To balance the chemical reaction for the tarnishing of silver, we need to ensure that the number of each type of atom on the reactant side is equal to the number on the product side. The given reaction is:
[tex]$\square \, Ag (s) + \square \, H_2S (g) \rightarrow \square \, Ag_2S (s) + \square \, H_2 (g)$[/tex]
Let's go through this step by step:
1. Write down the unbalanced equation:
[tex]\[
\square \, Ag (s) + \square \, H_2S (g) \rightarrow \square \, Ag_2S (s) + \square \, H_2 (g)
\][/tex]
2. Identify the number of atoms of each element on both sides:
- Ag (Silver)
- H (Hydrogen)
- S (Sulfur)
3. Start by balancing the silver (Ag) atoms:
[tex]\[
\square \, Ag (s) + \square \, H_2S (g) \rightarrow 1 \, Ag_2S (s) + \square \, H_2 (g)
\][/tex]
We have 2 Ag atoms in [tex]\(Ag_2S\)[/tex] on the product side. So, we need 2 Ag atoms on the reactant side:
[tex]\[
2 \, Ag (s) + \square \, H_2S (g) \rightarrow 1 \, Ag_2S (s) + \square \, H_2 (g)
\][/tex]
4. Next, balance the hydrogen (H) atoms:
[tex]\[
2 \, Ag (s) + 1 \, H_2S (g) \rightarrow 1 \, Ag_2S (s) + \square \, H_2 (g)
\][/tex]
We have 2 H atoms in [tex]\(H_2S\)[/tex] on the reactant side and [tex]\(H_2\)[/tex] on the product side. Since [tex]\(H_2\)[/tex] contains 2 H atoms:
[tex]\[
2 \, Ag (s) + 1 \, H_2S (g) \rightarrow 1 \, Ag_2S (s) + 1 \, H_2 (g)
\][/tex]
5. Check the balance of sulfur (S) atoms last:
[tex]\[
2 \, Ag (s) + 1 \, H_2S (g) \rightarrow 1 \, Ag_2S (s) + 1 \, H_2 (g)
\][/tex]
We have 1 S atom in [tex]\(H_2S\)[/tex] on the reactant side and 1 S atom in [tex]\(Ag_2S\)[/tex] on the product side.
After balancing the equation, the coefficients are:
- 2 for Ag (solid)
- 1 for H_2S (gas)
- 1 for Ag_2S (solid)
- 1 for H_2 (gas)
Thus, the balanced chemical equation is:
[tex]\[
2 \, Ag (s) + 1 \, H_2S (g) \rightarrow 1 \, Ag_2S (s) + 1 \, H_2 (g)
\][/tex]
So the coefficients that balance the tarnishing reaction equation are:
- Coefficient for [tex]\(Ag\)[/tex]: 2
- Coefficient for [tex]\(H_2S\)[/tex]: 1
- Coefficient for [tex]\(Ag_2S\)[/tex]: 1
- Coefficient for [tex]\(H_2\)[/tex]: 1
In summary:
[tex]\[
\boxed{2 \, Ag (s) + 1 \, H_2S (g) \rightarrow 1 \, Ag_2S (s) + 1 \, H_2 (g)}
\][/tex]
