`2Zn + O_(2) rightarrow 2ZnO, Delta G^(@) = -616 J`
`2Zn + S_(2) rightarrow 2ZnS, Delta G^(@) = -293 J`
` S_(2) + 2O_(2) rightarrow 2SO_(2), Delta G^(@) = -408 J`
`Delta G^(@)` for the following reaction
`2ZnS + 3O_(2) rightarrow 2ZnO+ 2 SO_(2) ` is

Options

A. `-1462 J`
B. `-1317 J`
C. `-501 J`
D. `-731 J`

Answer

To find the standard Gibbs free energy change (ΔG°) for the reaction:

\[ 2ZnS + 3O_2 \rightarrow 2ZnO + 2SO_2 \]

we will use the given reactions and their corresponding ΔG° values. The strategy involves manipulating the given reactions (adding, reversing) to derive the target reaction.

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

1. \( 2Zn + O_2 \rightarrow 2ZnO \)
\( \Delta G° = -616 \, \text{J} \)

2. \( 2Zn + S_2 \rightarrow 2ZnS \)
\( \Delta G° = -293 \, \text{J} \)

3. \( S_2 + 2O_2 \rightarrow 2SO_2 \)
\( \Delta G° = -408 \, \text{J} \)

### Step 2: Manipulate the reactions to derive the target reaction.

- **Reverse the second reaction** to express \( ZnS \) in terms of \( Zn \) and \( S_2 \):

\[ 2ZnS \rightarrow 2Zn + S_2 \]
\( \Delta G° = +293 \, \text{J} \) (the sign changes when reversing)

- **Use the first reaction as it is**:

\[ 2Zn + O_2 \rightarrow 2ZnO \]
\( \Delta G° = -616 \, \text{J} \)

- **Use the third reaction as it is**:

\[ S_2 + 2O_2 \rightarrow 2SO_2 \]
\( \Delta G° = -408 \, \text{J} \)

### Step 3: Combine the reactions.

Now, we will add the modified second reaction, the first reaction, and the third reaction:

1. \( 2ZnS \rightarrow 2Zn + S_2 \)
\( \Delta G° = +293 \, \text{J} \)

2. \( 2Zn + O_2 \rightarrow 2ZnO \)
\( \Delta G° = -616 \, \text{J} \)

3. \( S_2 + 2O_2 \rightarrow 2SO_2 \)
\( \Delta G° = -408 \, \text{J} \)

When we add these reactions, we get:

\[ 2ZnS + 3O_2 \rightarrow 2ZnO + 2SO_2 \]

### Step 4: Calculate the total ΔG°.

Now, we can sum the ΔG° values:

\[ \Delta G° = (+293) + (-616) + (-408) \]

Calculating this gives:

\[ \Delta G° = 293 - 616 - 408 = 293 - 1024 = -731 \, \text{J} \]

### Conclusion

Thus, the standard Gibbs free energy change (ΔG°) for the reaction:

\[ 2ZnS + 3O_2 \rightarrow 2ZnO + 2SO_2 \]

is:

\[ \Delta G° = -731 \, \text{J} \]