Consider the equations below.

(1) [tex]\[Fe_2O_3(s) \rightarrow 2Fe(s) + \frac{3}{2}O_2(g)\][/tex]

(2) [tex]\[Fe_2O_3(s) + 3CO(g) \rightarrow 2Fe(s) + 3CO_2(g)\][/tex]

Which equation must be added to equation (1) to produce equation (2)?

A. [tex]\[CO(g) + \frac{1}{2}O_2(g) \rightarrow CO_2(g)\][/tex]

B. [tex]\[3CO_2(g) \rightarrow 3CO(g) + \frac{3}{2}O_2(g)\][/tex]

C. [tex]\[3CO(g) + \frac{3}{2}O_2(g) \rightarrow 3CO_2(g)\][/tex]

To determine which equation must be added to Equation (1) to produce Equation (2), we need to systematically analyze each option and see which one, when combined with Equation (1), results in Equation (2).

Let's begin by writing down the given equations:

Equation (1):
[tex]\[ \text{Fe}_2\text{O}_3 (s) \rightarrow 2 \text{Fe} (s) + \frac{3}{2} \text{O}_2 (g) \][/tex]

Equation (2):
[tex]\[ \text{Fe}_2\text{O}_3 (s) + 3 \text{CO} (g) \rightarrow 2 \text{Fe} (s) + 3 \text{CO}_2 (g) \][/tex]

Now, let's examine each option:

Option 1:
[tex]\[ \text{CO} (g) + \frac{1}{2} \text{O}_2 (g) \rightarrow \text{CO}_2 (g) \][/tex]

Adding this to Equation (1):

[tex]\[ \begin{aligned} \text{Fe}_2\text{O}_3 (s) &\rightarrow 2 \text{Fe} (s) + \frac{3}{2} \text{O}_2 (g) \\ \text{CO} (g) + \frac{1}{2} \text{O}_2 (g) &\rightarrow \text{CO}_2 (g) \\ \end{aligned} \][/tex]

Combining these two:

[tex]\[ \text{Fe}_2\text{O}_3 (s) + \text{CO} (g) + \frac{1}{2} \text{O}_2 (g) \rightarrow 2 \text{Fe} (s) + \text{CO}_2 (g) + \frac{3}{2} \text{O}_2 (g) \][/tex]

Or simplifying:

[tex]\[ \text{Fe}_2\text{O}_3 (s) + \text{CO} (g) \rightarrow 2 \text{Fe} (s) + \text{CO}_2 (g) + \text{O}_2 (g) \][/tex]

This does not match Equation (2).

Option 2:
[tex]\[ 3 \text{CO}_2 (g) \rightarrow 3 \text{CO} (g) + \frac{3}{2} \text{O}_2 (g) \][/tex]

Adding this to Equation (1):

[tex]\[ \begin{aligned} \text{Fe}_2\text{O}_3 (s) &\rightarrow 2 \text{Fe} (s) + \frac{3}{2} \text{O}_2 (g) \\ 3 \text{CO}_2 (g) &\rightarrow 3 \text{CO} (g) + \frac{3}{2} \text{O}_2 (g) \\ \end{aligned} \][/tex]

Combining these two:

[tex]\[ \text{Fe}_2\text{O}_3 (s) + 3 \text{CO}_2 (g) \rightarrow 2 \text{Fe} (s) + 3 \text{CO} (g) + \frac{3}{2} \text{O}_2 (g) + \frac{3}{2} \text{O}_2 (g) \][/tex]

Or simplifying:

[tex]\[ \text{Fe}_2\text{O}_3 (s) + 3 \text{CO}_2 (g) \rightarrow 2 \text{Fe} (s) + 3 \text{CO} (g) + 3 \text{O}_2 (g) \][/tex]

This does not match Equation (2).

Option 3:
[tex]\[ 3 \text{CO} (g) + \frac{3}{2} \text{O}_2 (g) \rightarrow 3 \text{CO}_2 (g) \][/tex]

Adding this to Equation (1):

[tex]\[ \begin{aligned} \text{Fe}_2\text{O}_3 (s) &\rightarrow 2 \text{Fe} (s) + \frac{3}{2} \text{O}_2 (g) \\ 3 \text{CO} (g) + \frac{3}{2} \text{O}_2 (g) &\rightarrow 3 \text{CO}_2 (g) \\ \end{aligned} \][/tex]

Combining these two:

[tex]\[ \text{Fe}_2\text{O}_3 (s) + 3 \text{CO} (g) + \frac{3}{2} \text{O}_2 (g) \rightarrow 2 \text{Fe} (s) + \frac{3}{2} \text{O}_2 (g) + 3 \text{CO}_2 (g) \][/tex]

Or simplifying:

[tex]\[ \text{Fe}_2\text{O}_3 (s) + 3 \text{CO} (g) \rightarrow 2 \text{Fe} (s) + 3 \text{CO}_2 (g) \][/tex]

This matches Equation (2).

Therefore, the correct equation to be added is:

[tex]\[ 3 \text{CO} (g) + \frac{3}{2} \text{O}_2 (g) \rightarrow 3 \text{CO}_2 (g) \][/tex]

So, the correct option is:

[tex]\[ \boxed{3} \][/tex]