Question

Theoretically, one can obtain zinc from an ore containing zinc sulfide, \(\mathrm{ZnS},\) by the reaction $$ \mathrm{ZnS}(s) \longrightarrow \mathrm{Zn}(s)+\mathrm{S}(s) $$ (a) Show by calculation that this reaction is not feasible at \(25^{\circ} \mathrm{C}\). (b) Show that by coupling the above reaction with the reaction $$ \mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) $$ the overall reaction, in which \(\mathrm{Zn}\) is obtained by roasting in oxygen, is feasible at \(25^{\circ} \mathrm{C}\).

Short answer

a) \(\mathrm{ZnS}(s) \longrightarrow \mathrm{Zn}(s)+\mathrm{S}(s)\) b) Combined reaction: \(\mathrm{ZnS}(s) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{Zn}(s) + \mathrm{SO}_{2}(g)\) Answer: a) The first reaction is not feasible at \(25^{\circ}\mathrm{C}\) because the standard Gibbs free energy change (\(\Delta G^{\circ}\)) is positive (205.2 kJ/mol). b) The combined reaction is feasible at \(25^{\circ}\mathrm{C}\) because the overall standard Gibbs free energy change (\(\Delta G^{\circ}_{overall}\)) is negative (-95.2 kJ/mol).

Step-by-step solution

(a) Determine the feasibility of the first reaction

Using the standard formation Gibbs free energies for \(\mathrm{ZnS}\), \(\mathrm{Zn}\), and \(\mathrm{S}\): \(\Delta G^{\circ}_{f, \mathrm{ZnS}}=-205.2\,\mathrm{kJ/mol}\), \(\Delta G^{\circ}_{f, \mathrm{Zn}}=0\) (since it's an elemental solid), \(\Delta G^{\circ}_{f, \mathrm{S}}=0\) (since it's an elemental solid), Now, we can calculate the standard Gibbs free energy change for the reaction: \(\Delta G^{\circ} = \Delta G^{\circ}_{f, \mathrm{Zn}} + \Delta G^{\circ}_{f, \mathrm{S}} - \Delta G^{\circ}_{f, \mathrm{ZnS}} = 0+0-(-205.2) = 205.2\,\mathrm{kJ/mol}\) Since \(\Delta G^{\circ}>0\), the reaction is not feasible at \(25^{\circ}\mathrm{C}\).

(b) Determine the feasibility of the combined reaction

For the combined reaction, we also need the standard formation Gibbs free energy of \(\mathrm{SO}_{2}\): \(\Delta G^{\circ}_{f, \mathrm{SO}_{2}}=-300.4\,\mathrm{kJ/mol}\) For the reaction: \(\mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)\), \(\Delta G^{\circ}_{S+O_2} = \Delta G^{\circ}_{f, \mathrm{SO}_{2}} - \Delta G^{\circ}_{f, \mathrm{S}} = -300.4 - 0 = -300.4\,\mathrm{kJ/mol}\) Now, we can calculate the standard Gibbs free energy change for the overall reaction: \(\Delta G^{\circ}_{overall} = \Delta G^{\circ} + \Delta G^{\circ}_{S+O_2} = 205.2 - 300.4 = -95.2\,\mathrm{kJ/mol}\) Since \(\Delta G^{\circ}_{overall}<0\), the overall reaction in which \(\mathrm{Zn}\) is obtained by roasting in oxygen is feasible at \(25^{\circ}\mathrm{C}\).

Key concepts

Chemical Thermodynamics

Chemical thermodynamics is the branch of physical chemistry that deals with the relationship between heat and other forms of energy, such as work. It focuses on the energy changes associated with chemical reactions and the direction in which these reactions will proceed. The key concept in chemical thermodynamics is the thermodynamic potential, and one of the most important of these potential is Gibbs free energy, denoted as \(G\).

Gibbs free energy combines the concepts of enthalpy (heat content), entropy (degree of disorder), and temperature to provide information about the spontaneity of a process. Specifically, the change in Gibbs free energy, \(\Delta G\), determines whether a reaction can occur spontaneously under constant pressure and temperature. A reaction with negative \(\Delta G\) is energetically favorable and can proceed spontaneously, while a positive value suggests an unfavorable reaction that will not spontaneously proceed in the forward direction under the given conditions.

Reaction Feasibility

The feasibility of a chemical reaction is influenced by \(\Delta G\), the change in Gibbs free energy. To determine whether a reaction is feasible or not, one should know the standard formation Gibbs free energies of the reactants and products, which are denoted by \(\Delta G^\circ_{f}\).

The standard Gibbs free energy change for a reaction is found by subtracting the sum of the \(\Delta G^\circ_{f}\) values for the reactants from the sum for the products. If the resulting \(\Delta G^\circ\) value is negative, the reaction is feasible under standard conditions. If it's positive, the reaction is not spontaneously feasible at \(25^\circ C\), which is considered standard temperature. Understanding this concept is crucial as it informs us about the potential for a reaction to occur without external input of energy.

Zinc Extraction

Zinc extraction commonly involves the process of roasting, where zinc sulfide \(\mathrm{ZnS}\) is converted into zinc oxide \(\mathrm{ZnO}\) and then reduced to metallic zinc. However, directly decomposing \(\mathrm{ZnS}\) into zinc and sulfur is not feasible at room temperature, as demonstrated by the positive \(\Delta G^\circ\) value.

By coupling this unfavorable reaction with another reaction, such as the combustion of sulfur to form sulfur dioxide \(\mathrm{SO}_{2}\), the overall \(\Delta G^\circ\) can become negative, thus making the extraction process feasible. This is an excellent example of how reaction coupling can be employed to drive a non-spontaneous reaction forward, a strategy not only used in industrial processes but also in biological systems, such as the synthesis of ATP in our bodies.

Standard Formation Gibbs Free Energies

Standard formation Gibbs free energies \(\Delta G^\circ_{f}\) are a set of tabulated values that represent the change in Gibbs free energy when one mole of a compound forms from its constituent elements in their standard states. A standard state is the pure form of the substance at one atmosphere of pressure and \(25^\circ C\), which is the common reference temperature.

These values are essential for determining reaction feasibility and for predicting the direction of chemical reactions. When calculating the overall \(\Delta G^\circ\) for a reaction, it is important to consider that elements in their standard state, like solid zinc or solid sulfur in the exercises given, have \(\Delta G^\circ_{f}\) values of zero. The use of these standard values helps simplify calculations and allows chemists and students alike to make quick predictions about reaction spontaneity in thermochemical equations.