Question

One of the classic methods for the determination of 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 periodate ion; the products are the permanganate and iodate ions. Write balanced chemical equations for both of these steps.

Short answer

The balanced chemical equations for the two steps are: \(4Fe + 4Mn + 20HNO_{3} \rightarrow 4Mn^{2+} + 20NO_{2} + 10H_{2}O\) \(5Mn^{2+} + 5IO_{4}^{-} + 6H^+ \rightarrow 5MnO_{4}^{-} + 5IO_{3}^{-} + 3H_{2}O\)

Step-by-step solution

Write unbalanced chemical equations

For the first step, we need to write the reaction between steel and nitric acid that leads to the formation of manganese(II) ion and nitrogen dioxide gas. The steel is represented by its main component, iron (Fe), and manganese (Mn). So, the equation would be: \(Fe + Mn + HNO_{3} \rightarrow Mn^{2+} + NO_{2} + H_{2}O\) For the second step, the manganese(II) ion reacts with periodate ions in an acidic medium to form permanganate and iodate ions. The equation would be: \(Mn^{2+} + IO_{4}^{-} + H^+ \rightarrow MnO_{4}^{-} + IO_{3}^{-} + H_{2}O\)

Balance the chemical equations

To balance the first chemical equation, we will adjust the coefficients of each species for atomic balance: \[4Fe + 4Mn + 20HNO_{3} \rightarrow 4Mn^{2+} + 20NO_{2} + 10H_{2}O\] Now, let's balance the second chemical equation: \[5Mn^{2+} + 5IO_{4}^{-} + 6H^+ \rightarrow 5MnO_{4}^{-} + 5IO_{3}^{-} + 3H_{2}O\] So, the balanced chemical equations for both steps are: \(4Fe + 4Mn + 20HNO_{3} \rightarrow 4Mn^{2+} + 20NO_{2} + 10H_{2}O\) \(5Mn^{2+} + 5IO_{4}^{-} + 6H^+ \rightarrow 5MnO_{4}^{-} + 5IO_{3}^{-} + 3H_{2}O\)