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Sagot :
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]
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]
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