The factor of `DeltaG` values is important in metallurgy. The `DeltaG` values for the following reactions at 800°C are given as :
`S_(2)(s) + 2O_(2)(g) to 2SO_(2)(g), DeltaG =-544 kJ`
`2Zn(s) + S_(2)(s) to 2ZnS(s), DeltaG=-293` kJ
`2Zn(s) + O_(2)(g) to 2ZnO(s), DeltaG = -480` kJ
Calculate the `DeltaG` for the reaction:
`2ZnS(s) + 3O_(2)(g) to 2ZnO(s) + 2SO_(2)(g)`

Explanation

To calculate the ΔG for the reaction:

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

we will use the given ΔG values of the related reactions.

### Step 1: Write down the given reactions and their ΔG values.

1. \( S_2(s) + 2O_2(g) \rightarrow 2SO_2(g) \) \[ \Delta G = -544 \, \text{kJ} \]
2. \( 2Zn(s) + S_2(s) \rightarrow 2ZnS(s) \) \[ \Delta G = -293 \, \text{kJ} \]
3. \( 2Zn(s) + O_2(g) \rightarrow 2ZnO(s) \) \[ \Delta G = -480 \, \text{kJ} \]

### Step 2: Rearrange the reactions to match the target reaction.

We need to manipulate the given reactions to arrive at the desired equation:

1. **Reverse the second reaction** to get \( 2ZnS(s) \) on the left:
\[ 2ZnS(s) \rightarrow 2Zn(s) + S_2(s) \quad \Delta G = +293 \, \text{kJ} \]

2. **Use the first reaction as is**:
\[ S_2(s) + 2O_2(g) \rightarrow 2SO_2(g) \quad \Delta G = -544 \, \text{kJ} \]

3. **Use the third reaction as is**:
\[ 2Zn(s) + O_2(g) \rightarrow 2ZnO(s) \quad \Delta G = -480 \, \text{kJ} \]

### Step 3: Combine the reactions.

Now we will add these modified reactions together:

- From the reversed second reaction:
\[ 2ZnS(s) \rightarrow 2Zn(s) + S_2(s) \quad (+293 \, \text{kJ}) \]

- From the first reaction:
\[ S_2(s) + 2O_2(g) \rightarrow 2SO_2(g) \quad (-544 \, \text{kJ}) \]

- From the third reaction:
\[ 2Zn(s) + O_2(g) \rightarrow 2ZnO(s) \quad (-480 \, \text{kJ}) \]

### Step 4: Write the overall reaction.

Combining these gives:
\[ 2ZnS(s) + 3O_2(g) \rightarrow 2ZnO(s) + 2SO_2(g) \]

### Step 5: Calculate the total ΔG.

Now, we sum the ΔG values:
\[ \Delta G = +293 \, \text{kJ} - 544 \, \text{kJ} - 480 \, \text{kJ} \]
\[ \Delta G = 293 - 544 - 480 \]
\[ \Delta G = 293 - 1024 \]
\[ \Delta G = -731 \, \text{kJ} \]

### Final Answer:
\[ \Delta G = -731 \, \text{kJ} \]