`2Zn+O_(2)to2ZnO," "DeltaG^(@)=-606J` . . . (i)
`2Zn+2Sto2ZnS," "DeltaG^(@)=-293J` . . .(ii)
`2S+2O_(2)to2SO_(2)(g)," "DeltaG^(@)=-408J` . . . (iii)
`DeltaG^(@)` for the following reaction
`2ZnS+3O_(2)to2ZnO+2SO_(2)`
would be:

Options

A. `-731 J`
B. `-1317 J`
C. `-501 J`
D. `+ 731 J`

Answer

To calculate the ΔG° for the reaction \(2ZnS + 3O_2 \rightarrow 2ZnO + 2SO_2\), we will use the given reactions and their respective ΔG° values. Here’s the step-by-step solution:

### Step 1: Write down the given reactions and their ΔG° values
1. \(2Zn + O_2 \rightarrow 2ZnO\), ΔG° = -606 J (Reaction 1)
2. \(2Zn + 2S \rightarrow 2ZnS\), ΔG° = -293 J (Reaction 2)
3. \(2S + 2O_2 \rightarrow 2SO_2\), ΔG° = -408 J (Reaction 3)

### Step 2: Reverse Reaction 2
Since we need \(ZnS\) on the reactant side, we reverse Reaction 2:
\[ 2ZnS \rightarrow 2Zn + 2S \]
The ΔG° for the reversed reaction becomes:
\[ ΔG° = +293 J \]

### Step 3: Keep Reaction 3 as it is
We will use Reaction 3 directly:
\[ 2S + 2O_2 \rightarrow 2SO_2 \]
The ΔG° remains:
\[ ΔG° = -408 J \]

### Step 4: Combine the reactions
Now we combine the reversed Reaction 2 and Reaction 3 with Reaction 1:
1. \(2Zn + O_2 \rightarrow 2ZnO\) (ΔG° = -606 J)
2. \(2ZnS \rightarrow 2Zn + 2S\) (ΔG° = +293 J)
3. \(2S + 2O_2 \rightarrow 2SO_2\) (ΔG° = -408 J)

When we add these reactions, we can cancel out the common species:
- The \(2Zn\) from the reversed Reaction 2 cancels with the \(2Zn\) from Reaction 1.
- The \(2S\) from Reaction 3 cancels with the \(2S\) from the reversed Reaction 2.

### Step 5: Write the final reaction
The remaining species give us:
\[ 2ZnS + 3O_2 \rightarrow 2ZnO + 2SO_2 \]

### Step 6: Calculate the total ΔG°
Now we sum the ΔG° values:
\[ ΔG° = (-606 J) + (+293 J) + (-408 J) \]
Calculating this gives:
\[ ΔG° = -606 + 293 - 408 = -721 J \]

### Conclusion
Thus, the ΔG° for the reaction \(2ZnS + 3O_2 \rightarrow 2ZnO + 2SO_2\) is \(-721 J\).

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