Elemental sulfur is formed by the reaction of zinc sulfide with oxygen: (b) At what temperature, if any, the reaction will become nonspontaneous?

Verified step by step guidance

1. <insert step 1> Identify the chemical reaction: \( \text{ZnS} + \text{O}_2 \rightarrow \text{ZnO} + \text{SO}_2 \).
2. <insert step 2> Use the Gibbs free energy equation: \( \Delta G = \Delta H - T\Delta S \), where \( \Delta G \) is the change in Gibbs free energy, \( \Delta H \) is the change in enthalpy, \( T \) is the temperature in Kelvin, and \( \Delta S \) is the change in entropy.
3. <insert step 3> Determine the \( \Delta H \) and \( \Delta S \) for the reaction using standard enthalpy and entropy values from a data table.
4. <insert step 4> Set \( \Delta G = 0 \) to find the temperature at which the reaction becomes nonspontaneous, and solve for \( T \) using the equation \( T = \frac{\Delta H}{\Delta S} \).
5. <insert step 5> Ensure the units are consistent (e.g., convert \( \Delta H \) from kJ to J if necessary) and solve for \( T \) to find the temperature at which the reaction becomes nonspontaneous.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that helps predict the spontaneity of a reaction. A reaction is spontaneous when the change in Gibbs Free Energy (ΔG) is negative. The relationship between enthalpy (ΔH), entropy (ΔS), and temperature (T) is given by the equation ΔG = ΔH - TΔS, where T is in Kelvin. Understanding this concept is crucial for determining the conditions under which a reaction becomes nonspontaneous.

Spontaneity and Temperature

The spontaneity of a reaction can depend on temperature, particularly when the enthalpy and entropy changes are of different signs. For example, if a reaction is exothermic (ΔH < 0) and has an increase in entropy (ΔS > 0), it will generally be spontaneous at all temperatures. Conversely, if ΔH > 0 and ΔS < 0, the reaction will be nonspontaneous at all temperatures. Identifying the temperature at which spontaneity changes requires analyzing these thermodynamic parameters.

Phase Changes and Reaction Conditions

The conditions under which a reaction occurs, including temperature and pressure, can significantly influence the products formed and their stability. In the case of the reaction between zinc sulfide and oxygen, the temperature can affect the equilibrium position and the Gibbs Free Energy. Understanding how phase changes and reaction conditions impact the formation of products like elemental sulfur is essential for predicting when the reaction will become nonspontaneous.