Question

(a) Which geometry and central atom hybridization would you expect in the series \(\mathrm{BH}_{4}^{-}, \mathrm{CH}_{4}, \mathrm{NH}_{4}^{+}\)? (b) What would you expect for the magnitude and direction of the bond dipoles in this series? (c) Write the formulas for the analogous species of the elements of period 3 ; would you expect them to have the same hybridization at the central atom?

Short answer

(a) All three molecules, BH₄⁻, CH₄, and NH₄⁺, have a tetrahedral geometry and sp³ hybridization at the central atom. (b) The bond dipoles in all three molecules have small electronegativity differences and are symmetrical, resulting in a net dipole moment of zero. (c) The analogous species for Period 3 elements are AlH₄⁻, SiH₄, and PH₄⁺. They all have the same tetrahedral molecular geometry and sp³ hybridization at the central atom.

Step-by-step solution

Geometry and hybridization of BH₄⁻

To determine the molecular geometry of BH₄⁻, first count the number of electron pairs around the central B atom (1 bond pair for each hydrogen and 1 lone pair). Since there are 4 electron pairs, BH₄⁻ has a tetrahedral geometry. The hybridization of the B atom is therefore sp³.

Geometry and hybridization of CH₄

Similar to BH₄⁻, CH₄ has 4 bond pairs around the central C atom, so it also has a tetrahedral geometry and sp³ hybridization.

Geometry and hybridization of NH₄⁺

NH₄⁺ has four bond pairs around the central N atom, giving it a tetrahedral geometry and sp³ hybridization like the other two molecules. 2. Bond dipoles:

Bonds in BH₄⁻

The electronegativity difference between B (2.04) and H (2.20) is small, and since all bonds are symmetrical around the central atom, the net dipole moment of BH₄⁻ is zero.

Bonds in CH₄

The electronegativity difference between C (2.55) and H (2.20) is also small, and the bonds are symmetric, so the net dipole moment of CH₄ is zero as well.

Bonds in NH₄⁺

Like the other two molecules, the electronegativity difference between N (3.04) and H (2.20) is small and the bonds are symmetrical, so the net dipole moment of NH₄⁺ is zero. 3. Analogy to Period 3 elements:

Analogous species in period 3

The analogous species for the elements of Period 3 would be: AlH₄⁻ (Aluminum Hydride ion), SiH₄ (Silicon Hydride), and PH₄⁺ (Phosphonium ion).

Hybridization of analogous species

AlH₄⁻ is similar to BH₄⁻, with the Al atom in the center bonding to four H atoms. It has a tetrahedral geometry and sp³ hybridization. SiH₄ is like CH₄, also with a tetrahedral geometry and sp³ hybridization. PH₄⁺, like NH₄⁺, has a tetrahedral geometry and sp³ hybridization. All of these Period 3 elements have analogous species with the same tetrahedral molecular geometry and sp³ hybridization at the central atom.

Key concepts

Tetrahedral Geometry

Tetrahedral geometry is a common molecular shape that results when a central atom forms four bonds directed towards the corners of a geometric tetrahedron. Picture this shape like a three-dimensional pyramid with a triangular base, where each of the three-dimensional lines sticking out from the center represents a bond.

• This structure results when there are four areas of electron density around the central atom.
• The angles between each pair of bonds in a perfect tetrahedral geometry are about 109.5 degrees.
• It's commonly observed in molecules like \( \text{CH}_4 \) (methane), where the central carbon atom is bonded to four hydrogen atoms symmetrically.

In the exercise provided, \( \text{BH}_4^- \), \( \text{CH}_4 \), and \( \text{NH}_4^+ \) all exhibit this tetrahedral geometry. This is due to each central atom having four bonds organized symmetrically in space.

Hybridization

Hybridization is a concept in chemistry used to explain the formation and arrangement of bonds in molecules. Through hybridization, atomic orbitals on the central atom mix to form new hybrid orbitals.

• For tetrahedral geometry, the hybridization state is \( ext{sp}^3 \). This denotes the mixing of one s and three p orbitals.
• This hybridization results in four equivalent hybrid orbitals, each participating in the formation of a sigma bond with hydrogen atoms, as seen in \( \text{CH}_4 \), \( \text{BH}_4^- \), and \( \text{NH}_4^+ \).
• The concept helps explain the observed bond angles and molecular shapes.

In our series, all molecules share this \( ext{sp}^3 \) hybridization at their central atom, resulting in uniform tetrahedral geometries.

Bond Dipoles

Bond dipoles occur when there is an electronegativity difference between two atoms bonded together. Electronegativity is a measure of an atom's ability to attract shared electrons. In molecules like \( \text{CH}_4 \) and \( \text{NH}_4^+ \), the electronegativity differences are minimal:

• For \( \text{CH}_4 \), carbon's electronegativity is 2.55, and hydrogen's is 2.20.
• This small difference means each C-H bond is slightly polar.
• However, the tetrahedral symmetry ensures that these bond dipoles cancel out, leading to a net dipole moment of zero.
• Similarly, \( \text{NH}_4^+ \) and \( \text{BH}_4^- \) have their individual bond dipoles cancel out due to their symmetrical bond arrangements.

Understanding bond dipoles is crucial in predicting whether a molecule is polar or nonpolar.

Electronegativity

Electronegativity is a fundamental chemical property that describes an atom's ability to attract and bind with electrons. It plays a crucial role in determining a molecule's polarity.

• A higher electronegativity means stronger pull on electron pairs, leading potentially to more polar bonds.
• When examining molecules like \( \text{NH}_4^+ \), \( \text{CH}_4 \), and \( \text{BH}_4^- \), slight differences in electronegativity between the central atoms and hydrogen contribute to small bond dipoles.
• However, the tetrahedral geometry minimizes the overall polarity as bond dipoles cancel out, leading to non-polar molecules.

In this way, electronegativity allows us to predict and explain molecular behavior and interaction.

Period 3 Elements

Period 3 elements in the periodic table include elements from sodium (Na) to argon (Ar). When considering analogs such as \( \text{AlH}_4^- \), \( \text{SiH}_4 \), and \( \text{PH}_4^+ \), these molecules can also adopt tetrahedral geometry and \( ext{sp}^3 \) hybridization:

• \( \text{SiH}_4 \) (silicon hydride) mirrors \( \text{CH}_4 \) in structure and hybridization.
• \( \text{AlH}_4^- \) functions similarly to \( \text{BH}_4^- \) with aluminum at the center.
• \( \text{PH}_4^+ \) bears resemblance to \( \text{NH}_4^+ \), showcasing a similar arrangement.

This demonstrates that period 3 elements can form molecules with geometries and properties akin to their period 2 counterparts, exhibiting analogous chemical behavior. Understanding this helps in predicting and drawing parallels between chemistry across different elemental periods.