Calculate the caloric content of table sugar (sucrose, C12H22O11), given that the standard enthalpy of formation of sucrose is -2226.1 kJ/mol. For comparison, the standard enthalpy of formation of palmitic acid (C16H32O2), a dietary fat found in beef and butter, is -208 kJ/mol. Use H2O(l) in the balanced chemical equations, as the metabolism of these compounds produces liquid water.

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Identify the balanced chemical equation for the combustion of sucrose: \[ \text{C}_{12}\text{H}_{22}\text{O}_{11}(s) + 12\text{O}_2(g) \rightarrow 12\text{CO}_2(g) + 11\text{H}_2\text{O}(l) \]

Calculate the standard enthalpy change for the combustion of sucrose 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 sucrose and the known values for \( \text{CO}_2(g) \) and \( \text{H}_2\text{O}(l) \) to find \( \Delta H_{\text{comb}} \).

Convert the enthalpy change from kJ/mol to calories by using the conversion factor: \( 1 \text{ kJ} = 239.006 \text{ cal} \).

Compare the caloric content of sucrose with that of palmitic acid by considering their respective enthalpy changes.

Key Concepts

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

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 is a crucial concept in thermodynamics, allowing chemists to calculate the energy changes associated with chemical reactions. For example, the given value for sucrose indicates how much energy is released or absorbed during its formation from carbon, hydrogen, and oxygen.

Caloric Content and Energy Release

Caloric content refers to the amount of energy that can be obtained from food when metabolized. In the context of chemical reactions, this energy is often derived from the enthalpy changes associated with the combustion or metabolism of compounds. By calculating the enthalpy change for sucrose, one can determine its caloric value, which is essential for understanding its role in nutrition and energy balance.

Balanced Chemical Equations

Balanced chemical equations represent the conservation of mass in a chemical reaction, showing the relationship between reactants and products. In this question, the balanced equations for the metabolism of sucrose and palmitic acid will help determine the total energy released during their breakdown. This is important for comparing the caloric content of different substances and understanding their metabolic pathways.

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Textbook Question

Dry ice is solid carbon dioxide. Instead of melting, solid carbon dioxide sublimes according to the equation: CO₂(s) → CO₂(g) ◀ When carbon dioxide sublimes, the gaseous CO₂ is cold enough to cause water vapor in the air to condense, forming fog. When dry ice is added to warm water, heat from the water causes the dry ice to sublime more quickly. The evaporating carbon dioxide produces a dense fog often used to create special effects. In a simple dry ice fog machine, dry ice is added to warm water in a Styrofoam cooler. The dry ice produces fog until it evaporates away, or until the water gets too cold to sublime the dry ice quickly enough. Suppose that a small Styrofoam cooler holds 15.0 L of water heated to 85 °C. Use standard enthalpies of formation to calculate the change in enthalpy for dry ice sublimation, and calculate the mass of dry ice that should be added to the water so that the dry ice completely sublimes away when the water reaches 25 °C. Assume no heat loss to the surroundings. (The ΔH°_f for CO₂(s) is –427.4 kJ/mol.)

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Textbook Question

A 25.5-g aluminum block is warmed to 65.4 °C and plunged into an insulated beaker containing 55.2 g water initially at 22.2 °C. The aluminum and the water are allowed to come to thermal equilibrium. Assuming that no heat is lost, what is the final temperature of the water and aluminum?

If 50.0 mL of ethanol (density = 0.789 g/mL) initially at 7.0 °C is mixed with 50.0 mL of water (density = 1.0 g/mL) initially at 28.4 °C in an insulated beaker, and assuming that no heat is lost, what is the final temperature of the mixture?

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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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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Open Question

Hydrogen and methanol have both been proposed as alternatives to hydrocarbon fuels. Use standard enthalpies of formation to calculate the amount of heat released per kilogram of methanol fuel and per kilogram of hydrogen fuel.