Reduction of mercury(II) oxide with zinc gives metallic mercury: (b) Estimate at what temperature, if any, the reaction will become nonspontaneous

Verified step by step guidance

1. Identify the chemical equation for the reaction: Mercury(II) oxide (HgO) reacts with zinc (Zn) to produce metallic mercury (Hg) and zinc oxide (ZnO). The equation is: \( HgO(s) + Zn(s) \rightarrow Hg(l) + ZnO(s) \).
2. Understand the concept of Gibbs free energy (\( \Delta G \)), which determines the spontaneity of a reaction. The reaction is nonspontaneous when \( \Delta G > 0 \).
3. Use the equation \( \Delta G = \Delta H - T\Delta S \) to relate the enthalpy change (\( \Delta H \)), entropy change (\( \Delta S \)), and temperature (T) of the reaction. Here, \( \Delta H \) and \( \Delta S \) are constants at a given pressure for this reaction.
4. Calculate the temperature at which \( \Delta G \) becomes positive. Rearrange the equation to solve for T: \( T = \frac{\Delta H}{\Delta S} \).
5. Find the values of \( \Delta H \) and \( \Delta S \) for the reaction from a standard thermodynamic table and substitute them into the equation to estimate 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 at constant temperature and pressure if the change in Gibbs Free Energy (ΔG) is negative. The relationship between ΔG, enthalpy (ΔH), and entropy (ΔS) is given by the equation ΔG = ΔH - TΔS, where T is the temperature in Kelvin.

Spontaneity and Temperature

The spontaneity of a reaction can depend on temperature, particularly when considering the signs of ΔH and ΔS. If ΔH is negative (exothermic) and ΔS is positive (increase in disorder), the reaction is spontaneous at all temperatures. Conversely, if ΔH is positive and ΔS is negative, the reaction is nonspontaneous at all temperatures. The temperature at which the reaction becomes nonspontaneous can be found by setting ΔG to zero and solving for T.

Phase Changes and Reaction Conditions

The physical state of reactants and products can influence the reaction's spontaneity. In the case of mercury(II) oxide reduction, the phase changes from solid to liquid (metallic mercury) must be considered. The enthalpy and entropy changes associated with these phase transitions can significantly affect the Gibbs Free Energy, thus determining the temperature at which the reaction shifts from spontaneous to nonspontaneous.