Question

The molecule tetraborane has the formula \(\mathrm{B}_{4} \mathrm{H}_{10}\) (a) Show that this is an electron-deficient molecule. (b) How many bridge bonds must occur in the molecule? (c) Show that butane, \(\mathrm{C}_{4} \mathrm{H}_{10},\) is not electron deficient.

Short answer

(a) Tetraborane is electron deficient because it has 22 electrons, enough for only 11 bonds, even though a total of 13 are required. (b) Two 3-center-2-electron bonds must occur in the molecule. (c) Butane is not electron deficient because it has 26 electrons, enough for the 13 bonds required for all atoms.

Step-by-step solution

Determine Electron number for Tetraborane

Tetraborane has 4 boron atoms, each with 3 valence electrons and 10 hydrogen atoms each with a single electron, thus it in total has \(4*3 + 10*1=22\) electrons. This amount should be enough for a total of \(22/2= 11 \) bonds.

Compare to Required Bonds

Tetraborane molecule has 14 atoms, and so if each atom were to form a two-electron bond, they would require a total of \(14-1= 13 \) bonds. As calculated in step 1, only 11 bonds worth of electrons are available. Hence, tetraborane is electron deficient.

Calculate Bridge Bonds

As tetraborane is electron deficient, it must have less 2-center-2-electron bonds and more of 3-center-2-electron or bridge bonds. Given that two 3-center-2-electron bonds replace three 2-center-2-electron bonds, the total number of 3-center-2-electron bonds must be equal to \(13 - 11 = 2\) bonds.

Determine Electron number for Butane

Butane carries 4 carbon atoms each providing 4 valence electrons and 10 hydrogen atoms each providing 1 valence electron. Therefore, the total number of electrons in butane is \(4 * 4 + 10 * 1 = 26 \) . This provides \(26/2=13 \) 2-electron bonds.

Compare to Required Bonds for Butane

Butane carries 14 atoms and if each atom needs a 2-electron bond, the total number of bonds required is \(14-1= 13 \). Thus butane has enough electrons for each atom to engage in a 2-electron bond, and it is not electron deficient.

Key concepts

Tetraborane

Tetraborane is a fascinating compound with the chemical formula \( \mathrm{B}_{4} \mathrm{H}_{10} \). It consists of four boron atoms and ten hydrogen atoms. This compound is unique because it is electron deficient. An electron-deficient compound does not have enough electrons to form the standard version of covalent bonds between all its atoms.
Tetraborane is different from conventional molecules that have enough electrons to form bonds with all atoms perfectly paired. In tetraborane, the total number of electrons can make only 11 conventional pairs of electrons, or bonds, because it has 22 electrons. However, with 14 atoms, it would ideally need 13 bonds if each bond were like a typical 2-center-2-electron bond. The shortage points to its electron deficiency.

Bridge Bonds

Bridge bonds are a fascinating aspect of tetraborane's structure, particularly the '3-center-2-electron bonds.' These bonds are specially adapted to address electron shortages in electron-deficient molecules like tetraborane. In a bridge bond, two electrons are shared among three atoms, rather than a traditional bond where two electrons are shared between just two atoms.
This method of bonding allows tetraborane to stabilize its structure despite not having enough electrons for every pair of atoms to share. The molecule of tetraborane compensates for its electron deficiency with these bridge bonds, allowing it to maintain structural integrity.

Butane

Butane, written as \( \mathrm{C}_{4} \mathrm{H}_{10} \), is a simple saturated hydrocarbon that does not share the electron deficiency issue found in tetraborane. With four carbon atoms, each having four valence electrons, and ten hydrogen atoms providing one valence electron each, it totals 26 valence electrons.
This number is sufficient to provide 13 two-electron bonds needed for a fully saturated bond structure with no deficiency. Each atom forms enough bonds to satisfy its bonding requirements completely, making butane electron-efficient.

Valence Electrons

Valence electrons are crucial in determining the bonding capacities and behaviors of molecules like tetraborane and butane. They are the electrons found in the outermost shell of an atom and are responsible for forming bonds with other atoms.
In tetraborane, boron atoms each contribute three valence electrons and hydrogen contributes one. In total, this sums up to 22 electrons in the tetraborane molecule for bonding purposes.
Comparatively, in butane, carbon atoms supply four valence electrons, and hydrogen supplies one, leading to a total of 26 electrons. This sufficient number allows butane to form necessary bonds without any shortages.

2-center-2-electron Bonds

A 2-center-2-electron bond is the most common type of chemical bond, also known simply as a covalent bond. In these bonds, each involved center, or atom, shares two electrons, allowing them to join.
In a stable molecule with sufficient electrons, like butane, atoms bond directly with enough electrons for each central pair, resulting in stable structures. These bonds are straightforward because they involve a pair of electrons shared just between two atoms.

3-center-2-electron Bonds

The 3-center-2-electron bonds are an inventive solution for electron-deficient molecules. In these bonds, one pair of electrons is shared between three atoms, rather than just two, enabling a reduction in the number of electrons required to maintain a stable bond structure.
These bonds are crucial for molecules like tetraborane because they adjust to the available electrons and ensure that stability is achieved. This adjustment allows tetraborane to balance its structural needs without requiring all atoms to contribute to the ideal configurations typical in non-deficient molecules.