To solve for the balanced chemical equation provided:
[tex]\[ \text{CuO} + \text{NH}_3 \rightarrow \text{Cu} + \text{H}_2\text{O} + \text{N}_2 \][/tex]
We need to ensure that the number of atoms of each element is the same on both sides of the equation. Here are the steps to balance the equation:
1. Write down the unbalanced equation:
[tex]\[ \text{CuO} + \text{NH}_3 \rightarrow \text{Cu} + \text{H}_2\text{O} + \text{N}_2 \][/tex]
2. List the number of atoms of each element present in the unbalanced equation:
- Left Side:
- Cu: 1
- O: 1
- N: 1
- H: 3
- Right Side:
- Cu: 1
- O: 1
- N: 2
- H: 2
3. Begin balancing elements that appear in only one reactant and one product first. In this case, balance nitrogen (N) atoms:
There are 2 nitrogen atoms on the right side in [tex]\(\text{N}_2\)[/tex] and only 1 nitrogen atom on the left side in [tex]\(\text{NH}_3\)[/tex]. Therefore, we need to multiply [tex]\(\text{NH}_3\)[/tex] by 2:
[tex]\[ \text{CuO} + 2\text{NH}_3 \rightarrow \text{Cu} + \text{H}_2\text{O} + \text{N}_2 \][/tex]
4. Update the count of each element:
- Left Side:
- Cu: 1
- O: 1
- N: 2
- H: 6
- Right Side:
- Cu: 1
- O: 1
- N: 2
- H: 2
Notice, as a result of the updating process that Hydrogen (H) atoms are not balanced yet.
5. Balance the hydrogen (H) atoms next:
There are 6 hydrogen atoms on the left side and only 2 hydrogen atoms on the right side. Therefore, we need to multiply [tex]\(\text{H}_2\text{O}\)[/tex] by 3:
[tex]\[ \text{CuO} + 2\text{NH}_3 \rightarrow \text{Cu} + 3\text{H}_2\text{O} + \text{N}_2 \][/tex]
6. Update the count of each element again:
- Left Side:
- Cu: 1
- O: 1
- N: 2
- H: 6
- Right Side:
- Cu: 1
- O: 3
- N: 2
- H: 6
After balancing the hydrogen atoms, the oxygen atoms are imbalanced.
7. Balance the oxygen (O) atoms last:
There are 3 oxygen atoms on the right side and only 1 oxygen atom on the left side. Thus, we need to multiply [tex]\(\text{CuO}\)[/tex] by 3:
[tex]\[ 3\text{CuO} + 2\text{NH}_3 \rightarrow 3\text{Cu} + 3\text{H}_2\text{O} + \text{N}_2 \][/tex]
8. Final count of each element:
- Left Side:
- Cu: 3
- O: 3
- N: 2
- H: 6
- Right Side:
- Cu: 3
- O: 3
- N: 2
- H: 6
As shown above, the number of atoms for each element is the same on both sides of the equation, showing that the equation is balanced.
Therefore, the balanced chemical equation is:
[tex]\[ 3\text{CuO} + 2\text{NH}_3 \rightarrow 3\text{Cu} + 3\text{H}_2\text{O} + \text{N}_2 \][/tex]
