Question

For each of the following molecules or ions, indicate the bond angle expected between the central atom and any two adjacent hydrogen atoms. a. \(\mathrm{H}_{2} \mathrm{O}\) b. \(\mathrm{NH}_{3}\) c. \(\mathrm{NH}_{4}^{+}\) d. \(\mathrm{CH}_{4}\)

Short answer

The bond angles between the central atom and two adjacent hydrogen atoms for the given molecules or ions are as follows: a. H2O: \(104.5^{\circ}\) b. NH3: \(107.3^{\circ}\) c. NH4+: \(109.5^{\circ}\) d. CH4: \(109.5^{\circ}\)

Step-by-step solution

Identifying the central atom in each molecule/ion

For each molecule/ion, identify the central atom. Here, the central atoms are: a. H2O: Oxygen (O) b. NH3: Nitrogen (N) c. NH4+: Nitrogen (N) d. CH4: Carbon (C)

Determine the electron-pair geometry for each molecule/ion

Determine the electron-pair geometry based on the VSEPR (Valence Shell Electron Pair Repulsion) theory. This theory states that electron pairs around a central atom will arrange themselves in a way to minimize repulsion between them. a. H2O: Oxygen has 2 bonding pairs (from two hydrogen atoms) and 2 lone pairs. According to VSEPR, the electron-pair geometry should be tetrahedral. b. NH3: Nitrogen has 3 bonding pairs (from three hydrogen atoms) and 1 lone pair. According to VSEPR, the electron-pair geometry should be tetrahedral. c. NH4+: Nitrogen has 4 bonding pairs (from four hydrogen atoms) and no lone pairs. According to VSEPR, the electron-pair geometry should be tetrahedral. d. CH4: Carbon has 4 bonding pairs (from four hydrogen atoms) and no lone pairs. According to VSEPR, the electron-pair geometry should be tetrahedral.

Determine the bond angle for each molecule/ion

Now that we know the electron-pair geometry for each molecule/ion, we can determine the bond angle between the central atom and adjacent hydrogen atoms. a. H2O: The electron-pair geometry is tetrahedral, but since there are two lone pairs, this results in a bent molecular geometry. The bond angle between the oxygen atom and two adjacent hydrogen atoms is approximately \(104.5^{\circ}\). b. NH3: The electron-pair geometry is tetrahedral with one lone pair, which results in a trigonal pyramidal molecular geometry. The bond angle between the nitrogen atom and two adjacent hydrogen atoms is approximately \(107.3^{\circ}\). c. NH4+: The electron-pair geometry is tetrahedral with no lone pairs, which results in a tetrahedral molecular geometry. The bond angle between the nitrogen atom and two adjacent hydrogen atoms is approximately \(109.5^{\circ}\). d. CH4: The electron-pair geometry is tetrahedral with no lone pairs, which results in a tetrahedral molecular geometry. The bond angle between the carbon atom and two adjacent hydrogen atoms is approximately \(109.5^{\circ}\). In summary: a. H2O: Bond angle = \(104.5^{\circ}\) b. NH3: Bond angle = \(107.3^{\circ}\) c. NH4+: Bond angle = \(109.5^{\circ}\) d. CH4: Bond angle = \(109.5^{\circ}\)

Key concepts

Molecular Geometry

Molecular geometry refers to the three-dimensional arrangement of atoms in a molecule. It is influenced by the number of bonding pairs and lone pairs of electrons surrounding the central atom. Understanding molecular geometry is crucial as it affects the molecule's physical and chemical properties, including reactivity and polarity.

• Bent Geometry: For example, in water (\(\mathrm{H}_{2}\mathrm{O}\)), the molecular geometry is described as bent. This occurs because the two lone pairs on oxygen repel the bonded hydrogen atoms, pushing them closer together.
• Trigonal Pyramidal Geometry: Ammonia (\(\mathrm{NH}_3\)) has this geometry, where one lone pair on nitrogen results in a pyramid-like shape with a flat base of three hydrogen atoms.
• Tetrahedral Geometry: Both methane (\(\mathrm{CH}_4\)) and the ammonium ion (\(\mathrm{NH}_4^+\)) exhibit tetrahedral geometry. Here, the central atom is bonded to four hydrogen atoms symmetrically, with no lone pairs involved.

These geometries are determined using VSEPR theory, which helps predict the arrangement that minimizes repulsion between electron pairs effectively.

Bond Angles

Bond angles are the angles between adjacent lines representing bonds in a molecule, crucially influencing molecular shape and properties. The value of bond angles is dictated by the minimizing of repulsions between electrons in bonded and unbonded pairs.

• Water (\(\mathrm{H}_{2}\mathrm{O}\)): The bond angle is approximately \(104.5^{\circ}\). This smaller angle results from the two lone pairs on oxygen, which exert additional repulsion on the hydrogen atoms, forcing them closer together.
• Ammonia (\(\mathrm{NH}_3\)): With a bond angle around \(107.3^{\circ}\), the lone pair on nitrogen slightly compresses the \(109.5^{\circ}\) angle expected from a perfect tetrahedral shape.
• Methane (\(\mathrm{CH}_{4}\)) and Ammonium Ion (\(\mathrm{NH}_4^+\)): The bond angles here are both \(109.5^{\circ}\), typical of a perfect tetrahedral geometry. With no lone pairs, there is uniform repulsion between identical bond pairs, maintaining the standard angle.

Understanding bond angles is essential in predicting molecular behavior and reactive tendencies.

Electron-Pair Geometry

Electron-pair geometry is the organization of electron pairs (bonding and lone pairs) around the central atom, which influences the molecular geometry. In VSEPR theory, electron pairs arrange to minimize repulsive forces between them, leading to predictable geometrical shapes.

• Tetrahedral Electron-Pair Geometry: This common geometry involves four regions of electron density. Examples include \(\mathrm{H}_2\mathrm{O}\), \(\mathrm{NH}_3\), \(\mathrm{CH}_4\), and \(\mathrm{NH}_4^+\), despite having different molecular geometries due to varying numbers of lone pairs.
• Influence of Lone Pairs: Lone pairs occupy more space than bonding pairs. This results in molecular shapes such as bent (\(\mathrm{H}_2\mathrm{O}\)) or trigonal pyramidal (\(\mathrm{NH}_3\)) because lone pairs compress bond angles more significantly.

Recognizing electron-pair geometry helps in understanding the foundational layout for molecular geometry and subsequent bond angle adjustments due to lone pairs.