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 (a) four \(2 \mathrm{c}-2 \mathrm{e}\) bonds and two \(3 \mathrm{c}-2 \mathrm{e}\) bonds (b) two \(2 \mathrm{c}\)-2e 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 \(2 \mathrm{c}\)-2e bonds and four \(3 \mathrm{c}\)-2e bonds

Step-by-Step Solution

Answer

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

Step 1: Understand Different Bond Types

A 2-center-2-electron bond (2c-2e) is a conventional covalent bond where two electrons are shared between two atoms. A 3-center-2-electron bond (3c-2e) involves three atoms sharing two electrons, typically found in electron-deficient compounds like diborane.

Step 2: Visualize Diborane Structure

Diborane \(\mathrm{B}_2\mathrm{H}_6\) consists of two boron atoms and six hydrogen atoms. Each boron atom forms four bonds: two single bonds with terminal hydrogens and two bridging bonds with hydrogen atoms shared between both borons.

Step 3: Identify the Types of Bonds in Diborane

In \(\mathrm{B}_2\mathrm{H}_6\), there are four terminal B-H bonds. These are all 2-center-2-electron bonds because each consists of two electrons shared directly between a B and H atom. There are also two bridging hydrogens forming bonds with three atoms (B-H-B), which are 3-center-2-electron bonds.

Step 4: Match the Bond Types to Options

Given that there are four 2c-2e bonds (the B-H terminal bonds) and two 3c-2e bonds (the B-H-B bridging bonds), compare these findings with the answer choices. Option (a) states four 2c-2e bonds and two 3c-2e bonds, which matches our analysis.

Key Concepts

2-center-2-electron bond

When we talk about a 2-center-2-electron bond, we are referring to a type of chemical bond that is pretty straightforward and easy to understand. This is the classic covalent bond we often learn about in basic chemistry. In this bond, two electrons are shared between two atoms. Think of it like sharing a chocolate bar equally between two people. Each person gets an equal share, and both are satisfied!

Key points when understanding this concept include:

• It is the most common form of covalent bonding.
• It requires two electrons and involves just two atoms.
• This direct sharing results in a strong bond, giving the molecule stability.

In diborane (\(\mathrm{B}_2\mathrm{H}_6\)), the terminal B-H bonds are examples of 2-center-2-electron bonds. Here, each hydrogen is directly bonded to a boron atom with two electrons shared, one originating from each participating atom.

3-center-2-electron bond

In chemistry, a 3-center-2-electron bond is more complex but fascinating. These are found primarily in compounds known as electron-deficient compounds, like diborane. Here, three atoms share just two electrons. Yes, it's like trying to share that same chocolate bar not just between two, but three people. The outcome isn't as individually satisfying for all involved, yet it maintains the connection between them.

This bond type:

• Occurs often when electrons are insufficient for forming traditional 2c-2e bonds.
• Involves three atoms (often includes a bridging atom).
• Provides stability through a unique way of sharing.

In diborane, the 3-center-2-electron bond is seen in the bridging hydrogen atoms, which share these two electrons with two boron atoms (B-H-B). This makes diborane structurally stable even though it lacks the full electron count for typical covalent bonds.

Electron-deficient compounds

Electron-deficient compounds are intriguing because they don't follow the typical bonding principles many assume are universal. These compounds, including diborane, often lack a full set of electrons to form traditional bonds. This electron shortfall is what makes them distinct and often leads to unusual bonding situations, such as those involving 3-center-2-electron bonds.

Attributes of electron-deficient compounds:

• They often don't meet the octet rule because of fewer than needed electrons.
• Frequently, they employ unique bonding strategies (like 3c-2e bonds) to gain stability.
• They are commonly found in areas of chemistry involving complex hydrides and boron compounds.

Understanding electron-deficiency is key to understanding how compounds like diborane form and exhibit the properties they do.

Covalent bonds

Covalent bonds are the cornerstone of many chemical compounds, as they are formed when two atoms share a pair or more of electrons. These shared pairs ensure that each participating atom achieves a stable electron configuration, often fulfilling the octet rule—having eight electrons in the outermost shell for stability. However, exceptions exist, such as in electron-deficient compounds.

Important aspects of covalent bonds include:

• They can form single, double, or triple bonds, depending on the number of shared electron pairs.
• They are strong and usually lead to stable chemical structures.
• They are prevalent in organic molecules, making up the backbone of organic chemistry.

In diborane, covalent bonding can be observed in the 2-center-2-electron bonds between boron and terminal hydrogen atoms, stabilizing, albeit in an electron-deficient context. Understanding covalent bonds is crucial to understanding molecular structure and reactivity.