Problem 75 - Chemistry and Chemical Reactivity

Question

A Balance the following equations involving organic compounds. (a) \(\mathrm{Ag}^{+}(\mathrm{aq})+\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CHO}(\mathrm{aq}) \longrightarrow\) \(\mathrm{Ag}(\mathrm{s})+\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq}) \quad\) (acid solution) (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(\mathrm{aq}) \longrightarrow\) \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\mathrm{aq})+\mathrm{Cr}^{3+}(\mathrm{aq}) \quad\) (acid solution)

Step-by-Step Solution

Answer

(a) \( \mathrm{C}_6\mathrm{H}_5\mathrm{CHO} + \mathrm{H}_2\mathrm{O} + 2\mathrm{Ag}^+ \rightarrow \mathrm{C}_6\mathrm{H}_5\mathrm{CO}_2\mathrm{H} + 2\mathrm{H}^+ + 2\mathrm{Ag} \); (b) \( 3\mathrm{CH}_3\mathrm{CH}_2\mathrm{OH} + \mathrm{H}_2\mathrm{O} + \mathrm{Cr}_2\mathrm{O}_7^{2-} + 14\mathrm{H}^+ \rightarrow 3\mathrm{CH}_3\mathrm{CO}_2\mathrm{H} + 2\mathrm{Cr}^{3+} + 11\mathrm{H}_2\mathrm{O} \).

Step 1: Identify Redox Reactions

For each reaction, determine the oxidation and reduction half-reactions. In reaction (a), silver is reduced from \( \mathrm{Ag}^+ \) to \( \mathrm{Ag} \), and benzaldehyde \( \mathrm{C}_6\mathrm{H}_5\mathrm{CHO} \) is oxidized to benzoic acid \( \mathrm{C}_6\mathrm{H}_5\mathrm{CO}_2\mathrm{H} \). In reaction (b), ethanol \( \mathrm{CH}_3\mathrm{CH}_2\mathrm{OH} \) is oxidized to acetic acid \( \mathrm{CH}_3\mathrm{CO}_2\mathrm{H} \), and dichromate \( \mathrm{Cr}_2\mathrm{O}_7^{2-} \) is reduced to \( \mathrm{Cr}^{3+} \).

Step 2: Write Oxidation and Reduction Half-Reactions

Write the half-reactions for the oxidation and reduction processes. For (a), oxidation half-reaction: \( \mathrm{C}_6\mathrm{H}_5\mathrm{CHO} \rightarrow \mathrm{C}_6\mathrm{H}_5\mathrm{CO}_2\mathrm{H} \). Reduction half-reaction: \( \mathrm{Ag}^+ \rightarrow \mathrm{Ag} \). For (b), oxidation half-reaction: \( \mathrm{CH}_3\mathrm{CH}_2\mathrm{OH} \rightarrow \mathrm{CH}_3\mathrm{CO}_2\mathrm{H} \). Reduction half-reaction: \( \mathrm{Cr}_2\mathrm{O}_7^{2-} \rightarrow \mathrm{Cr}^{3+} \).

Step 3: Balance Each Half-Reaction

Balance each half-reaction for (a) in terms of atoms and charge. The oxidation needs water and hydrogen ions: \( \mathrm{C}_6\mathrm{H}_5\mathrm{CHO} + \mathrm{H}_2\mathrm{O} \rightarrow \mathrm{C}_6\mathrm{H}_5\mathrm{CO}_2\mathrm{H} + 2\mathrm{H}^+ + 2\mathrm{e}^- \). The reduction involves electrons: \( \mathrm{Ag}^+ + \mathrm{e}^- \rightarrow \mathrm{Ag} \). For (b), the oxidation: \( \mathrm{CH}_3\mathrm{CH}_2\mathrm{OH} + \mathrm{H}_2\mathrm{O} \rightarrow \mathrm{CH}_3\mathrm{CO}_2\mathrm{H} + 4\mathrm{H}^+ + 4\mathrm{e}^- \). The reduction of dichromate: \( \mathrm{Cr}_2\mathrm{O}_7^{2-} + 14\mathrm{H}^+ + 6\mathrm{e}^- \rightarrow 2\mathrm{Cr}^{3+} + 7\mathrm{H}_2\mathrm{O} \).

