Question

Calculate the enthalpy change for the oxidation of pyruvic acid to acetic acid under standard conditions. $$ 2 \mathrm{CH}_{3} \mathrm{COCOOH}(/)+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{CH}_{3} \mathrm{COOH}(/)+2 \mathrm{CO}_{2}(\mathrm{~g}) $$ The heats of combustion of pyruvic acid and acetic acid under standard conditions are \(-227 \mathrm{kcal} / \mathrm{mol}\) and \(-207 \mathrm{kcal} / \mathrm{mol}\), respectively. Heats of combustion are determined by reacting pyruvic or acetic acid with \(\mathrm{O}_{2}(\mathrm{~g})\) to give \(\mathrm{H}_{2} \mathrm{O}(/)\) and \(\mathrm{CO}_{2}\) (g). Hint: First write balanced chemical equations for the combustion processes.

Short answer

The enthalpy change is +40 kcal.

Step-by-step solution

Write Combustion Equations

First, write the standard combustion reactions for pyruvic acid and acetic acid using the given heats of combustion. For pyruvic acid: \[ \mathrm{CH}_3 \mathrm{COCOOH} + 2\mathrm{O}_2 \rightarrow 2\mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} \]The heat of combustion is \(-227 \mathrm{kcal/mol}\).For acetic acid: \[ \mathrm{CH}_3 \mathrm{COOH} + 2\mathrm{O}_2 \rightarrow 2\mathrm{CO}_2 + 2\mathrm{H}_2\mathrm{O} \]The heat of combustion is \(-207 \mathrm{kcal/mol}\).

Use Combustion Enthalpy to Find Desired Reaction's Enthalpy

The target reaction is the oxidation of pyruvic acid to acetic acid, plus some oxygen rearrangement:\[ 2 \mathrm{CH}_3 \mathrm{COCOOH} + \mathrm{O}_2 \rightarrow 2 \mathrm{CH}_3 \mathrm{COOH} + 2 \mathrm{CO}_2 \]We know from Hess's law that the total enthalpy change for a reaction series is the sum of enthalpy changes for each reaction. Therefore, compute the enthalpy change of the target reaction using the given heats of combustion:1. The enthalpy change of 2 moles of pyruvic acid combusting: \[ 2 \times (-227) = -454 \text{ kcal} \]2. The enthalpy change of 2 moles of acetic acid combusting: \[ 2 \times (-207) = -414 \text{ kcal} \]3. Calculate the target reaction's enthalpy change: Enthalpy change = Combustion enthalpy of products - Combustion enthalpy of reactants. \[ (-414) - (-454) = +40 \text{ kcal} \]

Conclude the Enthalpy Change

The enthalpy change for the oxidation of pyruvic acid to acetic acid is \(+40 \text{ kcal}\). This final number accounts for the conversion of those species under standard conditions. Hence, the reaction is endothermic, indicating it requires energy input.

Key concepts

Oxidation Reaction

An oxidation reaction involves the transfer of electrons, leading to an increase in oxidation state. During these reactions, one substance loses electrons, often to oxygen, reflecting the process in the term 'oxidation'. In the context of chemical reactions, particularly involving organic compounds, oxidation can also refer to the increase in the number of bonds to oxygen or the decrease in the number of bonds to hydrogen.
In the oxidation of pyruvic acid to acetic acid, oxidation involves the transformation of carbon structures. This process not only affects the oxidation state but also results in the breaking and forming of chemical bonds. Oxidation reactions are fundamental to many biochemical processes, including those that provide energy within the cell.

Pyruvic Acid

Pyruvic acid (CH₃COCOOH) is a key organic compound in biochemistry. It plays a crucial role in cellular respiration, serving as an intermediate in several metabolic pathways. Pyruvic acid results from the breakdown of glucose via glycolysis, a process occurring in the cytoplasm of cells, and is subsequently involved in the Krebs cycle.
This compound can exist in two forms: as pyruvic acid itself or as its conjugate base pyruvate, depending on the pH of the surrounding environment. In oxidative metabolism, pyruvic acid is converted to acetyl-CoA, which then enters the Krebs cycle. Understanding the role and transformations of pyruvic acid is crucial for comprehending energy production in organisms.

Acetic Acid

Acetic acid (CH₃COOH) is a simple carboxylic acid known for its role as a key metabolic intermediate and as a component of vinegar. In biochemistry, acetic acid molecules are central to lipid biosynthesis and energy production.
In cellular metabolism, acetic acid is often found as acetyl-CoA, a crucial molecule that delivers the acetyl group to the Krebs cycle (or Citric Acid Cycle) for energy extraction. It results from the oxidation of pyruvic acid as depicted in the given reaction, emphasizing its role in metabolic pathways. The conversion of pyruvic acid to acetic acid involves a strategic rearrangement of molecular components within cellular processes.

Heats of Combustion

Heats of combustion refer to the energy released as heat when a compound undergoes complete combustion, usually with oxygen. This energy is expressed in kilocalories per mole (kcal/mol) or kilojoules per mole (kJ/mol).
In the given exercise, the heats of combustion for pyruvic acid and acetic acid are crucial for calculating enthalpy changes using Hess's Law. They indicate how much energy is released when these compounds are burned in gaseous oxygen to form carbon dioxide and water. Understanding these values aids in determining the energy efficiency of different reactions and their potential as energy sources.

Hess's Law

Hess's Law states that the total enthalpy change in a chemical reaction is the same, no matter how the reaction occurs, provided the initial and final conditions are constant. This is a reflection of the conservation of energy, suggesting that energy changes are state functions and depend only on the state of the initial and final products, not the path taken.
In the context of the exercise, Hess's Law allows us to determine the enthalpy change for the oxidation of pyruvic acid to acetic acid by using the known heats of combustion. By summing the enthalpy changes of the combustion reactions for pyruvic acid and acetic acid, we find that the overall enthalpy change for the target reaction is +40 kcal, indicating that it is an endothermic process. Understanding and applying Hess's Law is fundamental in calculating enthalpy changes for reactions that may not be directly measurable.