(a) What are the \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angles in diamond? (b) What are they in graphite (in one sheet)? (c) What atomic orbitals are involved in the stacking of graphite sheets with each other?

The carbon atoms in diamond are arranged in a tetrahedral structure, where each carbon atom is bonded to four other carbon atoms. This arrangement results in a three-dimensional network with each bond having equal length and bond angle.

In diamond, the bond angle can be calculated using the tetrahedral angle formula. The tetrahedral angle is given by: \[\cos^{-1}\left(\frac{-1}{3}\right) \approx 109.47^{\circ}\] So, the \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angle in diamond is approximately 109.47 degrees.

Graphite has a layered structure, where carbon atoms are arranged in a hexagonal pattern within each sheet, and these sheets are stacked on top of each other. Each carbon atom in the sheet is bonded to three other carbon atoms within the same sheet, and these bonds create a planar structure.

As the carbon atoms in graphite sheets are arranged in a hexagonal pattern, the bond angle between them can be calculated using the hexagonal angle formula. The hexagonal angle is given by: \[180^{\circ} - \frac{360^{\circ}}{6} = 120^{\circ}\] So, the \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angle in one graphite sheet is 120 degrees.

The atomic orbitals involved in the bonding within a single graphite sheet are sp2 hybridized orbitals, as each carbon atom forms three sigma bonds with its neighboring carbon atoms. The remaining unhybridized p-orbitals (2pz orbitals) are responsible for the weak interactions between graphite sheets. These interactions are known as van der Waals forces or London dispersion forces. In summary: (a) The \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angle in diamond is approximately 109.47 degrees. (b) The \(\mathrm{C}-\mathrm{C}-\mathrm{C}-\mathrm{C}\) bond angle in one graphite sheet is 120 degrees. (c) The atomic orbitals involved in the stacking of graphite sheets are the unhybridized p-orbitals (2pz orbitals) that form weak van der Waals forces between the sheets.