Question

Write the balanced net ionic equation for the reaction between \(\mathrm{MnO}_{4}\) - ion and \(\mathrm{Fe}^{2+}\) ion in acid solution.

Short answer

The balanced net ionic equation for the reaction between \( \mathrm{MnO}_{4}^{ - } \) ion and \( \mathrm{Fe}^{2+} \) ion in acid solution is: \[ \mathrm{MnO}_{4}^{ - } + 8\mathrm{H}^{+} + 5\mathrm{Fe}^{2+} \rightarrow \mathrm{Mn}^{2+} + 4\mathrm{H}_{2}\mathrm{O} + 5\mathrm{Fe}^{3+} \]

Step-by-step solution

Write the unbalanced equation

First, an unbalanced equation can be written down representing the reaction: \[ \mathrm{MnO}_{4}^{ - } + \mathrm{Fe}^{2+} \rightarrow \mathrm{Mn}^{2+} + \mathrm{Fe}^{3+}\]

Balance the atoms other than O and H

At this stage, the manganese (\( \mathrm{Mn} \)) and iron (\( \mathrm{Fe} \)) atoms are already balanced. Therefore, there is no need for any adjustments.

Balance the oxygen atoms with water molecules

There are 4 oxygen atoms on the left side of the equation and none on the right. Water molecules (\( \mathrm{H}_{2}\mathrm{O} \)) can now be added to the right side to balance the oxygen atoms: \[ \mathrm{MnO}_{4}^{ - } + \mathrm{Fe}^{2+} \rightarrow \mathrm{Mn}^{2+} + \mathrm{Fe}^{3+} + 4\mathrm{H}_{2}\mathrm{O} \]

Balance hydrogen atoms with H+ ions

Balancing the hydrogen atoms present in the water molecules is achieved by adding hydrogen ions (\( \mathrm{H}^{+} \)) to the left side of the equation. Now the equation becomes: \[ \mathrm{MnO}_{4}^{ - } + \mathrm{Fe}^{2+} + 8\mathrm{H}^{+} \rightarrow \mathrm{Mn}^{2+} + \mathrm{Fe}^{3+} + 4\mathrm{H}_{2}\mathrm{O} \]

Balance the charges by adding electrons

After the atoms are balanced, now balance the charges. There is a positive charge on the left side of the equation, which can be balanced by adding 5 electrons. Now the equation is: \[ \mathrm{MnO}_{4}^{ - } + 8\mathrm{H}^{+} + 5\mathrm{e}^{-} \rightarrow \mathrm{Mn}^{2+} + 4\mathrm{H}_{2}\mathrm{O} \] \[ \mathrm{Fe}^{2+} \rightarrow \mathrm{Fe}^{3+} + \mathrm{e}^{-} \]

Make the number of electrons of two half-reactions equal

To balance the two half reactions, adjust the coefficients so the number of electrons in both reactions are equal. In this case, multiplying the second equation by 5 gives: \[ 5\mathrm{Fe}^{2+} \rightarrow 5\mathrm{Fe}^{3+} + 5\mathrm{e}^{-} \]

Combine the half-reactions and write the final balanced equation

Combine the two equations above to the final balanced net ionic equation and eliminate the electrons from both sides: \[ \mathrm{MnO}_{4}^{ - } + 8\mathrm{H}^{+} + 5\mathrm{Fe}^{2+} \rightarrow \mathrm{Mn}^{2+} + 4\mathrm{H}_{2}\mathrm{O} + 5\mathrm{Fe}^{3+} \]

Key concepts

Chemical Reaction Balancing

Balancing a chemical equation ensures the law of conservation of mass is upheld, meaning the number of atoms for each element must be the same on both sides of the equation. For the reaction between the permanganate ion (\r\(\mathrm{MnO}_4^-\)) and the iron(II) ion (\r\(\mathrm{Fe}^{2+}\)), we initially noted that manganese and iron were balanced. However, oxygen and hydrogen, as well as charges, were not. To balance these, we added water (\r\(\mathrm{H}_2\mathrm{O}\)) to account for oxygen and then hydrogen ions (\r\(\mathrm{H}^+\)) to balance hydrogen atoms. Lastly, we added electrons to balance the overall charge, an essential step in redox reactions. Balancing equations can sometimes be challenging, but with practice, students can quickly identify the steps needed to create a balanced equation.

Oxidation-Reduction Reactions

Oxidation-reduction (redox) reactions involve the transfer of electrons from one substance to another. In our exercise, \r\(\mathrm{MnO}_4^-\) is reduced to \r\(\mathrm{Mn}^{2+}\) and \r\(\mathrm{Fe}^{2+}\) is oxidized to \r\(\mathrm{Fe}^{3+}\). The key to writing half-reactions for redox processes involves identifying the species that gain electrons (reduction) and those that lose electrons (oxidation). Balancing these half-reactions separately and then combining them ensures both mass and charge are conserved. Remember, in a balanced redox reaction, the number of electrons lost in the oxidation process must equal the number of electrons gained during reduction, as seen when we adjusted the iron half-reaction by multiplying by 5 to match the manganese half-reaction.

Stoichiometry

Stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction. In the net ionic equation for the reaction between \r\(\mathrm{MnO}_4^-\) and \r\(\mathrm{Fe}^{2+}\), the stoichiometric coefficients provide the ratio in which reactants react to form products. Step 6 of our solution is crucial, where we ensure the stoichiometry of electrons is correct. By multiplying the iron half-reaction by 5, we equated the electron transfer to balance the overall reaction. Stoichiometry doesn't just stop at balancing reactions; it also allows chemists to predict the amount of product formed or reactant needed, which is the backbone of all chemical manufacturing and laboratory work.