Write the chemical formula for each of the following compounds, and indicate the oxidation state of nitrogen in each: (a) dinitrogen trioxide, (b) dinitrogen pentoxide, (c) hydrogen cyanide, (d) ammonium nitrate, (e) iron(III) nitrite, \((\mathbf{f})\) nitrogen trichloride.

To write the chemical formula for each compound, we need to balance the charges of the elements involved. We'll do this for each compound listed: a) Dinitrogen trioxide: There are 2 nitrogen (N) atoms and 3 oxygen (O) atoms. Chemical formula: \(N_2O_3\) b) Dinitrogen pentoxide: There are 2 nitrogen (N) atoms and 5 oxygen (O) atoms. Chemical formula: \(N_2O_5\) c) Hydrogen cyanide: There is 1 hydrogen (H) atom, 1 carbon (C) atom, and 1 nitrogen (N) atom. Chemical formula: \(HCN\) d) Ammonium nitrate: This compound contains 1 ammonium ion (\(NH_4^+\)) and 1 nitrate ion (\(NO_3^-\)). Chemical formula: \(NH_4NO_3\) e) Iron(III) nitrite: This compound contains 1 iron (Fe) ion with a charge of +3 and 3 nitrite ions (\(NO_2^-\)) to balance the charge. Chemical formula: \(Fe(NO_2)_3\) f) Nitrogen trichloride: There is 1 nitrogen (N) atom and 3 chlorine (Cl) atoms. Chemical formula: \(NCl_3\)

We will apply the oxidation state rules to find the oxidation state of nitrogen in each compound: a) In \(N_2O_3\), the oxidation state of oxygen is typically -2. The overall charge of the molecule is 0, and there are two nitrogen atoms, so the combined oxidation state of the nitrogen atoms is +6 (3 x (-2) = -6). For each nitrogen atom, the oxidation state is +3. Oxidation state of N in \(N_2O_3\): +3 b) In \(N_2O_5\), the oxidation state of oxygen is typically -2. The overall charge of the molecule is 0, and there are two nitrogen atoms, so the combined oxidation state of the nitrogen atoms is +10 (5 x (-2) = -10). For each nitrogen atom, the oxidation state is +5. Oxidation state of N in \(N_2O_5\): +5 c) In \(HCN\), the oxidation state of hydrogen is typically +1, and carbon's oxidation state is +2 (since it's part of a cyanide ion). Nitrogen's oxidation state balances the charge in the cyanide ion. Oxidation state of N in \(HCN\): -3 d) In \(NH_4NO_3\), the ammonium ion (NH4+) has an oxidation state of +1 for hydrogen and -3 for nitrogen, and the nitrate ion (\(NO_3^-\)) has an oxidation state of -2 for oxygen and +5 for nitrogen. Oxidation states of N in \(NH_4NO_3\): -3 (in ammonium) and +5 (in nitrate) e) In \(Fe(NO_2)_3\), the iron ion has an oxidation state of +3, and the oxidation state of oxygen in nitrite ions is typically -2. Nitrogen balances the charge in the nitrite ion. Oxidation state of N in \(Fe(NO_2)_3\): +3 f) In \(NCl_3\), the oxidation state of chlorine is typically -1. Nitrogen balances the charge in the molecule. Oxidation state of N in \(NCl_3\): +3