Problem 34 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following is a false statement? (a) boron hydrides are formed when dil. HCl reacts with \(\mathrm{Mg}_{3} \mathrm{~B}_{2}\) (b) all the B -H bond distances in \(\mathrm{B}_{2} \mathrm{H}_{6}\) are equal (c) \(\mathrm{BH}_{3}\) is not a stable compound (d) the boron hydrides are readily hydrolyzed

Step-by-Step Solution

Answer

The false statement is (b) because not all B-H bond distances in \( \mathrm{B}_{2} \mathrm{H}_{6} \) are equal.

Step 1: Analyze statement (a)

Statement (a) says that boron hydrides are formed when dilute HCl reacts with \( \mathrm{Mg}_{3} \mathrm{~B}_{2} \). This is true because \( \mathrm{Mg}_{3} \mathrm{~B}_{2} \) reacts with acids to form boron hydrides. Thus, statement (a) is true.

Step 2: Analyze statement (b)

Statement (b) claims that all the B-H bond distances in \( \mathrm{B}_{2} \mathrm{H}_{6} \) are equal. In \( \mathrm{B}_{2} \mathrm{H}_{6} \) (diborane), there are two types of B-H bonds: the terminal B-H bonds are normal while the bridging B-H bonds are longer. Therefore, this statement is false.

Step 3: Analyze statement (c)

Statement (c) states that \( \mathrm{BH}_{3} \) is not a stable compound. This is true because \( \mathrm{BH}_{3} \) is highly reactive and tends to form dimers like \( \mathrm{B}_{2} \mathrm{H}_{6} \). Thus, statement (c) is true.

Step 4: Analyze statement (d)

Statement (d) says that boron hydrides are readily hydrolyzed. This is true as boron hydrides, such as diborane, react exothermically with water. Thus, statement (d) is true.

Key Concepts

Diborane

Diborane, with the formula \( \mathrm{B}_{2} \mathrm{H}_{6} \), is one of the simplest boron hydrides and is often used as a starting material in chemical reactions. Unlike many other hydrides, diborane is a dimer consisting of two boron atoms and six hydrogen atoms. The structure is characterized by four terminal hydrogen atoms bonded to the boron atoms and two bridging hydrogen atoms that connect both boron atoms. This unique configuration is known as a three-center two-electron bond and distinguishes diborane from many other chemical compounds in bonding nature.
The boron atoms are sp\(^3\) hybridized, resulting in a complex structural arrangement that contributes to its reactivity and instability compared to other simple hydrides.

• Used in organic synthesis such as hydroboration reactions.
• Highly flammable and requires careful handling due to its ability to ignite spontaneously in moist air.

B-H Bond Distances

In diborane, the bond distances between boron and hydrogen differ based on their positions in the molecule. The intricacies of these bond distances are crucial when studying the physical and chemical properties of diborane. Two types of bonds are present:

• Terminal B-H bonds: These are single bonds from a boron directly to a hydrogen atom, having a typical bond length of about 1.19 angstroms.
• Bridging B-H bonds: These connect two boron atoms via one hydrogen atom, creating a unique bond known as a banana bond due to its curved shape and longer bond length, about 1.33 angstroms.

These variations in bond lengths indicate a difference in electron distribution among the hydrogen atoms, which influences the molecule's overall stability and reactivity. The distinction in bond distances highlights the complexity of diborane's bonding model compared to simpler hydrides. Understanding these differences is critical for predicting reactions involving boron hydrides.

Reactivity of BH3

Boron trihydride, \( \mathrm{BH}_{3} \), although a hypothetical molecule in gas phase, plays an important role in chemistry as the simplest boron hydride. In practice, \( \mathrm{BH}_{3} \) is rarely isolated because it is highly reactive and unstable, primarily existing as a part of dimers like diborane \( \mathrm{B}_{2} \mathrm{H}_{6} \). Its reactivity stems from boron’s electron deficiency, giving the molecule a strong tendency to polymerize or bond with other atoms to achieve a stable electronic configuration.
This high reactivity means that \( \mathrm{BH}_{3} \) is not typically found on its own. Instead, it is stabilized in complexes such as those with ethers or amines, known as borane adducts. These adducts are important in industrial and laboratory applications such as hydroboration, a process that adds boron and hydrogen across alkenes to form organoboranes.

• Boron trihydride's instability is utilized to form valuable chemical bonds in synthesis.
• Its reactivity is a key feature in organic transformations and reduction reactions.

Hydrolysis of Boron Hydrides

Boron hydrides, including compounds like diborane, are known for their reactivity with water. When these hydrides undergo hydrolysis, they react exothermically, or heat is released, producing boric acid and hydrogen gas.
These reactions are significant for understanding the chemistry of boron and its behavior in aqueous environments. For instance, diborane reacts with water as:
\[ \mathrm{B}_{2} \mathrm{H}_{6} + 6 \mathrm{H}_2\mathrm{O} \rightarrow 2 \mathrm{H}_{3}\mathrm{BO}_{3} + 6 \mathrm{H}_2 \]
This equation illustrates not only the generation of hydrogen gas, which can be harnessed as a green fuel but also shows the formation of boric acid, an essential industrial chemical. Due to this hydrolytic behavior, handling and storage conditions for boron hydrides must be meticulously controlled to prevent unwanted reactions. Understanding the hydrolysis of boron hydrides is pivotal for both safety and the exploration of new applications in sustainable energy and chemistry.