Rank the structures in order of decreasing electrophilic strength and justify your ranking based on ...

To rank structures in order of decreasing electrophilic strength, we need to consider how easily an electrophile can accept a pair of electrons. Electrophilic strength is often associated with the presence of a positive charge or a partial positive charge on an atom, which makes it more susceptible to attack by nucleophiles. According to molecular orbital theory, the electrophilic strength of a molecule or ion is influenced by the energy and occupancy of its lowest unoccupied molecular orbital (LUMO). A lower energy LUMO indicates a stronger electrophile because it can more readily accept a pair of electrons.

Let's consider three hypothetical structures A, B, and C, and assume that they are all carbocations, which are common electrophiles in organic chemistry. The structures are as follows:

- Structure A: A primary carbocation (a carbon atom with a positive charge attached to one other carbon atom)
- Structure B: A secondary carbocation (a carbon atom with a positive charge attached to two other carbon atoms)
- Structure C: A tertiary carbocation (a carbon atom with a positive charge attached to three other carbon atoms)

Now, let's rank these structures in order of decreasing electrophilic strength:

1. Tertiary Carbocation (Structure C): This carbocation is the most stable due to hyperconjugation and inductive effects from the three alkyl groups attached to the positively charged carbon. These effects delocalize the positive charge, lowering the energy of the LUMO, making it a stronger electrophile.

2. Secondary Carbocation (Structure B): This carbocation is less stable than the tertiary carbocation because it has only two alkyl groups to stabilize the positive charge. Therefore, its LUMO is at a higher energy compared to the tertiary carbocation, making it a weaker electrophile than Structure C but still stronger than Structure A.

3. Primary Carbocation (Structure A): This carbocation is the least stable because it has only one alkyl group to stabilize the positive charge. As a result, its LUMO is at the highest energy among the three, making it the weakest electrophile.

In summary, the order of decreasing electrophilic strength based on molecular orbital theory and considering the stability of the carbocations is as follows:

$$\text{Tertiary Carbocation (C)}>\text{Secondary Carbocation (B)}>\text{Primary Carbocation (A)}$$

This ranking is justified by the stabilization provided by alkyl groups through hyperconjugation and inductive effects, which lower the energy of the LUMO, making the carbocation a stronger electrophile.