To balance the given chemical reaction equation, we need to ensure that the number of atoms for each element is the same on both the reactant and the product sides. Here is the step-by-step process:
1. The initial unbalanced chemical equation is:
[tex]\[
\text{Ag} (s) + \text{H}_2\text{S} (g) \rightarrow \text{Ag}_2\text{S} (s) + \text{H}_2 (g)
\][/tex]
2. Identify the elements involved in the reaction. We have:
- Silver (Ag)
- Hydrogen (H)
- Sulfur (S)
3. Start balancing the elements that appear in only one reactant and one product.
4. Balancing Silver (Ag):
On the reactant side, we have 1 Ag. On the product side, [tex]$\text{Ag}_2\text{S}$[/tex] contains 2 Ag atoms. Therefore, we need 2 Ag atoms on the reactant side:
[tex]\[
2 \text{Ag} (s) + \text{H}_2\text{S} (g) \rightarrow \text{Ag}_2\text{S} (s) + \text{H}_2 (g)
\][/tex]
5. Balancing Hydrogen (H):
On the reactant side, [tex]$\text{H}_2\text{S}$[/tex] contains 2 H atoms. On the product side, [tex]$\text{H}_2$[/tex] also contains 2 H atoms. The hydrogen atoms are already balanced:
[tex]\[
2 \text{Ag} (s) + \text{H}_2\text{S} (g) \rightarrow \text{Ag}_2\text{S} (s) + \text{H}_2 (g)
\][/tex]
6. Balancing Sulfur (S):
On the reactant side, [tex]$\text{H}_2\text{S}$[/tex] contains 1 S atom. On the product side, [tex]$\text{Ag}_2\text{S}$[/tex] also contains 1 S atom. The sulfur atoms are also balanced:
[tex]\[
2 \text{Ag} (s) + \text{H}_2\text{S} (g) \rightarrow \text{Ag}_2\text{S} (s) + \text{H}_2 (g)
\][/tex]
7. Verify that all elements are balanced:
- Silver (Ag): 2 atoms on both sides
- Hydrogen (H): 2 atoms on both sides
- Sulfur (S): 1 atom on both sides
8. The final balanced equation is:
[tex]\[
2 \text{Ag} (s) + \text{H}_2\text{S} (g) \rightarrow \text{Ag}_2\text{S} (s) + \text{H}_2 (g)
\][/tex]
Therefore, the coefficients that balance the tarnishing reaction equation are:
- For [tex]$Ag$[/tex]: 2
- For [tex]$H_2S$[/tex]: 1
- For [tex]$Ag_2S$[/tex]: 1
- For [tex]$H_2$[/tex]: 1
