To balance the 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 each type of atom is the same on both sides of the equation.
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Counting the atoms:
- Left side:
- H: 2 (from H2SO4) + 1 (from HI) = 3
- S: 1 (from H2SO4)
- O: 4 (from H2SO4)
- I: 1 (from HI)
- Right side:
- H: 2 (from H2S) + 2 (from H2O) = 4
- S: 1 (from H2S)
- O: 1 (from H2O)
- I: 2 (from I2)
- Left side:
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Balancing the equation:
- Start with S, which is already balanced.
- Balance I and H by adjusting the coefficients:
- Following the original reaction, we can start with 8 HI to balance the iodine.
- This leads to new counts (portray this as \( \text{H}_2\text{SO}_4 + 8 \text{HI} \)):
- Left side: H (2 + 8) = 10, S (1), O (4), I (8)
- Right side coming from \( \text{H}_2\text{S} + 4 \text{I}_2 + 4 \text{H}_2\text{O} \)
- Right side: H (2 + 4) = 6, S (1), O (4), I (8)
- So the balanced reaction becomes: \[ \text{H}_2\text{SO}_4 + 8 \text{HI} \rightarrow \text{H}_2\text{S} + 4 \text{I}_2 + 4 \text{H}_2\text{O} \]
Thus, the correctly balanced chemical equation from the options you provided is:
H2SO4 + 8HI → H2S + 4I2 + 4H2O.