Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
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]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
