Question

A molecule may be represented by three structures having energies $E_1,E_2$ and $E_3$, respectively. The energies of these structures follow the order \(E_{3}

Short answer

Option (2) $E_0-E_3$.

Step-by-step solution

- Understand the Concept of Resonance Energy

Resonance energy is the difference between the expected energy of the molecule if it were described by the most stable single structure and the observed experimental energy of the molecule.

- Identify the Most Stable Structure

Since the energies are ordered such that $E_3<E_2<E_1$, the most stable structure corresponds to the lowest energy, which is $E_3$.

- Calculate the Resonance Energy

The resonance energy is calculated as the difference between the experimental bond energy $E_0$ and the energy of the most stable structure $E_3$. Therefore, the resonance energy is $E_0-E_3$.

- Find the Correct Option

From the given options, Option (2) $E_0-E_3$ matches our result.

Key concepts

molecular structure energy

Molecular structure energy refers to the total energy contained within a molecule. This energy accounts for all interactions between atoms, including bonding and non-bonding interactions. Molecules can often be represented by multiple resonance structures, each with a distinct energy level. The stability of each resonance structure is inversely proportional to its energy — lower energy structures are more stable. When comparing structures, the one with the lowest energy is the most stable and significantly contributes to the actual structure of the molecule. Understanding molecular structure energy is key to predicting molecular behavior, stability, and reactivity.

bond energy

Bond energy is the measure of the amount of energy required to break one mole of bonds in a substance to separate it into individual atoms. This concept is fundamental in understanding chemical reactions and molecular stability. Higher bond energies indicate stronger bonds, contributing to overall molecular stability. In the context of the given problem, bond energy helps in understanding the resonance energy by comparing the experimental bond energy (E_{0}) and energies of different structures (E_{1}, E_{2}, E_{3}). The experimental bond energy often reflects the actual observed stability, influenced by resonance and the collective contribution of all possible structures.

chemical stability

Chemical stability refers to the likelihood of a chemical substance to maintain its original structure and not change to another form spontaneously. It involves the molecule's tendency to resist decomposition or reaction under normal conditions. Factors influencing chemical stability include molecular structure energy, bond energy, and resonance energy. Resonance stabilization particularly enhances chemical stability as it lowers the overall energy of the molecule, making it less reactive and more stable. In the given problem, the resonance energy calculation shows how much more stable the molecule is due to resonance compared to its most stable individual structure.