Problem 84 - Chemistry and Chemical Reactivity

Question

A Write balanced equations for the following reduction half-reactions involving organic compounds. (a) \(\mathrm{HCO}_{2} \mathrm{H} \rightarrow \mathrm{CH}_{2} \mathrm{O} \quad\) (acid solution) (b) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H} \rightarrow \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3} \quad\) (acid solution) (c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO} \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH} \quad\) (acid solution) (d) \(\mathrm{CH}_{3} \mathrm{OH} \rightarrow \mathrm{CH}_{4}\) (acid solution)

Step-by-Step Solution

Answer

Balanced half-reactions: (a) \(\mathrm{HCO}_{2} \mathrm{H} + 2\mathrm{H}^{+} + 2\mathrm{e}^{-} \rightarrow \mathrm{CH}_{2} \mathrm{O} + \mathrm{H}_{2}\mathrm{O}\); (b) \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H} + 8\mathrm{H}^{+} + 8\mathrm{e}^{-} \rightarrow \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3} + 2\mathrm{H}_{2}\mathrm{O}\); (c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO} + 2\mathrm{H}^{+} + 2\mathrm{e}^{-} \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\); (d) \(\mathrm{CH}_{3} \mathrm{OH} + 2\mathrm{H}^{+} + 2\mathrm{e}^{-} \rightarrow \mathrm{CH}_{4} + \mathrm{H}_{2}\mathrm{O}\).

Step 1: Analyze the Reaction (a)

Identify the changes in the organic molecule structure during the reduction of \(\mathrm{HCO}_{2} \mathrm{H}\) to \(\mathrm{CH}_{2} \mathrm{O}\). Formic acid is reduced to formaldehyde.

Step 2: Balancing Oxygen and Hydrogen (a)

In an acidic solution, water \(\mathrm{H}_{2}\mathrm{O}\) and hydrogen ions \( \mathrm{H}^+ \) are used to balance the oxygen and hydrogen atoms. There are 2 oxygens on the left, but only 1 on the right. Add one \(\mathrm{H}_{2}\mathrm{O}\) to the left to balance the oxygens: \(\mathrm{HCO}_{2} \mathrm{H} + \mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{CH}_{2} \mathrm{O}\). Add 2 \(\mathrm{H}^+\) to the left to balance hydrogens: \(\mathrm{HCO}_{2} \mathrm{H} + 2\mathrm{H}^{+} + 2\mathrm{e}^{-} \rightarrow \mathrm{CH}_{2} \mathrm{O} + \mathrm{H}_{2}\mathrm{O}\).

Step 3: Analyze Reaction (b)

Identify the changes during the reduction of \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H}\) to \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}\). Benzoic acid is reduced to toluene.

Step 4: Balancing Oxygen and Hydrogen (b)

Again, use \(\mathrm{H}^+\) and \(\mathrm{H}_{2}\mathrm{O}\) to balance the changes. Remove the \(\mathrm{COOH}\) group and replace it with \(\mathrm{CH}_{3}\). Balanced equation: \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H} + 8\mathrm{H}^{+} + 8\mathrm{e}^{-} \rightarrow \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3} + 2\mathrm{H}_{2}\mathrm{O}\).

Step 5: Analyze Reaction (c)

Convert \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO}\) to \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\). Aldehyde to alcohol.

Step 6: Balancing the Reaction (c)

Add \(\mathrm{H}^+\) to complete the reduction. Under acidic conditions: \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO} + 2\mathrm{H}^{+} + 2\mathrm{e}^{-} \rightarrow \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\).

Step 7: Analyze Reaction (d)

Convert \(\mathrm{CH}_{3} \mathrm{OH}\) to \(\mathrm{CH}_{4}\). Methanol is reduced to methane.

Step 8: Balancing the Reaction (d)

Add necessary \(\mathrm{H}_2\) and \(\mathrm{H}^+\) to balance the reduction. The balanced equation is \(\mathrm{CH}_{3} \mathrm{OH} + 2\mathrm{H}^{+} + 2\mathrm{e}^{-} \rightarrow \mathrm{CH}_{4} + \mathrm{H}_{2}\mathrm{O}\).

Key Concepts

Organic Chemistry

Organic chemistry is a branch of chemistry that focuses on the study of carbon-containing compounds. These compounds typically also contain hydrogen, and may include elements such as nitrogen, oxygen, sulfur, and phosphorus. Organic molecules are diverse and can be found in numerous materials and processes, from living organisms to synthetic products.
One common theme in organic chemistry is the study of functional groups, which are specific groupings of atoms that characterize the properties and reactions of organic molecules. The functional groups involved in the reduction reactions mentioned in the exercise include carboxylic acids (e.g., \(\mathrm{COOH}\)) and alcohols (e.g., \(\mathrm{OH}\)).
Reduction reactions in organic chemistry typically involve the gain of electrons or hydrogen atoms, leading to a decrease in oxidation state of the central carbon atom. Understanding the structure and reactivity of organic molecules allows chemists to predict and optimize chemical reactions, including those of biological importance.

Half-Reaction Balancing

Balancing half-reactions is a fundamental skill in chemistry that involves equating the electrons lost in oxidation with those gained in reduction. The goal is to ensure that the number of atoms and charges are balanced on both sides of a chemical equation. This step is crucial when dealing with redox (reduction-oxidation) reactions which involve the transfer of electrons.
For instance, when reducing formic acid (\(\mathrm{HCO}_2\mathrm{H}\)) to formaldehyde (\(\mathrm{CH}_2\mathrm{O}\)), we must ensure that the number of carbon, hydrogen, and oxygen atoms is the same on both sides.

• Identify the oxidation changes: Which elements gain or lose electrons.
• Balance the atoms involved in each half-reaction initially.
• Use \(\mathrm{H}^+\) (in acidic solutions) and \(\mathrm{e}^-\) to balance the charge.

This method keeps the equation stable, allowing the elements to properly transfer between the reacting molecules.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions where reactants are transformed into products. They are essential for understanding chemical processes as they display the reactants, products, and the necessary stoichiometry.
In a chemical equation, the substances on the left of the arrow are called the reactants and those on the right are the products. For example, the reduction of benzoic acid to toluene can be symbolized as:
\[\mathrm{C}_6\mathrm{H}_5\mathrm{CO}_2\mathrm{H} + 8\mathrm{H}^{+} + 8\mathrm{e}^{-} \rightarrow \mathrm{C}_6\mathrm{H}_5\mathrm{CH}_3 + 2\mathrm{H}_2\mathrm{O}\]
This equation shows that one mole of benzoic acid reacts with eight moles of protons and eight electrons to form one mole of toluene and two moles of water. Proper balancing of chemical equations is essential for quantitative chemical analysis and for understanding reaction mechanisms.

Acidic Solution

An acidic solution is characterized by an increased concentration of hydrogen ions \(\mathrm{H}^+\). Such solutions often facilitate redox reactions by providing a source of protons to balance charges during the process.
In acidic solutions, it's common to balance complex reactions by introducing \(\mathrm{H}_2\mathrm{O}\) and \(\mathrm{H}^+\) ions. This allows the chemist to neutralize extra oxygen atoms or additional positive charges that arise during reduction or oxidation.

• In the reduction of ethanol to methane, \(\mathrm{H}^+\) is used to ensure the hydrogens are balanced.
• Acidic conditions also simplify balancing by using available protons to fill in gaps due to lost or added electrons.

Understanding how acidic conditions alter reaction dynamics is pivotal for constructing accurate and complete chemical equations for reduction half-reactions.