Question

The three species \(\mathrm{NH}_{2}^{-}, \mathrm{NH}_{3}\), and \(\mathrm{NH}_{4}^{+}\) have \(\mathrm{H}-\mathrm{N}-\mathrm{H}\) bond angles of \(105^{\circ}, 107^{\circ}\), and \(109^{\circ}\), respectively. Explain this variation in bond angles.

Short answer

The variation in H-N-H bond angles among NH₂⁻, NH₃, and NH₄⁺ can be explained by the differences in electron pair repulsions due to the presence of lone pairs on the nitrogen atom. In NH₂⁻, two lone pairs cause a greater repulsive effect, resulting in a bond angle of \(105^\circ\). In NH₃, one lone pair causes a slightly decreased bond angle of \(107^\circ\). In NH₄⁺, without any lone pairs, the bond angle is very close to the ideal tetrahedral angle of \(109^\circ\).

Step-by-step solution

Determine the electron pair geometry of each species

To start, we need to determine the electron pair geometries of the three species. We do this by counting the total number of electron pairs (both bonding and lone pairs) around the nitrogen atom and then identifying the corresponding geometry. - In NH₂⁻, nitrogen has two bonding pairs (with the two hydrogen atoms) and two lone pairs. This gives us a total of 4 electron pairs, resulting in a tetrahedral electron pair geometry. - In NH₃, nitrogen has three bonding pairs (with the three hydrogen atoms) and one lone pair. This also gives us a total of 4 electron pairs, resulting in a tetrahedral electron pair geometry. - In NH₄⁺, nitrogen has four bonding pairs (with the four hydrogen atoms) and no lone pairs. This gives us a total of 4 electron pairs, again resulting in a tetrahedral electron pair geometry.

Relate electron pair repulsion to bond angles

Now that we have the electron pair geometry for each species, we can explain the variation in H-N-H bond angles using the Valence Shell Electron Pair Repulsion (VSEPR) theory. The VSEPR theory states that electron pairs around a central atom repel each other, and these repulsions affect the shape and bond angles of the molecule. In a perfect tetrahedral geometry (e.g., methane, CH₄), the bond angle is \(109.5^\circ\), which is the ideal angle that minimizes electron pair repulsion. However, in our three species, the presence of lone pairs introduces additional repulsion that causes deviations from the ideal tetrahedral bond angle.

Explain the variation in bond angles

Now that we understand the electron geometries and the effect of lone pairs on bond angles, we can explain the variation in H-N-H bond angles for the three species: - In NH₂⁻, there are two lone pairs and two bonding pairs on the nitrogen atom. Lone pairs occupy more space and have a greater repulsive effect than bonding pairs. This causes the two bonding pairs to be pushed slightly closer together, resulting in a decreased H-N-H bond angle of \(105^\circ\). - In NH₃, there is one lone pair and three bonding pairs on the nitrogen atom. The lone pair again occupies more space and has a greater repulsive effect on the bonding pairs. This causes the bonding pairs to be pushed somewhat closer together, resulting in a slightly decreased H-N-H bond angle of \(107^\circ\). - In NH₄⁺, there are no lone pairs and four bonding pairs on the nitrogen atom. Without any lone pairs, the repulsion between the bonding pairs is minimized, and the H-N-H bond angle is very close to the ideal tetrahedral angle of \(109^\circ\). In conclusion, the variation in H-N-H bond angles among NH₂⁻, NH₃, and NH₄⁺ can be explained by the differences in electron pair repulsions due to the presence of lone pairs on the nitrogen atom. Lone pairs have a greater repulsive effect, causing the bond angles to deviate from the ideal tetrahedral angle of \(109.5^\circ\).

Key concepts

Electron Pair Geometry

Understanding the electron pair geometry is fundamental when exploring the structure of molecules.
It refers to the spatial arrangement of electron pairs (both bonding and non-bonding) around a central atom. These electron pairs can be thought of as occupying 'slots' around the atom, with each pair trying to be as far apart from the others as possible, to minimize repulsion.

In the case of NH₂^-, NH₃, and NH₄⁺, although they all have different numbers of bonding and lone pairs, the total number of electron pairs is the same. This total dictates that the electron pair geometry is tetrahedral. In a perfect tetrahedron, the angles between the electron pairs would be exactly 109.5 degrees.

However, the presence of lone pairs, which take up more space than bonding pairs, distorts this perfect geometry, affecting bond angles in a predictable way according to the Valence Shell Electron Pair Repulsion (VSEPR) theory.

Lone Pair Repulsion

Lone pair repulsion plays a pivotal role in determining the shape of a molecule.
Lone pairs are essentially pairs of electrons that are not involved in bonding and remain as localized electron clouds on an atom. These pairs are subject to repulsion from other electron pairs, but they have distinct characteristics: they occupy more space than bonding pairs and exert a stronger repulsive force.

This larger amount of space is not just a result of the electron cloud's size but also because lone pairs are closer to the nucleus and thus spread out more, compared to the electron density in a bond that is shared between two nuclei.

The Repulsive Hierarchy

Lone pair-lone pair (lp-lp) repulsions are stronger than lone pair-bonding pair (lp-bp) repulsions, which in turn are stronger than bonding pair-bonding pair (bp-bp) repulsions. This hierarchy is essential for predicting the shapes of molecules and understanding how the presence of lone pairs can lead to smaller bond angles in geometry.

H-N-H Bond Angle Variation

The H-N-H bond angle variation between NH₂^-, NH₃, and NH₄⁺ is a clear demonstration of how lone pairs affect molecular geometry.
Starting with the NH₂^- ion, with two lone pairs exerting strong repulsion, the bond angle is reduced to 105 degrees. As we move to NH₃, with one lone pair, the bond angle is slightly larger, 107 degrees, because the lone pair-bonding pair repulsion is less intense than the lone pair-lone pair repulsion present in NH₂^-.

Finally, for NH₄⁺, there are no lone pairs, and the bonding pairs are equally repelled in a tetrahedral arrangement resulting in a bond angle of 109 degrees, which is very close to the ideal tetrahedral angle.
This demonstrates how through the VSEPR theory, the number and type of electron pairs can predict the accurate molecular geometry and bond angles, revealing the remarkable consistency and predictability of molecular shapes.