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 \(109^{\circ}\), respec- tively. Explain this variation in hond

Short answer

The variation in H-N-H bond angles in NH2-, NH3, and NH4+ is due to the differences in their molecular shapes, which are determined by the number of bonding and nonbonding electron pairs around the nitrogen atom according to VSEPR theory. In NH2-, the bent molecular shape with 2 nonbonding electron pairs results in a smaller angle of \(105^{\circ}\). In NH3, the trigonal pyramidal shape with 1 nonbonding electron pair leads to a slightly larger angle of \(107^{\circ}\). Finally, in NH4+, the tetrahedral shape with no nonbonding electron pairs gives a symmetric angle of \(109^{\circ}\).

Step-by-step solution

Determine the number of electron pairs around the central nitrogen atom

In each species, we'll first identify the total number of valence electron pairs around the central nitrogen atom, then separate that into bonding and nonbonding electron pairs. 1. NH2-: Nitrogen has 5 valence electrons, and each hydrogen atom has 1 valence electron. One additional electron is present due to the negative charge. Therefore, there are a total of 5 + 2 + 1 = 8 valence electrons. There are 2 bonding electron pairs and 2 nonbonding electron pairs. 2. NH3: Nitrogen still has 5 valence electrons, and there are 3 hydrogen atoms. This gives us a total of 5 + 3 = 8 valence electrons. There are 3 bonding electron pairs and 1 nonbonding electron pair. 3. NH4+: Nitrogen still has 5 valence electrons, and there are 4 hydrogen atoms. However, due to the positive charge, we lose 1 electron. This gives us a total of 5 + 4 - 1 = 8 valence electrons. There are 4 bonding electron pairs and 0 nonbonding electron pairs.

Determine the electronic geometry and molecular shape according to VSEPR theory

Now that we know the number of bonding and nonbonding electron pairs, we can use VSEPR theory to determine the electronic geometry and molecular shape of each species. 1. NH2-: With 2 bonding pairs and 2 nonbonding pairs, the electronic geometry is tetrahedral, and the molecular shape is bent. 2. NH3: With 3 bonding pairs and 1 nonbonding pair, the electronic geometry is still tetrahedral, but the molecular shape is now trigonal pyramidal. 3. NH4+: With 4 bonding pairs and 0 nonbonding pairs, both the electronic geometry and the molecular shape are tetrahedral.

Relate the bond angles to the molecular shapes

Now, let's explain the variation in H-N-H bond angles based on the molecular shapes we found in Step 2. 1. NH2-: In the bent molecular shape, the nonbonding electron pairs occupy more space and push the bonding electron pairs closer together. This results in a smaller H-N-H bond angle of \(105^{\circ}\). 2. NH3: In the trigonal pyramidal shape, there is only one nonbonding electron pair, so there's less repulsion on the bonding electron pairs than in the bent shape. This leads to a slightly larger H-N-H bond angle of \(107^{\circ}\). 3. NH4+: In the tetrahedral shape, there are no nonbonding electron pairs, and the bonding pairs are evenly spaced around the central atom, giving a symmetric H-N-H bond angle of \(109^{\circ}\). In conclusion, the variation in H-N-H bond angles in NH2-, NH3, and NH4+ is due to the differences in their molecular shapes, which are determined by the number of bonding and nonbonding electron pairs around the nitrogen atom according to VSEPR theory.

Key concepts

Molecular Shapes

Molecular shapes are essential in understanding how molecules interact and behave in different environments. Using the VSEPR theory (Valence Shell Electron Pair Repulsion), we can predict these shapes by looking at the number and types of electron pairs surrounding a central atom. This theory posits that electron pairs, both bonding and nonbonding, repel each other and arrange themselves to minimize their mutual repulsion.

• In \(\text{NH extsubscript{2} extsuperscript{-}}\), the shape is bent because there are two bonding pairs and two nonbonding pairs of electrons. The nonbonding pairs repel the bonding pairs more strongly, causing the shape to bend.
• For \(\text{NH extsubscript{3}}\), the shape is trigonal pyramidal. Here, the nitrogen is surrounded by three hydrogen atoms and one lone pair. The lone pair's presence slightly distorts the arrangement, forming this pyramidal shape.
• With \(\text{NH extsubscript{4} extsuperscript{+}}\), the shape is tetrahedral. All electron pairs are bonding, so they spread out symmetrically in three dimensions, creating a balanced tetrahedral shape.

Understanding these shapes helps in predicting the molecules' reactivity and interaction, highlighting why small changes in electron pair arrangements lead to different molecular geometries.

Bond Angles

Bond angles are a direct consequence of the molecular shapes determined by the VSEPR theory. They dictate how far apart atoms in a molecule are from each other. In nitrogen compounds, the nitrogen center is often a key player in defining these angles.
The differences in the bond angles among \(\text{NH extsubscript{2} extsuperscript{-}}\), \(\text{NH extsubscript{3}}\), and \(\text{NH extsubscript{4} extsuperscript{+}}\) reflect the varying electron pair arrangements:

• In \(\text{NH extsubscript{2} extsuperscript{-}}\), angular repulsion between two lone pairs results in a smaller bond angle of \(105^{\circ}\). The lone pairs exert a higher repulsive force compared to bonding pairs, compressing the angle.
• With \(\text{NH extsubscript{3}}\), there is only one lone pair, leading to less compression of the bond angles, resulting in a slightly larger angle of \(107^{\circ}\).
• For \(\text{NH extsubscript{4} extsuperscript{+}}\), the tetrahedral shape with no lone pairs means the bond angles are an ideal \(109^{\circ}\), as all electron pairs spread out equally due to uniform repulsion forces.

These subtle differences impact the compounds' physical and chemical properties, guiding us in when analyzing chemical reactions and properties.

Nitrogen Compounds

Nitrogen compounds play a vital role in both chemistry and life sciences. These compounds highlight how nitrogen's valence electrons greatly influence molecular behaviors. With five valence electrons, nitrogen forms interesting compounds like \(\text{NH extsubscript{2} extsuperscript{-}}\), \(\text{NH extsubscript{3}}\), and \(\text{NH extsubscript{4} extsuperscript{+}}\). Each provides a unique example of how nitrogen interacts with other elements.

• \(\text{NH extsubscript{2} extsuperscript{-}}\), or amide ion, contains additional electron which increases electron-electron repulsion, influencing its molecular shape.
• \(\text{NH extsubscript{3}}\) or ammonia, represents a fundamental nitrogen compound essential in fertilizers and many industrial processes. Its geometry facilitates hydrogen bonding, making it a solvent in certain reactions.
• The ammonium ion, \(\text{NH extsubscript{4} extsuperscript{+}}\), is a product of acids reacting with ammonia. Its tetrahedral shape and balanced electron distribution make it stable and widely used in fertilizers.

These compounds demonstrate nitrogen's versatility, from influencing environmental dynamics to enabling life-sustaining processes.