Three of the forms of elemental carbon are graphite,...

Three of the forms of elemental carbon are graphite, diamond, and buckminsterfullerene. The entropies at $298 \mathrm{~K}$ for graphite and diamond are listed in Appendix C. (a) Account for the difference in the $S^{\circ}$ values of graphite and diamond in light of their structures (Figure 12.30$)$. (b) What would you expect for the $S^{\circ}$ value of buckminsterfullerene (Figure $\left.12.47\right)$ relative to the values for graphite and diamond? Explain.

Key Concepts

Standard Molar Entropy

Standard molar entropy is a thermodynamic quantity that measures the degree of disorder or randomness in a substance at a specified temperature, typically 298 K. It reflects the number of microscopic configurations that correspond to the macroscopic state of the material, and higher entropy indicates a greater number of accessible microstates.

Crystal Structure and Bonding

The crystal structure and the nature of bonding within a material play a crucial role in determining its entropy. Materials with more open or less tightly constrained structures often have more accessible vibrational modes, and thus higher entropy. For example, a structure with layers held together by weaker forces can allow for greater vibrational freedom than one with a rigid three-dimensional network, where atoms are more strongly held in fixed positions.

Molecular Degrees of Freedom

In addition to lattice vibrations in extended solids, the intrinsic molecular structure, such as that of a discrete molecule, contributes to the overall entropy through additional rotational and vibrational degrees of freedom. Molecules that exist as separate entities rather than as part of an extended network can often rotate or vibrate freely in ways that further increase their entropy relative to materials with continuous lattices.

Transcript

00:01 Let's look at the relative entropies of various allotropes of carbon.

00:07 So listed here are the standard entropys of diamond and graphite.

00:12 You can see that the entropy of graphite is larger than that of diamond, but both diamond and graphite are carbon.

00:21 And so what is it about each of these that make the entropies of them different? and remember that entropy in a lot of ways is really just based on translational, vibrational, and rotational energies.

00:38 And so when we think about a diamond in its structure, remember that diamond is carbon that is put together in a network covalent fashion in a tetrahedral structure.

00:50 We can keep drawing these seas further out and further out and further out.

00:54 But they're all locked into place in all three dimensions.

00:59 When we deal with graphite, graphite is in a trigonal planar structure.

01:06 And since it's in a plane, you can think of them as like sheets.

01:10 So if we just rotate this a little to look at it on its side, you would really just see these four carbons.

01:19 The other two back here, these two would be hidden.

01:23 And so you have a sheet and you would have a number of sheets of these to form.

01:32 The graphite.

01:34 Now, why is this important? in a tetrahedral structure, all three dimensions are locked, but in graphite, only two dimensions are locked.

01:48 So what that means is that there can be motion from left to right in each of these...

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