Give the formula of (a) an anion in which \(S\) has an oxidation number of \(-2\). (b) two anions in which \(\mathrm{S}\) has an oxidation number of \(+4\). (c) two different acids of sulfur.

To determine an anion where sulfur has an oxidation number of -2, we need to consider that anions are negatively charged, and sulfur needs to gain 2 electrons to reach the oxidation state of -2. When sulfur gains two electrons, it forms a sulfide anion, represented as \(\mathrm{S}^{2-}\). So, the answer is: $$\mathrm{S}^{2-}$$

Now, we need to find two anions where sulfur has an oxidation number of +4. To determine these, let's look at oxyanions of sulfur, which are anions containing sulfur and oxygen atoms. We'll find two anions where the total charge of the oxygen atoms equals the charge of sulfur minus 4: 1. The first anion we'll consider is the sulfate ion. The sulfate ion has the formula \(\mathrm{SO_4^{2-}}\). In this ion, there are four oxygen atoms, each with an oxidation state of -2. The total charge of the four oxygen atoms is \(-8\). Therefore, the charge of the sulfur atom in the sulfate ion is: $$\mathrm{-4 = Charge\ of\ S + Charge\ of\ O}$$ $$\mathrm{+4}$$ So, the first anion is the sulfate ion, \(\mathrm{SO_4^{2-}}\). 2. The second anion we'll consider is the thiosulfate ion. The thiosulfate ion has the formula \(\mathrm{S_2O_3^{2-}}\). In this ion, there are three oxygen atoms with an oxidation state of -2 and another sulfur atom with an oxidation state of -2. Therefore, the total charge of all atoms in the ion, except for the one sulfur atom we're considering, is -8. So, the charge of the sulfur atom in question is: $$\mathrm{-4 = Charge\ of\ S + Charge\ of\ O + Charge\ of\ S}$$ $$\mathrm{+4}$$ Thus, the second anion is the thiosulfate ion, \(\mathrm{S_2O_3^{2-}}\). The two anions where sulfur has an oxidation number of +4 are: $$\mathrm{SO_4^{2-}}$$ $$\mathrm{S_2O_3^{2-}}$$

Finally, we need to find two different acids of sulfur. Acids containing sulfur usually have the general formula \(\mathrm{H_2SO_n}\), where \(\mathrm{n}\) is an integer. 1. The first acid we'll consider is sulfuric acid. Sulfuric acid has the formula \(\mathrm{H_2SO_4}\). It is formed when the sulfate ion (\(\mathrm{SO_4^{2-}}\)) gains two hydrogen atoms from a proton donor: $$\mathrm{H_2SO_4}$$ 2. The second acid we'll consider is sulfurous acid. Sulfurous acid has the formula \(\mathrm{H_2SO_3}\). It is formed when the bisulfite ion (\(\mathrm{HSO_3^{-}}\)) gains a hydrogen atom from a proton donor: $$\mathrm{H_2SO_3}$$ The two acids of sulfur are: $$\mathrm{H_2SO_4} \ (sulfuric\ acid)$$ $$\mathrm{H_2SO_3} \ (sulfurous\ acid)$$