Find the amount (in moles) of C-C bonds that must be broken when 1.0 mole of C(g) is formed from

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Find the amount (in moles) of C-C bonds that must be broken...

Find the amount (in moles) of $\mathrm{C}-\mathrm{C}$ bonds that must be broken when 1.0 mole of $\mathrm{C}(g)$ is formed from C(diamond). Calculate the $\Delta H$ of sublimation of diamond from the data in Appendix II, Table $\mathrm{B}$. Then do the calculation using the $\mathrm{C}-\mathrm{C}$ bond energy in Table $10.3 .$ Suggest a reason for the difference between the two values.

Key Concepts

Experimental vs Theoretical Energy Differences

The difference between sublimation enthalpies obtained experimentally and the values calculated using average bond energies arises due to factors such as lattice stabilization, cooperative interactions in the solid, and the limitations of using gas-phase bond energies to describe a bulk solid. These discrepancies highlight the complexity of solid-state bonding and the challenges in accurately modeling the energetics of extended systems using simplistic bond energy concepts.

Thermochemical Cycles and Hess's Law

Thermochemical cycles, which rely on Hess’s law, allow us to determine the overall enthalpy change of a process by combining known reaction enthalpies from related processes. This approach is particularly useful when direct measurement is difficult, such as in evaluating the sublimation enthalpy from a complex solid lattice. It establishes a connection between experimental data and theoretical calculations based on bond energies.

Bond Energy

Bond energy, or bond enthalpy, refers to the energy required to break one mole of bonds in the gas phase. When analyzing processes such as the formation of gaseous atoms from a solid lattice, bond energies provide a means to estimate the energy per bond that is needed for the transformation. This concept is essential for comparing theoretical energy estimates based on individual bond strengths with experimentally determined values.

Sublimation

Sublimation is the process by which a substance transitions directly from a solid phase to a gas phase without passing through a liquid state. In thermodynamics, this transformation requires overcoming the cohesive forces that hold the solid together, and the energy required for this is quantified by the sublimation enthalpy. It is a critical concept for understanding phase changes and the energy changes involved in breaking the bonds within a solid lattice.

Three-Dimensional Lattice Structures

In solids like diamond, atoms are arranged in a three-dimensional network with strong covalent bonds connecting them. This structure means that each atom is bonded to several neighbors (in diamond, each carbon atom is tetrahedrally coordinated) and the overall energy required to liberate an atom into the gas phase is determined by the collective energy of these bonds. Understanding the networked nature of the lattice is crucial when calculating the total bond breakage per mole of atoms formed.

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