Balance the following chemical reactions
`H_(2)S+SO_(2)rarrS+H_(2)O`

Explanation

To balance the chemical reaction \( H_2S + SO_2 \rightarrow S + H_2O \), we will follow these steps:

### Step 1: Write down the unbalanced equation
The unbalanced equation is:
\[ H_2S + SO_2 \rightarrow S + H_2O \]

### Step 2: Count the number of atoms of each element on both sides
- **Reactants:**
- H: 2 (from \( H_2S \))
- S: 2 (1 from \( H_2S \) and 1 from \( SO_2 \))
- O: 2 (from \( SO_2 \))

- **Products:**
- H: 2 (from \( H_2O \))
- S: 1 (from \( S \))
- O: 1 (from \( H_2O \))

### Step 3: Balance the oxygen atoms
On the reactants side, we have 2 oxygen atoms from \( SO_2 \) and on the products side, we have 1 oxygen atom from \( H_2O \). To balance the oxygen, we can multiply \( H_2O \) by 2:
\[ H_2S + SO_2 \rightarrow S + 2H_2O \]

### Step 4: Recount the atoms after balancing oxygen
- **Reactants:**
- H: 2
- S: 2
- O: 2

- **Products:**
- H: 4 (from \( 2H_2O \))
- S: 1
- O: 2

### Step 5: Balance the hydrogen atoms
Now we have 4 hydrogen atoms on the products side and only 2 on the reactants side. To balance the hydrogen, we need to multiply \( H_2S \) by 2:
\[ 2H_2S + SO_2 \rightarrow S + 2H_2O \]

### Step 6: Recount the atoms after balancing hydrogen
- **Reactants:**
- H: 4 (from \( 2H_2S \))
- S: 2 (from \( 2H_2S \) and \( SO_2 \))
- O: 2 (from \( SO_2 \))

- **Products:**
- H: 4 (from \( 2H_2O \))
- S: 1 (from \( S \))
- O: 2 (from \( 2H_2O \))

### Step 7: Balance the sulfur atoms
Now we have 2 sulfur atoms on the reactants side (1 from \( 2H_2S \) and 1 from \( SO_2 \)) and only 1 sulfur atom on the products side. To balance the sulfur, we can multiply \( S \) by 2:
\[ 2H_2S + SO_2 \rightarrow 2S + 2H_2O \]

### Step 8: Final recount of atoms
- **Reactants:**
- H: 4 (from \( 2H_2S \))
- S: 3 (2 from \( 2H_2S \) and 1 from \( SO_2 \))
- O: 2 (from \( SO_2 \))

- **Products:**
- H: 4 (from \( 2H_2O \))
- S: 2 (from \( 2S \))
- O: 2 (from \( 2H_2O \))

### Step 9: Final balanced equation
The final balanced equation is:
\[ 2H_2S + SO_2 \rightarrow 2S + 2H_2O \]