Palmitic acid (C₁₆H₃₂O₂) is a dietary fat found in beef and butter. The caloric content of palmitic acid is typical of fats in general. Which dietary substance (sugar or fat) contains more Calories per gram? The standard enthalpy of formation of palmitic acid is -208 kJ/mol and that of sucrose is -2226.1 kJ/mol. [Use H₂O(l) in the balanced chemical equations because the metabolism of these compounds produces liquid water.]

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Identify the chemical formulas for palmitic acid (C_{16}H_{32}O_{2}) and sucrose (C_{12}H_{22}O_{11}).

Write the balanced chemical equations for the combustion of palmitic acid and sucrose, ensuring that the products are CO_{2}(g) and H_{2}O(l).

Calculate the enthalpy change for the combustion of 1 mole of each compound using the standard enthalpy of formation values provided.

Convert the enthalpy change from kJ/mol to kJ/g by dividing the enthalpy change by the molar mass of each compound.

Compare the energy content per gram of palmitic acid and sucrose to determine which has more Calories per gram.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Caloric Content of Macromolecules

Fats, such as palmitic acid, provide approximately 9 Calories per gram, while carbohydrates, like sugars, provide about 4 Calories per gram. This difference in caloric density is due to the higher number of carbon and hydrogen atoms in fats, which release more energy upon oxidation during metabolism.

Standard Enthalpy of Formation

The standard enthalpy of formation is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It provides insight into the stability and energy content of a compound. In this context, comparing the enthalpy values of palmitic acid and sucrose helps understand their energy release during metabolism.

Metabolism and Energy Release

Metabolism refers to the biochemical processes that convert food into energy. During metabolism, fats and sugars undergo oxidation, producing energy and byproducts like water and carbon dioxide. Understanding these metabolic pathways is crucial for evaluating the energy yield of different dietary substances.

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Textbook Question

Palmitic acid (C₁₆H₃₂O₂) is a dietary fat found in beef and butter. The caloric content of palmitic acid is typical of fats in general. Write a balanced equation for the complete combustion of palmitic acid and calculate the standard enthalpy of combustion. What is the caloric content of palmitic acid in Cal/g? The standard enthalpy of formation of palmitic acid is -208 kJ/mol and that of sucrose is -2226.1 kJ/mol. [Use H₂O(l) in the balanced chemical equations because the metabolism of these compounds produces liquid water.]

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