Problem 14 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following is the electron deficient molecule? (a) \(\mathrm{C}_{2} \mathrm{H}_{6}\) (b) \(\mathrm{B}_{2} \mathrm{H}_{6}\) (c) \(\mathrm{SiH}_{4}\) (d) \(\mathrm{PH}_{3}\)

Step-by-Step Solution

Answer

The electron-deficient molecule is ext{B}_{2} ext{H}_{6}.

Step 1: Understanding Electron Deficiency

An electron-deficient molecule is one that does not have enough electrons to form the standard two-electron bonds expected from their known chemical structure. Usually, these are compounds of elements that tend to follow the octet rule but cannot complete their octet in standard conditions.

Step 2: Examine Each Molecule for Electron Deficiency

We need to look at the electron configurations of the given molecules to identify the electron-deficient one. Let's review them one by one: - extbf{(a) } ext{In } ext{C}_{2} ext{H}_{6} ext{(ethane), carbon forms four bonds, each carbon is happy with a full octet.} - extbf{(b) } ext{In } ext{B}_{2} ext{H}_{6} ext{(diborane), boron usually has 3 valence electrons. Traditionally, it would seek 5 additional electrons to satisfy the octet rule, however, in B}_{2} ext{H}_{6}, it forms three bonds and is left electron-deficient as it cannot complete its octet.} - extbf{(c) } ext{In } ext{SiH}_{4} ext{(silane), silicon forms four single bonds, thus satisfying its octet.} - extbf{(d) } ext{In } ext{PH}_{3} ext{(phosphine), phosphorus forms three bonds and holds a lone pair, completing its octet.}

Step 3: Identify Electron Deficient Molecule

Based on the above analysis, diborane ( ext{B}_{2} ext{H}_{6}) is electron-deficient as each boron atom forms only three bonds and has only six electrons in its valence shell, thus lacking a full octet.

Key Concepts

Octet Rule

The octet rule is a fundamental principle in chemistry. It states that atoms tend to form bonds until they are surrounded by eight valence electrons, achieving a stable electron configuration similar to noble gases.
This rule explains many chemical bonding tendencies in molecules.
For example, in carbon, with four valence electrons, it needs four more to complete its octet. Hence, it forms four covalent bonds, like in methane \(\mathrm{CH}_{4}\).

• Limitations: The rule generally applies to main-group elements. However, some molecules, like certain transitioned metals or those involving elements like hydrogen, boron, and aluminum, do not comply fully.
• Systems and Exceptions: For small molecules like \(\mathrm{B}_{2}\mathrm{H}_{6}\) (diborane), octet completion is unachievable due to the inherent lack of electrons, leading to electron deficiency.

While the octet rule is a good guide, it's essential to recognize its limitations with certain compounds to understand their unique structures.

Diborane Structure

Diborane \(\mathrm{B}_{2}\mathrm{H}_{6}\) is a fascinating example of an electron-deficient compound due to its unique bonding approach. In this molecule, we see the formation of unusual 'three-center two-electron' bonds or 'bridge bonds.'
These are necessary to hold the atoms together despite lacking enough electrons to form ordinary covalent bonds.

• Diborane consists of two boron atoms each forming 4 hydride bonds: 2 regular hydrogen bonds and 2 bridge bonds.
• In these bonds, a pair of electrons is shared between three atoms instead of the usual two, a clear deviation from traditional octet rule bonding.

This structure is both an answer to diborane's electron deficiency and an interesting study of how molecular structures can adapt to fulfill bonding requirements.

Electron Configuration

Electron configuration describes the distribution of electrons in an atom's orbitals. This organization helps predict an atom's bonding behavior and chemical properties.
For elements like boron in diborane, the electron configuration can be illustrated as \(1s^2 2s^2 2p^1\).

• In a boron atom, only three electrons are in the valence shell, making it electron-deficient for octet completion.
• This scarcity of electrons is pivotal in determining boron's bonding pattern in molecules it forms.

The overall goal of observing electron configurations is to understand chemical reactivity and stability through electron arrangements, highlighting why some atoms, like boron in \(\mathrm{B}_{2}\mathrm{H}_{6}\), do not meet the octet rule and instead form specialized bonds.

Valence Electrons

Valence electrons are the outermost electrons that play a key role in forming chemical bonds.
Their number usually determines an atom's ability to follow the octet rule in bonding processes.

• For most elements, achieving a stable electron configuration involves gaining, losing, or sharing valence electrons.
• Boron, for example, has three valence electrons, insufficient for full octet formation.

In compounds such as \(\mathrm{B}_{2}\mathrm{H}_{6}\), this limitation leads to the creation of shared structures, compensating for their electron deficiency. Understanding how valence electrons engage in chemical interactions is critical to anticipating molecule behaviors and designing stable compounds.