Write the balanced half-reaction for the change of \(\mathrm{SO}_{2}(a q)\) to \(\mathrm{HSO}_{4}^{-}(a q)\) in acidic solution.

Short Answer

Expert verified
The balanced half-reaction for the change of \(\mathrm{SO}_{2}(a q)\) to \(\mathrm{HSO}_{4}^{-}(a q)\) in acidic solution is \(\mathrm{SO}_{2}(a q) + 2H_2O \rightarrow \mathrm{HSO}_{4}^{-}(a q) + 4H^+ + 2e^-\)

Step by step solution

01

Balance Sulfur Atoms

Start by balancing the atoms that change oxidation state, in this case sulfur. This gives us \(\mathrm{SO}_{2}(a q)\) to \(\mathrm{HSO}_{4}^{-}(a q)\). No balancing is needed for Sulfur because there's one in each side.
02

Balance Oxygen Atoms

We balance the oxygen atoms by adding the appropriate number of water molecules on the side deficient in oxygen. In this case, add 2 H\(_2\)O to the left side: \(\mathrm{SO}_{2}(a q) + 2H_2O \rightarrow \mathrm{HSO}_{4}^{-}(a q)\)
03

Balance Hydrogen Atoms

Hydrogen atoms are balanced by adding the appropriate number of H\(^+\) ions on the side that needs hydrogen. Add 4 H\(^+\) to the right side: \(\mathrm{SO}_{2}(a q) + 2H_2O \rightarrow \mathrm{HSO}_{4}^{-}(a q) + 4H^+\)
04

Balance Charges

To balance the charge, we add electrons to the more positive side. In this case, add 2 electrons to the right side: \(\mathrm{SO}_{2}(a q) + 2H_2O \rightarrow \mathrm{HSO}_{4}^{-}(a q) + 4H^+ + 2e^-\). Now, the charge is balanced.

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