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 \( \text{H}_2\text{SO}_4 + \text{HI} \rightarrow \text{H}_2\text{S} + \text{I}_2 + \text{H}_2\text{O} \), we need to ensure that the number of atoms of each element is the same on both sides of the equation.

Let's break it down:

1. **Count the atoms on the reactant side:**
- H (hydrogen): 2 (from H₂SO₄) + 1 (from HI) = 3
- S (sulfur): 1 (from H₂SO₄)
- O (oxygen): 4 (from H₂SO₄)
- I (iodine): 1 (from HI)

2. **Count the atoms on the product side before balancing:**
- H (hydrogen): 2 (from H₂S) + 2 (from H₂O) = 4
- S (sulfur): 1 (from H₂S)
- O (oxygen): 1 (from H₂O)
- I (iodine): 2 (from I₂)

From these initial counts, we can see that the number of atoms are not balanced.

Now, let's check each option:

- **Option A:** H₂SO₄ + HI → H₂S + I₂ + H₂O
- This is not balanced (count as previously shown).

- **Option B:** H₂SO₄ + 8HI → H₂S + 4I₂ + 4H₂O
- Reactant side: H: 2 + 8 = 10, S: 1, O: 4, I: 8
- Product side: H: 2 + 8 = 10, S: 1, O: 4, I: 8
- This is balanced.

- **Option C:** 2H₂SO₄ + 2HI → 2H₂S + I₂ + 4H₂O
- Reactant side: H: 4 + 2 = 6, S: 2, O: 8, I: 2
- Product side: H: 4 + 8 = 12, S: 2, O: 4, I: 2
- This is not balanced.

- **Option D:** H₂SO₄ + 8HI → H₂S + 8I₂ + 4H₂O
- Reactant side: H: 2 + 8 = 10, S: 1, O: 4, I: 8
- Product side: H: 2 + 8 = 10, S: 1, O: 4, I: 16
- This is not balanced.

The only option that shows a correctly balanced chemical equation is:

**B. H₂SO₄ + 8HI → H₂S + 4I₂ + 4H₂O**