Let's balance each equation step by step:
### 1. Balancing the equation \( \square \text{SiO}_2 + \square \text{CaC}_2 \rightarrow \square \text{Si} + \square \text{CaO} + \square \text{CO}_2 \)
- First, let's count the number of each type of atom on both sides of the equation:
- On the left side:
- Silicon (Si): 1 Si in \( \text{SiO}_2 \)
- Oxygen (O): 2 O in \( \text{SiO}_2 \)
- Calcium (Ca): 1 Ca in \( \text{CaC}_2 \)
- Carbon (C): 2 C in \( \text{CaC}_2 \)
- On the right side:
- Silicon (Si): 1 Si
- Oxygen (O): 1 O in \( \text{CaO} \) + 2 O in \( \text{CO}_2 \) = 3 O
- Calcium (Ca): 1 Ca in \( \text{CaO} \)
- Carbon (C): 1 C in \( \text{CO}_2 \)
- From this, we see that the coefficients need to balance the equation as:
- \( 1 \text{SiO}_2 \) \( +1 \text{CaC}_2 \rightarrow 1 \text{Si} \) \( +1 \text{CaO} \) \( +1 \text{CO}_2 \)
Thus, the balanced equation is:
[tex]\[ 1 \text{SiO}_2 + 1 \text{CaC}_2 \rightarrow 1 \text{Si} + 1 \text{CaO} + 1 \text{CO}_2 \][/tex]
### 2. Balancing the equation \( \square \text{NH}_3 + \square \text{O}_2 \rightarrow \square \text{NO} + \square \text{H}_2\text{O} \)
- First, let's count the number of each type of atom on both sides of the equation:
- On the left side:
- Nitrogen (N): 1 N in \( \text{NH}_3 \)
- Hydrogen (H): 3 H in \( \text{NH}_3 \)
- Oxygen (O): 2 O in \( \text{O}_2 \)
- On the right side:
- Nitrogen (N): 1 N in \( \text{NO} \)
- Hydrogen (H): 2 H in \( \text{H}_2\text{O} \)
- Oxygen (O): 1 O in \( \text{NO} \) + 1 O in \( \text{H}_2\text{O} \) = 2 O
- To balance the equation:
- We see we need 2 molecules of \( \text{NH}_3 \) to have 2 Nitrogen and 6 Hydrogen.
- This gives us 2 \( \text{NO} \) on the right side.
- To balance the Hydrogen, we needed 3 molecules of \( \text{H}_2\text{O} \), which gives us 6 Hydrogen atoms.
- Finally, to balance Oxygen, we need 2.5 molecules of \( \text{O}_2 \), which gives us 5 Oxygen atoms, 2 of which combine to make 2 \( \text{NO} \) and 3 which combine with Hydrogen to make 3 \( \text{H}_2\text{O} \).
Thus, the balanced equation is:
[tex]\[ 2 \text{NH}_3 + 2.5 \text{O}_2 \rightarrow 2 \text{NO} + 3 \text{H}_2\text{O} \][/tex]
So the final coefficients are:
1. \(1 \text{SiO}_2\) \( + \) \(1 \text{CaC}_2\) \( \rightarrow \) \(1 \text{Si} \) \( + \) \(1 \text{CaO} \) \( + \) \(1 \text{CO}_2 \)
2. [tex]\(2 \text{NH}_3 \)[/tex] [tex]\( + \)[/tex] [tex]\(2.5 \text{O}_2 \)[/tex] [tex]\( \rightarrow \)[/tex] [tex]\(2 \text{NO} \)[/tex] [tex]\( + \)[/tex] [tex]\(3 \text{H}_2\text{O} \)[/tex]
