Problem 200 - A Complete Resource Book in Chemistry for JEE Main

Question

The structure of diborane \(\left(\mathrm{B}_{2} \mathrm{H}_{6}\right)\) contains \(\quad[\$ (a) four \)2 \mathrm{c}-2 \mathrm{e}\( bonds and two \)3 \mathrm{c}-2 \mathrm{e}\( bonds (b) two \)2 \mathrm{c}-2 \mathrm{e}\( bonds and four \)3 \mathrm{c}-2 \mathrm{e}\( bonds (c) two \)2 \mathrm{c}-2 \mathrm{e}\( bonds and two \)3 \mathrm{c}-3 \mathrm{e}\( bonds (d) four \)2 \mathrm{c}-2 \mathrm{e}\( bonds and four \)3 \mathrm{c}-2 \mathrm{e}$ bonds

Step-by-Step Solution

Answer

Option (a): four 2c-2e bonds and two 3c-2e bonds.

Step 1: Understanding the Terms

In the context of chemical bonding, a '2c-2e bond' refers to a two-center, two-electron bond, which is a traditional single covalent bond between two atoms. Meanwhile, a '3c-2e bond' (three-center, two-electron bond) involves three atoms sharing two electrons, often seen in electron-deficient compounds like diborane (B_2H_6).

Step 2: Analyze Diborane Structure

Diborane (B_2H_6) consists of two boron atoms and six hydrogen atoms. The molecule features two types of hydrogen atoms: terminal and bridging hydrogens. The terminal hydrogens form regular covalent bonds with boron atoms, whereas the bridging hydrogens form unusual three-center, two-electron bonds with the boron atoms.

Step 3: Count the 2c-2e Bonds

Each boron atom in diborane forms two covalent 2c-2e bonds with two terminal hydrogen atoms. Thus, four 2c-2e bonds exist in total (two per boron).

Step 4: Count the 3c-2e Bonds

The four hydrogen atoms that are part of the bridge form four 3c-2e bonds with the two boron atoms in diborane. Each bridge involves one hydrogen atom sharing its electron with two boron atoms, completing the bond structure.

Step 5: Verify Against Options

From the analysis, diborane contains four 2c-2e bonds and two 3c-2e bonds (each bridge counting as a pair of 3c-2e bonds on its own since both bridges together constitute four 3c-2e interactions). This matches option (a).

Key Concepts

2c-2e Bond

In chemistry, a 2c-2e bond stands for a two-center, two-electron bond. This is the simplest type of covalent bond you can encounter. Picture it as a marriage between just two atoms sharing a pair of electrons. Both atoms contribute one electron to this bond, creating a stable, balanced structure. In diborane (220 6), this bond occurs between each boron atom and its terminal hydrogen atom. The concept is straightforward:

• Two atoms involved
• Each atom shares one electron
• Forms a classic covalent bond

This type of bonding is what forms the backbone of many molecules, ensuring all atoms achieve a more stable electron configuration.

3c-2e Bond

A 3c-2e bond stands for a three-center, two-electron bond, and it's a bit more complex. Imagine three atoms coming together but sharing only two electrons among them. This type of bond is less common and found in molecules that are electron-deficient, like diborane (220 6). In diborane, this idiosyncratic bond involves two boron atoms and one bridging hydrogen atom.

• Three atoms sharing two electrons
• Helps stabilize structures with fewer available electrons
• Found in electron-deficient compounds

The bridge hydrogen acts as a connector between the two boron atoms, holding them together with shared electrons despite there being fewer electrons than needed for traditional single bonds. This results in a unique and fascinating molecular bonding circumstance.

Electron-deficient Compounds

Electron-deficient compounds, such as diborane, are intriguing because they don't follow the standard rules for covalent bonding. In these compounds, there are not enough electrons to form traditional two-electron bonds for each pair of atoms. Despite this shortfall, they manage to maintain structure and stability through multi-centered bonds like the 3c-2e bond.

• Have fewer electrons than needed for conventional bonding
• Employ unusual bonding techniques for stability
• Often involve lightweight atoms like boron and hydrogen

This electron deficiency leads to the formation of bonds that might seem counterintuitive if you're strictly thinking of two atoms sharing two electrons. It invites curiosity and exploration into how atoms can creatively bond to maintain stability.

Covalent Bonding

Covalent bonding is a central concept in chemistry, covering the sharing of electrons between atoms. It's what gives molecules their form and function. Even in more complex structures like diborane, covalent bonds are at work, although in unconventional ways.

• Involves the sharing of electrons
• Primarily between nonmetals, like boron and hydrogen
• Comprises both standard two-center, two-electron bonds and the unusual three-center, two-electron bonds

In diborane, the combination of standard covalent bonding with multi-center bonds illustrates the flexibility and diversity of covalent interactions, ensuring that even in challenging electron environments, atoms can effectively bond to form stable compounds.