The `DeltaG` values for the following reactions at `800^(@)C` are
`S_(2)(g) + 2O_(2)(g) to 2SO_(2)(g) DeltaG = - 544 kJ`
`2Zn (s) + S_(2)(g) to 2ZnS(s) DeltaG = - 293 kJ`
`2Zn(s) + O_(2)(g) to 2ZnO(S) DeltaG = - 480 kJ`
The `DeltaG` for the reaction:
`2ZnS(s) + 3O_(2)(g) to 2ZnO(s) + 2SO_(2)(g)` is

Options

A. `-731 kJ`
B. `-773 kJ`
C. `-229 kJ`
D. `-357 kJ`

Answer

To find the ΔG for the reaction:

\[ 2ZnS(s) + 3O_2(g) \rightarrow 2ZnO(s) + 2SO_2(g) \]

we can use Hess's Law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps of the reaction.

### Step-by-Step Solution:

1. **Identify the Given Reactions and Their ΔG Values:**
- Reaction 1:
\[ S_2(g) + 2O_2(g) \rightarrow 2SO_2(g) \quad \Delta G_1 = -544 \, \text{kJ} \]
- Reaction 2:
\[ 2Zn(s) + S_2(g) \rightarrow 2ZnS(s) \quad \Delta G_2 = -293 \, \text{kJ} \]
- Reaction 3:
\[ 2Zn(s) + O_2(g) \rightarrow 2ZnO(s) \quad \Delta G_3 = -480 \, \text{kJ} \]

2. **Write the Target Reaction:**
\[ 2ZnS(s) + 3O_2(g) \rightarrow 2ZnO(s) + 2SO_2(g) \]

3. **Manipulate the Given Reactions:**
- We need to add Reaction 1 and Reaction 3, and reverse Reaction 2.
- Reversing Reaction 2 gives:
\[ 2ZnS(s) \rightarrow 2Zn(s) + S_2(g) \quad \Delta G = +293 \, \text{kJ} \]

4. **Add the Reactions:**
- Adding Reaction 1 and Reaction 3:
\[ S_2(g) + 2O_2(g) + 2Zn(s) + O_2(g) \rightarrow 2SO_2(g) + 2ZnO(s) \]
This simplifies to:
\[ S_2(g) + 3O_2(g) + 2Zn(s) \rightarrow 2SO_2(g) + 2ZnO(s) \]

5. **Subtract the Reversed Reaction 2:**
- Now we subtract the reversed Reaction 2:
\[ 2ZnS(s) \rightarrow 2Zn(s) + S_2(g) \]
- This gives us:
\[ 2ZnS(s) + 3O_2(g) \rightarrow 2ZnO(s) + 2SO_2(g) \]

6. **Calculate the ΔG for the Target Reaction:**
- According to Hess's Law:
\[ \Delta G_{\text{target}} = \Delta G_1 + \Delta G_3 - \Delta G_2 \]
- Substituting the values:
\[ \Delta G_{\text{target}} = (-544) + (-480) + 293 \]
\[ \Delta G_{\text{target}} = -544 - 480 + 293 \]
\[ \Delta G_{\text{target}} = -731 \, \text{kJ} \]

### Final Answer:
The ΔG for the reaction \( 2ZnS(s) + 3O_2(g) \rightarrow 2ZnO(s) + 2SO_2(g) \) is \(-731 \, \text{kJ}\).