---
title: "A materials-science student stores a polished sample of \\(\\text{C(s, diamond)}\\) at \\(298\\ \\text{K}\\) and \\(1\\ \\text{bar}\\). After \\(10\\ \\text{yr}\\), Raman spectroscopy detects no \\(\\text{C(s, graphite)}\\) above a \\(0.1\\%\\) detection limit. Relevant data for the conversion are shown below.  \\[ \\text{C(s, diamond)} \\rightarrow \\text{C(s, graphite)} \\]  | Quantity at \\(298\\ \\text{K}\\) | Value | |—|—| | \\(\\Delta H^\\circ\\) | \\(-1.9\\ \\text{kJ mol}^{-1}\\) | | \\(\\Delta S^\\circ\\) | \\(+3.4\\ \\text{J mol}^{-1}\\text{K}^{-1}\\) | | \\(E_{a,\\text{forward}}\\) | \\(700\\ \\text{kJ mol}^{-1}\\) |  Which statement best reconciles the spectroscopic observation with the thermodynamic and kinetic data?"
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url: "https://nerd-notes.com/ubq/120024/"
date_modified: "2026-08-21T08:32:45+00:00"
---

# A materials-science student stores a polished sample of \(\text{C(s, diamond)}\) at \(298\ \text{K}\) and \(1\ \text{bar}\). After \(10\ \text{yr}\), Raman spectroscopy detects no \(\text{C(s, graphite)}\) above a \(0.1\%\) detection limit. Relevant data for the conversion are shown below.

\[
\text{C(s, diamond)} \rightarrow \text{C(s, graphite)}
\]

| Quantity at \(298\ \text{K}\) | Value |
|—|—|
| \(\Delta H^\circ\) | \(-1.9\ \text{kJ mol}^{-1}\) |
| \(\Delta S^\circ\) | \(+3.4\ \text{J mol}^{-1}\text{K}^{-1}\) |
| \(E_{a,\text{forward}}\) | \(700\ \text{kJ mol}^{-1}\) |

Which statement best reconciles the spectroscopic observation with the thermodynamic and kinetic data?

A materials-science student stores a polished sample of \(\text{C(s, diamond)}\) at \(298\ \text{K}\) and \(1\ \text{bar}\). After \(10\ \text{yr}\), Raman spectroscopy detects no \(\text{C(s, graphite)}\) above a \(0.1\%\) detection limit. Relevant data for the conversion are shown below.

\[
\text{C(s, diamond)} \rightarrow \text{C(s, graphite)}
\]

| Quantity at \(298\ \text{K}\) | Value |
|---|---|
| \(\Delta H^\circ\) | \(-1.9\ \text{kJ mol}^{-1}\) |
| \(\Delta S^\circ\) | \(+3.4\ \text{J mol}^{-1}\text{K}^{-1}\) |
| \(E_{a,\text{forward}}\) | \(700\ \text{kJ mol}^{-1}\) |

Which statement best reconciles the spectroscopic observation with the thermodynamic and kinetic data?

- **A.** The conversion is thermodynamically unfavorable but kinetically negligible, because \(\Delta S^\circ>0\) makes \(-T\Delta S^\circ>0\), while the large \(E_a\) suppresses the rate.
- **B.** The conversion is thermodynamically unfavorable but kinetically negligible, because the large \(E_a\) both suppresses the rate and reverses the sign of \(\Delta G^\circ\).
- **C.** The conversion is thermodynamically favorable but kinetically negligible, because \(\Delta G^\circ<0\) favors \(\text{C(s, graphite)}\), whereas the large \(E_a\) makes successful barrier-crossing events extremely rare at \(298\ \text{K}\).
- **D.** The conversion is thermodynamically favorable but kinetically negligible, because the small magnitude of \(\Delta G^\circ\) directly makes the rate constant small, regardless of the value of \(E_a\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120024/*