Reduction of `Fe_(2)O_(3)` with `CO` is done below `710^@C`.
`Delta_(f) G^(Ө)` is negative at this temperature , this process is spontaneous.

Options

A. If both (A) and ( R) are correct and ( R) is the correct explanation of (A).
B. If both (A) and ( R) are correct, but ( R) is not the correct explanation of (A).
C. If (A) is correct, but ( R) is incorrect.
D. If (A) is incorrect, but ( R) is correct.

Answer

To solve the question regarding the reduction of \( \text{Fe}_2\text{O}_3 \) with \( \text{CO} \) below \( 710^\circ C \) and the spontaneity of the process, we can follow these steps:

### Step 1: Understand the Reaction
The reaction in question is the reduction of iron(III) oxide (\( \text{Fe}_2\text{O}_3 \)) by carbon monoxide (\( \text{CO} \)). The balanced chemical equation for this reaction is:
\[ \text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2 \]

### Step 2: Gibbs Free Energy and Spontaneity
For a reaction to be spontaneous, the change in Gibbs free energy (\( \Delta G \)) must be negative:
\[ \Delta G < 0 \]
This indicates that the reaction can proceed without the input of additional energy.

### Step 3: Temperature Dependence of \( \Delta G \)
The problem states that \( \Delta G \) is negative below \( 710^\circ C \). This means that at temperatures lower than \( 710^\circ C \), the reduction of \( \text{Fe}_2\text{O}_3 \) by \( \text{CO} \) is thermodynamically favorable.

### Step 4: Conclusion on Spontaneity
Since \( \Delta G \) is negative at temperatures below \( 710^\circ C \), we conclude that the reduction of \( \text{Fe}_2\text{O}_3 \) with \( \text{CO} \) is indeed spontaneous at these temperatures.

### Final Answer
Thus, the assertion that the reduction of \( \text{Fe}_2\text{O}_3 \) with \( \text{CO} \) is done below \( 710^\circ C \) because \( \Delta G \) is negative at this temperature is correct. Both the assertion and reason are correct, and the reason correctly explains the assertion.