Question

Determine the standard enthalpy change, entropy change, and free energy change for the conversion of diamond to graphite. Discuss the spontaneity of the conversion with respect to the enthalpy and entropy changes. Explain why diamond spontaneously changing into graphite is not observed.

Short answer

• The change of enthalpy is \(\Delta H = - 1.89\frac{{kJ}}{{mol}}\)
• The change of entropy is \(\Delta S = 3.36\frac{J}{{K \cdot mol}}\)
• The change of free energy is \(\Delta G = - 2.90\frac{{kJ}}{{mol}}\)
• The reaction is spontaneous. It is normally observed because the rate of the reaction is very slow.

Step-by-step solution

Definition of Gibbs free energy

Gibbs free energy, also known as Gibbs function, Gibbs energy, or free enthalpy, is a term used to measure the topmost quantum of work done in a thermodynamic system when temperature and pressure remain constant.

Determine the Change of entropy and enthalpy.

The reaction in question is:

\(C({\rm{ diamond }}) \to C(graphite)\)

We can calculate the enthalpy change using the formula

\(\Delta H = {H_f}({\rm{ products }}) - {H_f}({\rm{ reactants }})\)

We can look up the standard formation enthalpy changes in the table in AppendixG in the book.

\(\Delta H = {H_f}(C,{\rm{ graphite }}) - {H_f}(C,{\rm{ diamond }})\)

\(\begin{array}{l}\Delta H = (0 - 1.89)\frac{{k \cdot J}}{{mol}}\\\Delta H = - 1.89\frac{{kJ}}{{mol}}\end{array}\)

Hence, the change of enthalpy is \(\Delta H = - 1.89\frac{{kJ}}{{mol}}\)

We can calculate the entropy change using the formula

\(\Delta S = S({\rm{ products }}) - S({\rm{ reactants }})\)

We can look up the standard entropies in the table in AppendixG in the book.

\(\begin{array}{l}\Delta S = S(C,{\rm{ graphite }}) - S(C,{\rm{ diamond }})\\\Delta S = (5.740 - 2.38)\frac{J}{{K \cdot mol}}\\\Delta S = 3.36\frac{J}{{K \cdot mol}}\end{array}\)

Hence, the change of entropy is \(\Delta S = 3.36\frac{J}{{K \cdot mol}}\)

Determine the Change of free energy.

If we look at the formula for \(\Delta G\) :

\(\Delta G = \Delta H - T\Delta S\)

We can see that, if the enthalpy change is negative and the entropy change is positive, such as the case is with this reaction, \(\Delta G\) will surely be negative and the reaction therefore spontaneous. We can calculate the free energy change using the formula

\(\Delta G = {G_f}({\rm{ products }}) - {G_f}({\rm{ reactants }})\)

We can look up the standard formation free energy changes for each species in AppendixG in the book.

\(\begin{array}{l}\Delta G = {G_f}(C,{\rm{ graphite }}) - {G_f}(C,{\rm{ diamond }})\\\Delta G = (0 - 2.90)\frac{{k \cdot J}}{{mol}}\\\Delta G = - 2.90\frac{{kJ}}{{mol}}\end{array}\)

Even though the conversion of diamond to graphite is a spontaneous reaction, it is not normally observed because the rate of the reaction is very slow.

Hence, the change of free energy is \(\Delta G = - 2.90\frac{{kJ}}{{mol}}\)