One of the classic methods for determining the manganese content in steel involves converting all the manganese to the deeply colored permanganate ion and then measuring the absorption of light. The steel is first dissolved in nitric acid, producing the manganese(II) ion and nitrogen dioxide gas. This solution is then reacted with an acidic solution containing the periodate ion; the products are the permanganate and iodate ions. Write balanced chemical equations for both of these steps.

To write a balanced chemical equation for the dissolution of steel in nitric acid, we first need to identify the component of steel that contains manganese. Steel is an alloy mainly composed of iron and carbon, but it also contains trace amounts of manganese. The manganese content in steel is represented by Mn. The dissolution of steel in nitric acid (HNO₃) will produce manganese(II) ions (Mn²⁺) and nitrogen dioxide gas (NO₂). The initial chemical equation can be written as: Mn (s) + HNO₃ (aq) → Mn²⁺ (aq) + NO₂ (g) Now we need to balance the chemical equation. The reaction also produces H₂O (l) as a byproduct. The balanced chemical equation is: Mn (s) + 2 HNO₃ (aq) → Mn²⁺ (aq) + 2 NO₂ (g) + H₂O (l)

We now need to write a balanced chemical equation for the reaction of the solution containing manganese(II) ions (Mn²⁺) with an acidic solution containing the periodate ion (IO₄⁻). The products of this reaction are permanganate ions (MnO₄⁻) and iodate ions (IO₃⁻). The initial chemical equation can be written as: Mn²⁺ (aq) + IO₄⁻ (aq) → MnO₄⁻ (aq) + IO₃⁻ (aq) Now we need to balance the charges and the atoms in the equation. The balanced chemical equation for the reaction is: 2 Mn²⁺ (aq) + 5 IO₄⁻ (aq) + 12 H⁺ (aq) → 2 MnO₄⁻ (aq) + 5 IO₃⁻ (aq) + 6 H₂O (l) Both balanced chemical equations for the consecutive steps to determine the manganese content in steel are provided as follows: 1. Mn (s) + 2 HNO₃ (aq) → Mn²⁺ (aq) + 2 NO₂ (g) + H₂O (l) 2. 2 Mn²⁺ (aq) + 5 IO₄⁻ (aq) + 12 H⁺ (aq) → 2 MnO₄⁻ (aq) + 5 IO₃⁻ (aq) + 6 H₂O (l)