Problem 43 - General Chemistry: Principles and Modern Applications

Question

Write a balanced equation for these redox reactions. (a) The oxidation of nitrite ion to nitrate ion by permanganate ion, \(\mathrm{MnO}_{4}^{-}\), in acidic solution \(\left(\mathrm{MnO}_{4}^{-}\right.\) ion is reduced to \(\mathrm{Mn}^{2+}\) ). (b) The reaction of manganese(II) ion and permanganate ion in basic solution to form solid manganese dioxide. (c) The oxidation of ethanol by dichromate ion in acidic solution, producing chromium(III) ion, acetaldehyde \(\left(\mathrm{CH}_{3} \mathrm{CHO}\right),\) and water as products.

Step-by-Step Solution

Answer

The balanced equations for the redox reactions are: (a) \(6NO_{2}^- + 2MnO_{4}^- + 8H^+ \rightarrow 6NO_{3}^- + 2Mn^{2+} + 4H_2O \), (b) \(3Mn^{2+} + MnO_{4}^- + 2H_2O \rightarrow 4MnO_2 + 4OH^{-}\), (c) \(C_2H_5OH + Cr_{2}O_{7}^{2-} + 16H^+ \rightarrow CH_{3}CHO + 2Cr^{3+} + 11H_2O\).

Step 1: Balancing Redox Equation for Reaction (a)

Identify each half-reaction: oxidation half-reaction: nitrite ion (\(NO_{2}^-\)) to nitrate ion (\(NO_{3}^-\)); reduction half-reaction: permanganate ion (\(MnO_{4}^-\)) to manganese ion (\(Mn^{2+}\)). Balance the elements and then the charge in each half-reaction. Add the balanced half-reactions together to get the final balanced equation: \(6NO_{2}^- + 2MnO_{4}^- + 8H^+ \rightarrow 6NO_{3}^- + 2Mn^{2+} + 4H_2O \)

Step 2: Balancing Redox Equation for Reaction (b)

Identify each half-reaction: oxidation half-reaction: manganese(II) ion (\(Mn^{2+}\)) to manganese dioxide (\(MnO_{2}\)); reduction half-reaction: permanganate ion (\(MnO_{4}^-\)) to manganese dioxide (\(MnO_{2}\)). Balance the elements and then the charge in each half-reaction. Add the balanced half-reactions together to get the final balanced equation: \(3Mn^{2+} + MnO_{4}^- + 2H_2O \rightarrow 4MnO_2 + 4OH^{-}\)

Step 3: Balancing Redox Equation for Reaction (c)

Identify each half-reaction: oxidation half-reaction: ethanol (\(C_2H_5OH\)) to acetaldehyde (\(CH_{3}CHO\)); reduction half-reaction: dichromate ion (\(Cr_{2}O_{7}^{2-}\)) to chromium(III) ion (\(Cr^{3+}\)). Balance the elements and then the charge in each half-reaction. Add the balanced half-reactions together to get the final balanced equation: \(C_2H_5OH + Cr_{2}O_{7}^{2-} + 16H^+ \rightarrow CH_{3}CHO + 2Cr^{3+} + 11H_2O\)

Key Concepts

Balancing Chemical Equations

Balancing chemical equations is a crucial skill in chemistry. It ensures that the number of atoms for each element is conserved in a chemical reaction, reflecting the law of conservation of mass. To balance an equation, follow these steps:

• Identify the reactants and products in a reaction.
• Write the "skeleton" equation with all chemical formulas.
• Count the number of atoms for each element on both sides.
• Add coefficients to balance each element, starting with the most complex molecules.
• Check your work to ensure all elements are balanced and that the coefficients are in the simplest ratio.

Balancing is not just about mathematical accuracy—it's crucial for understanding the stoichiometry of reactions, which indicates the precise amount of reactants needed to obtain a certain amount of product.

Oxidation and Reduction

Oxidation and reduction, often called redox reactions, are processes where electrons are transferred between substances. Here's what you need to know:

• Oxidation: This is the loss of electrons by a molecule, atom, or ion. It often results in an increase in oxidation state.
• Reduction: This is the gain of electrons, resulting in a decrease in oxidation state.
• Redox reactions are split into two half-reactions: one for oxidation and one for reduction.
• Each half-reaction must be balanced in terms of both mass and charge.

Balancing redox reactions involves identifying these changes in electron transfer and is fundamental for understanding many chemical processes, including those in batteries and biological systems.

Permanganate Reactions

Permanganate ions (\( MnO_{4}^{-} \)) are powerful oxidizing agents used in various chemical reactions. Depending on the conditions, they can be reduced to different manganese species.

• In acidic solutions, they are typically reduced to \( Mn^{2+} \) as observed in many redox reactions.
• In neutral or basic conditions, permanganate may reduce to manganese dioxide \( MnO_{2} \), a solid that can form as a precipitate.
• Understanding these reactions helps predict the products and balance equations involving permanganate.

These reactions are frequently involved in laboratory procedures and industrial applications because of their strong oxidizing properties. Knowing how permanganate behaves under different conditions aids in controlling and utilizing chemical reactions effectively.