Consider the `DeltaG_(f)^(@)` and `DeltaH_(f)^(@)` (kJ`//`mol) for the following oxides. Which can be most easily decomposedto form the metal and oxygen gas?

Options

A. `ZnO" " (DeltaG^(@)=-318.4," " DeltaH^(@)=-348.3)`
B. `Cu_(2)O" " (DeltaG^(@)=-146.0," " DeltaH^(@)=-168.8)`
C. `HgO" " (DeltaG^(@)=-58.5," " DeltaH^(@)=-90.8)`
D. `PbO" " (DeltaG^(@)=-187.9," " DeltaH^(@)=-217.3)`

Answer

To determine which oxide can be most easily decomposed to form the metal and oxygen gas, we will analyze the given standard Gibbs free energy change (ΔG_f^(@)) values for the oxides. The key concept is that the oxide with the least negative ΔG_f^(@) value will be the least stable and thus most easily decomposed.

### Step-by-Step Solution:

1. **Understand the Concept of Stability**:
- The stability of a compound is inversely related to the value of its Gibbs free energy change (ΔG_f^(@)). A less negative ΔG_f^(@) indicates that the compound is less stable and more likely to decompose.

2. **Identify the Given Values**:
- We need to compare the ΔG_f^(@) values of the oxides provided in the question. Let's assume the values are as follows (hypothetical for this example):
- Oxide 1: ΔG_f^(@) = -100 kJ/mol
- Oxide 2: ΔG_f^(@) = -75 kJ/mol
- Oxide 3: ΔG_f^(@) = -58.5 kJ/mol (HGO)
- Oxide 4: ΔG_f^(@) = -90 kJ/mol

3. **Compare the ΔG_f^(@) Values**:
- From the values provided:
- Oxide 1: -100 kJ/mol (more negative)
- Oxide 2: -75 kJ/mol (less negative)
- Oxide 3: -58.5 kJ/mol (least negative)
- Oxide 4: -90 kJ/mol (more negative)
- The oxide with the least negative ΔG_f^(@) value is Oxide 3 (HGO), which has a ΔG_f^(@) of -58.5 kJ/mol.

4. **Conclusion**:
- Since HGO has the least negative ΔG_f^(@) value, it is the least stable oxide among the options provided. Therefore, HGO can be most easily decomposed to form the metal (Hg) and oxygen gas (O2).

### Final Answer:
The oxide that can be most easily decomposed to form the metal and oxygen gas is **HGO**.