Use the equation to answer the question. H_2SO_4 + HI -> H_2S + I_2 + H_2O Which option shows a correctly balanced chemical equation?

To balance the chemical equation provided, we need to ensure that the number of each type of atom on the reactant side (left) is equal to the number on the product side (right).

The unbalanced equation is:
\[ \text{H}_2\text{SO}_4 + \text{HI} \rightarrow \text{H}_2\text{S} + \text{I}_2 + \text{H}_2\text{O} \]

Let's count the elements in the unbalanced equation:

- Reactants:
- H: \(2 + 1 = 3\) (from H₂SO₄ and HI)
- S: 1 (from H₂SO₄)
- O: 4 (from H₂SO₄)
- I: 1 (from HI)

- Products:
- H: \(2 + 2 = 4\) (from H₂S and H₂O)
- S: 1 (from H₂S)
- O: 1 (from H₂O)
- I: 2 (from I₂)

Now, let's balance the equation step by step.

### Balancing Steps:
1. **Balance Iodine (I)**:
You have 2 iodines in products (I₂) and only 1 in the reactant (HI). So, we need 2 HI.
\[ \text{H}_2\text{SO}_4 + 2 \text{HI} \rightarrow \text{H}_2\text{S} + \text{I}_2 + \text{H}_2\text{O} \]

2. **Now recount atoms**:
- Reactants:
- H: \(2 + 2 = 4\)
- S: 1
- O: 4
- I: 2

- Products:
- H: \(2 + 2 = 4\)
- S: 1
- O: 1
- I: 2

3. **Balancing Oxygen (O)**:
There are 4 oxygens in the reactants but only 1 in the products. We can add a coefficient of 3 in front of H₂O to balance oxygen.
\[ \text{H}_2\text{SO}_4 + 2 \text{HI} \rightarrow \text{H}_2\text{S} + \text{I}_2 + 3 \text{H}_2\text{O} \]

4. **Now recount the atoms again**:
- At this point, let's recount all atoms:
- Reactants:
- H: \(2 + 2 = 4\) (We need to adjust)
- S: 1
- O: 4
- I: 2

- Products:
- H: \(2 + 2 + 6 = 8\) (from 3 H₂O)
- S: 1
- O: 3
- I: 2

5. **Balance Hydrogen**:
Now we have to adjust the hydrogen in a way that balances out.
To balance the H in products we need to adjust more OH's contributing.

After several adjustments in O, H will equate too.

### Final Balanced Equation:
No further coefficients are necessary for others, we arrive at the balance:
\[ \text{H}_2\text{SO}_4 + 2 \text{HI} \rightarrow \text{H}_2\text{S} + \text{I}_2 + 2 \text{H}_2\text{O} \]

The balanced equation is:
\[ \text{H}_2\text{SO}_4 + 2 \, \text{HI} \rightarrow \text{H}_2\text{S} + \text{I}_2 + 2 \, \text{H}_2\text{O} \]

This means we need to ensure all atoms including Hydrogen are counted when listing them out.