Consider the decomposition of a metal oxide to its elements, where M represents a generic metal. AG°(kJ/mol) Substance M20(s) -10.00 M,0(s) = 2 M(s) + 0,(g) M(s) What is the standard change in Gibbs energy for the reaction, as written, in the O2(g) forward direction? kJ/mol

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### Equilibrium Constant and Pressure Calculation

1. **Equilibrium Constant (K)**

   _What is the equilibrium constant of this reaction, as written, in the forward direction at 298 K?_

   \( K = \)   
   [Input area for numerical value]

2. **Equilibrium Pressure**

   _What is the equilibrium pressure of \( \text{O}_2(g) \) over \( \text{M}(s) \) at 298 K?_

   \( P_{\text{O}_2} = \)   
   [Input area for numerical value] atm

**Note**: The equations or expressions for K and \( P_{\text{O}_2} \) should be derived from the specific reaction conditions and stoichiometry. Ensure to provide proper context and calculations as necessary.
Transcribed Image Text:### Equilibrium Constant and Pressure Calculation 1. **Equilibrium Constant (K)** _What is the equilibrium constant of this reaction, as written, in the forward direction at 298 K?_ \( K = \) [Input area for numerical value] 2. **Equilibrium Pressure** _What is the equilibrium pressure of \( \text{O}_2(g) \) over \( \text{M}(s) \) at 298 K?_ \( P_{\text{O}_2} = \) [Input area for numerical value] atm **Note**: The equations or expressions for K and \( P_{\text{O}_2} \) should be derived from the specific reaction conditions and stoichiometry. Ensure to provide proper context and calculations as necessary.
**Title: Thermodynamics of Metal Oxide Decomposition**

**Introduction**

Consider the decomposition of a metal oxide to its elements, where M represents a generic metal. The chemical reaction is as follows:

\[ \text{M}_2\text{O}(s) \rightleftharpoons 2\text{M}(s) + \frac{1}{2}\text{O}_2(g) \]

**Question**

What is the standard change in Gibbs energy for the reaction, as written, in the forward direction?

**Data Table**

The table below provides the standard Gibbs energy of formation (\( \Delta G^\circ_f \)) for the substances involved in the reaction:

| Substance | \( \Delta G^\circ_f \) (kJ/mol) |
|-----------|---------------------------|
| \(\text{M}_2\text{O}(s)\) | \(-10.00\) |
| \(\text{M}(s)\)           | \(0\)     |
| \(\text{O}_2(g)\)         | \(0\)     |

**Calculation**

The standard change in Gibbs energy for the reaction (\( \Delta G^\circ_{rxn} \)) can be calculated using the formula:

\[
\Delta G^\circ_{rxn} = \left( \sum \Delta G^\circ_f \text{(products)} \right) - \left( \sum \Delta G^\circ_f \text{(reactants)} \right)
\]

**Result**

\[ \Delta G^\circ_{rxn} = \boxed{kJ/mol} \]

**Note:** Complete the calculation by substituting the given values into the formula to find the numerical result for \( \Delta G^\circ_{rxn} \).
Transcribed Image Text:**Title: Thermodynamics of Metal Oxide Decomposition** **Introduction** Consider the decomposition of a metal oxide to its elements, where M represents a generic metal. The chemical reaction is as follows: \[ \text{M}_2\text{O}(s) \rightleftharpoons 2\text{M}(s) + \frac{1}{2}\text{O}_2(g) \] **Question** What is the standard change in Gibbs energy for the reaction, as written, in the forward direction? **Data Table** The table below provides the standard Gibbs energy of formation (\( \Delta G^\circ_f \)) for the substances involved in the reaction: | Substance | \( \Delta G^\circ_f \) (kJ/mol) | |-----------|---------------------------| | \(\text{M}_2\text{O}(s)\) | \(-10.00\) | | \(\text{M}(s)\) | \(0\) | | \(\text{O}_2(g)\) | \(0\) | **Calculation** The standard change in Gibbs energy for the reaction (\( \Delta G^\circ_{rxn} \)) can be calculated using the formula: \[ \Delta G^\circ_{rxn} = \left( \sum \Delta G^\circ_f \text{(products)} \right) - \left( \sum \Delta G^\circ_f \text{(reactants)} \right) \] **Result** \[ \Delta G^\circ_{rxn} = \boxed{kJ/mol} \] **Note:** Complete the calculation by substituting the given values into the formula to find the numerical result for \( \Delta G^\circ_{rxn} \).
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