### Coupled Chemical Reactions and Equilibrium#### Problem StatementWhen the oxide of generic metal M is heated at 25.0 °C, a negligible amount of metal M is produced, demonstrating the following reaction:\[ \text{MO}_2(s) \rightleftharpoons \text{M}(s) + \text{O}_2(g) \quad \Delta G^\circ = 286.2 \, \text{kJ/mol} \]#### Coupling ReactionsWhen this reaction is coupled to the conversion of graphite to carbon dioxide, it becomes spontaneous. ##### Task 1: Chemical Equation**Question:** What is the chemical equation of this coupled process? Show that the reaction is in equilibrium. Include physical states and represent graphite as C(s).**User Input:**- Chemical equation: **105.5** *(Incorrect)*##### Task 2: Equilibrium Constant**Question:** What is the thermodynamic equilibrium constant for the coupled reaction?**User Input:**- \( K = 3.05 \times 10^{-18} \) *(Incorrect)*---#### Solutions and ExplanationsTo properly approach the problem, follow these steps:1. **Identify the individual reactions involved in the coupling:** - The reaction of metal oxide decomposition: \(\text{MO}_2(s) \rightleftharpoons \text{M}(s) + \text{O}_2(g) \) - The conversion of graphite to carbon dioxide: \(\text{C}(s) + \text{O}_2(g) \rightleftharpoons \text{CO}_2(g) \)2. **Add the Gibbs free energies of the individual reactions to determine the Gibbs free energy of the coupled reaction.**3. **Combine the reactions and verify the coupled reaction and its equilibrium.---By iterating through these steps, corrections must be implemented for the chemical equation and the equilibrium constant to validate the spontaneous nature of the coupled process.

Given data Reaction At 25 centigrade temperature Delta G=286.2 kj/mol

When the oxide of generic metal M is heated at 25.0 °C, a negligible amount of M is produced. MO₂ (s) M(s) + O₂(g) AG = 286.2. kJ mol When this reaction is coupled to the conversion of graphite to carbon dioxide, it becomes spontaneous. What is the chemical equation of this coupled process? Show that the reaction is in equilibrium. Include physical states and represent graphite as C(s).

When the oxide of generic metal M is heated at 25.0 °C, a negligible amount of M is produced. MO₂ (s) M(s) + O₂(g) AG = 286.2. kJ mol When this reaction is coupled to the conversion of graphite to carbon dioxide, it becomes spontaneous. What is the chemical equation of this coupled process? Show that the reaction is in equilibrium. Include physical states and represent graphite as C(s).

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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