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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Write the balanced chemical equation for the complete combustion of palmitic acid: \[ \text{C}_{16}\text{H}_{32}\text{O}_2 (s) + \text{O}_2 (g) \rightarrow \text{CO}_2 (g) + \text{H}_2\text{O} (l) \]

Balance the equation by ensuring the number of atoms of each element is the same on both sides. Start with carbon, then hydrogen, and finally oxygen.

Calculate the standard enthalpy of combustion using the formula: \[ \Delta H_{\text{comb}} = \sum \Delta H_f^{\circ} (\text{products}) - \sum \Delta H_f^{\circ} (\text{reactants}) \]

Use the given standard enthalpy of formation for palmitic acid and known values for \( \text{CO}_2 \) and \( \text{H}_2\text{O} \) to find \( \Delta H_{\text{comb}} \).

Convert the enthalpy of combustion from kJ/mol to Cal/g by dividing by the molar mass of palmitic acid and converting kJ to Cal (1 Cal = 4.184 kJ).

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Key Concepts

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

Combustion Reactions

Combustion reactions involve the reaction of a substance with oxygen to produce heat and light, typically resulting in the formation of carbon dioxide and water. In the case of palmitic acid, the complete combustion reaction can be represented by a balanced chemical equation that shows the reactants and products. Understanding how to balance these equations is crucial for accurately representing the stoichiometry of the reaction.

Enthalpy of Combustion

The enthalpy of combustion is the heat released when one mole of a substance is completely burned in oxygen under standard conditions. It is typically expressed in kJ/mol. To calculate the standard enthalpy of combustion for palmitic acid, one can use the enthalpy of formation values of the reactants and products, applying Hess's law to find the overall energy change during the reaction.

Caloric Content

Caloric content refers to the amount of energy provided by a substance when it is metabolized, usually expressed in calories per gram (Cal/g). For palmitic acid, this can be calculated from the enthalpy of combustion, as the energy released during combustion corresponds to the energy available for metabolism. Understanding the relationship between enthalpy and caloric content is essential for evaluating the nutritional value of dietary fats.

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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. 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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