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