Problem 60 - Chemistry Matter and Change

Question

Challenge For a \(\mathrm{NH}_{4}^{+}\) ion, identify its molecular shape, bond angle, and hybrid orbitals.

Step-by-Step Solution

Answer

The \(\mathrm{NH}_{4}^{+}\) ion has a tetrahedral shape, \(109.5^\circ\) bond angle, and \(sp^3\) hybrid orbitals.

Step 1: Identify the central atom and its valence electrons

The central atom in the ammonium ion, \(\mathrm{NH}_{4}^{+}\), is nitrogen (N). Nitrogen typically has 5 valence electrons. However, in \(\mathrm{NH}_{4}^{+}\), nitrogen shares electrons with four hydrogen atoms.

Step 2: Determine the charge and adjust electron count

Since \(\mathrm{NH}_{4}^{+}\) has a positive charge, this indicates the loss of one electron from the total valence electrons. Without this charge, there would be 5 (from N) + 1x4 (from each H) = 9 electrons, but we lose one due to the \(1^+\) charge.

Step 3: Use VSEPR theory to determine shape

According to the VSEPR (Valence Shell Electron Pair Repulsion) theory, \(\mathrm{NH}_{4}^{+}\) has four bonding pairs and no lone pairs. This leads to a tetrahedral shape.

Step 4: Determine bond angles

A tetrahedral molecular shape features bond angles of \(109.5^\circ\). Consequently, the \(\mathrm{H-N-H}\) bond angles in \(\mathrm{NH}_{4}^{+}\) are \(109.5^\circ\).

Step 5: Identify hybridization

The sp3 hybridization occurs when one s orbital and three p orbitals combine, which is found in the \(\mathrm{NH}_{4}^{+}\) ion due to the four equivalent \(\mathrm{N-H}\) bonds, indicating \(sp^3\) hybrid orbitals.

Key Concepts

Understanding Molecular Shape

Molecular shape refers to the 3D arrangement of atoms in a molecule. This arrangement is primarily influenced by the electron pair repulsion as explained by the VSEPR theory. For the ammonium ion, \(\mathrm{NH}_{4}^{+}\), the molecular shape is tetrahedral. This shape arises because four hydrogen atoms are symmetrically positioned around the nitrogen central atom. Each hydrogen atom connects to the nitrogen atom through a covalent bond.

The VSEPR theory suggests that electron pairs around a central atom will arrange themselves as far apart as possible to minimize repulsion. In the case of \(\mathrm{NH}_{4}^{+}\), the absence of lone pairs means only bond pairs are considered.

• This symmetrical distribution results in a geometric arrangement referred to as tetrahedral.
• This shape is common whenever a central atom forms four bonds.

Evaluating Bond Angles

Bond angles are crucial in determining the geometry of a molecule. In the tetrahedral shape of \(\mathrm{NH}_{4}^{+}\), the bond angles are found to be \(109.5^\circ\). This specific angle is a result of the symmetrical distribution of the hydrogen atoms around the nitrogen.

To understand why \(109.5^\circ\) is the bond angle in a tetrahedral shape:

• Imagine the hydrogen atoms spread out in 3D space, trying to stay as far from each other as possible, according to VSEPR theory.
• This results in equal bond angles, each exactly \(109.5^\circ\) apart from each other.

Such a configuration helps reduce electron pair repulsion, stabilizing the overall structure of the molecule.

Exploring sp3 Hybridization

Hybridization is a concept where atomic orbitals mix to form new hybrid orbitals, which influences bond formation. In \(\mathrm{NH}_{4}^{+}\), the nitrogen atom undergoes \(sp^3\) hybridization.

To break it down:

• Nitrogen starts with one s orbital and three p orbitals.
• These orbitals mix to form four equivalent \(sp^3\) hybrid orbitals.

Each \(sp^3\) orbital forms a covalent bond with a hydrogen atom, allowing for the four hydrogen atoms to evenly distribute around nitrogen in a tetrahedral arrangement.

The \(sp^3\) hybridization explains why the bonds in \(\mathrm{NH}_{4}^{+}\) are identical and contribute to the integrity of its tetrahedral shape.