{2}\) to make it isoelectronic with \(\mathrm{Li}_{2}\) so that it might be used in the warp drive? c. The reaction to make \(\mathrm{B}_{2}\) isoelectronic with \(\mathrm{Li}_{2}\) is generalized (where \(n=\) number of electrons determined in part b) as follows: $$ \mathrm{B}_{2} \longrightarrow \mathrm{B}_{2}^{n+}+n \mathrm{e}^{-} \quad \Delta H=6455 \mathrm{~kJ} / \mathrm{mol} $$ How much energy is needed to ionize \(1.5 \mathrm{~kg} \mathrm{~B}_{2}\) to the desired isoelectronic species?
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