One of the best-selling light, or low-calorie, beers is 4.2%alcohol by volume and a 355-mL serving contains 110Calories; remember: 1 Calorie = 1000 cal = 1 kcal. Toestimate the percentage of Calories that comes fromthe alcohol, consider the following questions.(a) Writea balanced chemical equation for the reaction of ethanol,C2H5OH, with oxygen to make carbon dioxideand water. (b) Use enthalpies of formation in AppendixC to determine ΔH for this reaction. (c) If 4.2% ofthe total volume is ethanol and the density of ethanolis 0.789 g/mL, what mass of ethanol does a 355-mL servingof light beer contain? (d) How many Calories arereleased by the metabolism of ethanol, the reaction frompart (a)? (e) What percentage of the 110 Calories comesfrom the ethanol?

Verified step by step guidance

1. (a) Write the balanced chemical equation for the combustion of ethanol: \[ \text{C}_2\text{H}_5\text{OH} + 3\text{O}_2 \rightarrow 2\text{CO}_2 + 3\text{H}_2\text{O} \]
2. (b) Use the enthalpies of formation to calculate \( \Delta H \) for the reaction: \[ \Delta H = \sum \Delta H_f^\circ(\text{products}) - \sum \Delta H_f^\circ(\text{reactants}) \]. Look up the \( \Delta H_f^\circ \) values for \( \text{C}_2\text{H}_5\text{OH} \), \( \text{CO}_2 \), and \( \text{H}_2\text{O} \) in Appendix C.
3. (c) Calculate the mass of ethanol in the beer: First, find the volume of ethanol: \( 0.042 \times 355 \text{ mL} \). Then, use the density to find the mass: \( \text{mass} = \text{volume} \times 0.789 \text{ g/mL} \).
4. (d) Calculate the Calories released by the metabolism of ethanol: Use the \( \Delta H \) from part (b) to find the energy released per mole of ethanol. Convert this energy to Calories using the conversion \( 1 \text{ Calorie} = 4.184 \text{ kJ} \).
5. (e) Determine the percentage of the 110 Calories that comes from ethanol: \( \text{Percentage} = \left( \frac{\text{Calories from ethanol}}{110} \right) \times 100 \% \).

Key Concepts

Balanced Chemical Equation

A balanced chemical equation represents a chemical reaction where the number of atoms for each element is the same on both sides of the equation. This ensures the law of conservation of mass is upheld. For the combustion of ethanol (C2H5OH), the balanced equation is: C2H5OH + 3O2 → 2CO2 + 3H2O, indicating that one molecule of ethanol reacts with three molecules of oxygen to produce two molecules of carbon dioxide and three molecules of water.

Enthalpy of Formation

The enthalpy of formation (ΔHf) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. It is crucial for calculating the overall enthalpy change (ΔH) of a reaction using the formula ΔH = ΣΔHf(products) - ΣΔHf(reactants). This concept allows us to quantify the energy changes associated with the combustion of ethanol, which is essential for understanding its caloric contribution.

Caloric Content and Density Calculations

To determine the mass of ethanol in a serving of beer, we use the volume percentage and the density of ethanol. Given that 4.2% of the beer's volume is ethanol, we can calculate the volume of ethanol in 355 mL of beer. Using the density of ethanol (0.789 g/mL), we can convert this volume to mass. Additionally, knowing the caloric content of ethanol allows us to calculate the total Calories released during its metabolism, which is necessary for answering the question about the percentage of Calories from ethanol.