Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
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]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.
