The following plot shows the potential energy of two Cl atoms as a function of the distance betw

step 1 We are given the following diagram, and this isn't perfect, but it's pretty close. And this is t

The following plot shows the potential energy of two Cl...

The following plot shows the potential energy of two $\mathrm{Cl}$ atoms as a function of the distance between them. (a) To what does an energy of zero correspond in this diagram? (b) According to the valence-bond model, why does the energy decrease as the $\mathrm{Cl}$ atoms move from a large separation to a smaller one? (c) What is the significance of the $\mathrm{Cl}-\mathrm{Cl}$ distance at the minimum point in the plot? (d) Why does the energy rise at $\mathrm{Cl}-\mathrm{Cl}$ distances less than that at the minimum point in the plot? (e) How can you estimate the bond strength of the $\mathrm{Cl}-\mathrm{Cl}$ bond from the plot? [Section 9.4]

Key Concepts

Bond Strength and Bond Dissociation Energy

Bond strength is related to the amount of energy required to break a chemical bond, which can be estimated from the difference between the energy at the equilibrium bond length and the reference state. This energy difference, known as the bond dissociation energy, quantifies the stability of the bond and the energy released when the bond is formed.

Repulsive Interactions

At internuclear distances shorter than the equilibrium bond length, repulsive interactions become dominant, largely due to electron-electron repulsion and the effects explained by the Pauli exclusion principle. These forces cause the potential energy to rise steeply as atoms are forced too close together, preventing nuclei from occupying the same space.

Equilibrium Bond Length

The equilibrium bond length is the specific internuclear distance at which the potential energy of the bonded system reaches a minimum. At this distance, the attractive forces (such as electron sharing) and the repulsive forces (from overlapping electron clouds and nuclei) are balanced, resulting in the most stable configuration of the molecule.

Reference Energy Level (Zero Energy Reference)

A zero energy reference is often chosen to represent a state where interacting particles (e.g., atoms) are infinitely separated and do not influence each other. This provides a baseline for measuring the change in energy as atoms form bonds or interact, and it is essential for comparing the energy of bonded configurations to non-interacting ones.

Potential Energy Diagrams

Potential energy diagrams graphically represent the energy of a system as a function of a particular parameter (such as the separation between atoms). In the context of chemical bonds, these diagrams illustrate how energy changes when atoms approach each other, highlighting regions of attraction and repulsion. They are crucial in understanding bond formation, molecular stability, and the dissociation process.

Valence Bond Model

The valence bond model explains chemical bonding by considering the overlap of atomic orbitals from different atoms, which leads to electron sharing and bond formation. This theory accounts for the decrease in energy as atoms approach each other due to the stabilizing effect of electron pairing in the overlapping region, resulting in a lower potential energy state compared to separated atoms.

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