Balance this chemical equation and classify it as combination, decomposition, single-replacement, or double-replacement: \(\mathrm{K}_{2} \mathrm{SO}_{3}+\mathrm{S}_{8} \rightarrow \mathrm{K}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\)

First, let's identify the reactants and products in the given equation: Reactants: \(\mathrm{K}_{2} \mathrm{SO}_{3}\) (potassium sulfite) and \(\mathrm{S}_{8}\) (sulfur) Products: \(\mathrm{K}_{2} \mathrm{S}_{2} \mathrm{O}_{3}\) (potassium thiosulfate)

Next, we need to balance the equation by making sure the number of atoms of each element is the same on both sides of the equation. The original equation: \(\mathrm{K}_{2} \mathrm{SO}_{3} + \mathrm{S}_{8} \rightarrow \mathrm{K}_{2} \mathrm{S}_{2} \mathrm{O}_{3}\) Balanced equation (with coefficients for the reactants and products): \(\mathrm{4K}_{2} \mathrm{SO}_{3} + 3\mathrm{S}_{8} \rightarrow 8\mathrm{K}_{2} \mathrm{S}_{2} \mathrm{O}_{3}\) On both sides of the equation, we now have 8 potassium atoms, 24 sulfur atoms, and 12 oxygen atoms.

Finally, we will classify the reaction according to the four possible types: combination, decomposition, single-replacement, or double-replacement. Combination: Two or more reactants combine to form a single product. This does not apply, as there are multiple products. Decomposition: A single reactant breaks apart into two or more products. This does not apply, as there are multiple reactants. Single-replacement: One element replaces another element in a compound. This does not apply, as no single element is being replaced. Double-replacement: The positive and negative ions in two ionic compounds exchange places. This does not apply, as there is only one ionic compound involved. None of the above categories perfectly fit our reaction, so this reaction is best described as a redox reaction (reduction-oxidation) where the oxidation state of sulfur in potassium sulfite is changing due to the gain of more sulfur atoms. The balanced chemical equation is: \(\mathrm{4K}_{2} \mathrm{SO}_{3} + 3\mathrm{S}_{8} \rightarrow 8\mathrm{K}_{2} \mathrm{S}_{2} \mathrm{O}_{3}\) The reaction is classified as a redox reaction.