Step 4: Balance Electrons and Combine Half-Reactions

Equalize the electrons in each half-reaction. For (a), multiply the reduction reaction by 2: \( 2\mathrm{Ag}^+ + 2\mathrm{e}^- \rightarrow 2\mathrm{Ag} \). Combine with oxidation: \( \mathrm{C}_6\mathrm{H}_5\mathrm{CHO} + \mathrm{H}_2\mathrm{O} + 2\mathrm{Ag}^+ \rightarrow \mathrm{C}_6\mathrm{H}_5\mathrm{CO}_2\mathrm{H} + 2\mathrm{H}^+ + 2\mathrm{Ag} \). For (b), multiply the oxidation half by 3 and combine with the reduction: \( 3\mathrm{CH}_3\mathrm{CH}_2\mathrm{OH} + \mathrm{H}_2\mathrm{O} + \mathrm{Cr}_2\mathrm{O}_7^{2-} + 14\mathrm{H}^+ \rightarrow 3\mathrm{CH}_3\mathrm{CO}_2\mathrm{H} + 2\mathrm{Cr}^{3+} + 11\mathrm{H}_2\mathrm{O} \).

Step 5: Verify and Ensure Mass and Charge Balance

Check that each side of the equations is balanced for mass and charge. For (a), both sides have equal numbers of each type of atom and the same overall charge. For (b), verify that atoms of each element and the net charges are balanced; they should both be zero. This confirms that the equations are correctly balanced under acidic conditions.

Key Concepts

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are chemical processes where electrons are transferred between substances. These reactions are critical in both organic and inorganic chemistry. In a redox reaction, one substance is oxidized (loses electrons) and another is reduced (gains electrons). Normal and many biological reactions depend on this electron transfer to occur.

• Oxidation refers to the loss of electrons. For example, in reaction (a), the organic compound benzaldehyde (\( \mathrm{C}_6\mathrm{H}_5\mathrm{CHO} \)) is oxidized to form benzoic acid (\( \mathrm{C}_6\mathrm{H}_5\mathrm{CO}_2\mathrm{H} \)).
• Reduction refers to the gain of electrons. In the same equation, \( \mathrm{Ag}^+ \) ions gain electrons to become \( \mathrm{Ag} \), solid silver.

Connecting this to the rules of redox reactions:

• The species that gets oxidized is known as the reducing agent.
• The species that gets reduced is called the oxidizing agent.

Understanding redox reactions is crucial for further studies in chemistry, including processes like corrosion, combustion, and cellular respiration.

Organic Chemistry

Organic chemistry, with its focus on carbon-containing compounds, is vast and encompasses a range of chemical reactions. In the given problems, the organic molecules undergo transformation through redox processes.
In reaction (b), ethanol (\( \mathrm{CH}_3\mathrm{CH}_2\mathrm{OH} \)) is converted to acetic acid (\( \mathrm{CH}_3\mathrm{CO}_2\mathrm{H} \)) when it is oxidized. This conversion involves the idea that the carbonyl group \( (\mathrm{C}=\mathrm{O}) \) replaces the alcohol group \( (\mathrm{-OH}) \).
Some fundamental concepts in organic chemistry include:

• The role of functional groups such as alcohols, aldehydes, and carboxylic acids, each participating differently in reactions.
• Redox reactions in organic chemistry can involve complex catalysts like \( \mathrm{Cr}_2\mathrm{O}_7^{2-} \) as seen here, which help in oxidizing organic molecules.
• The mechanistic pathway, which describes the steps and intermediates the molecules go through during the reaction.

Understanding these underlying principles is essential when studying organic transformations, whether simple or complex ones in multiple-step synthetic pathways.

Half-Reactions

In redox chemistry, breaking down reactions into half-reactions is a systematic way to understand the electron flow. Each half-reaction shows either oxidation or reduction separately, and by doing so, it makes balancing complex reactions feasible.
Half-reactions are crucial for balancing redox equations under various conditions.
For reaction (a), the oxidation involves benzaldehyde converting to benzoic acid, while the reduction sees \( \mathrm{Ag}^+ \) ions becoming metallic silver. Similarly, in reaction (b), the oxidation half-reaction involves ethanol becoming acetic acid.
Some important points about half-reactions include:

• Each half-reaction is balanced for mass and charge independently before combining them.
• The electrons lost in the oxidation half must match the electrons gained in the reduction half for a balanced equation overall.
• In acidic solutions, which we are dealing with, \( \mathrm{H}^+ \) ions and \( \mathrm{H}_2\mathrm{O} \) are used to balance hydrogen and oxygen atoms as seen in the exercise.

Mastering half-reactions provides a solid foundation for understanding all types of redox processes in chemistry.