Question

One of the best-selling light, or low-calorie, beers is 4.2\(\%\) alcohol by volume and a 12 -oz serving contains 110 Calories; remember: 1 Calorie \(=1000\) cal \(=1\) kcal. To estimate the percentage of Calories that comes from the alcohol, consider the following questions. (a) Write a balanced chemical equation for the reaction of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) , with oxygen to make carbon dioxide and water. (b) Use enthalpies of formation in Appendix \(\mathrm{C}\) to determine \(\Delta H\) for this reaction. \((\mathbf{c})\) If 4.2\(\%\) of the total volume is ethanol and the density of ethanol is \(0.789 \mathrm{g} / \mathrm{mL},\) what mass of ethanol does a 12 - oz serving of light beer contain? (\boldsymbol{d} ) How many Calories are released by the metabolism of ethanol, the reaction from part (a)? (e) What percentage of the 110 Calories comes from the ethanol?

Short answer

In a 12-oz serving of light beer with 4.2% alcohol content, the metabolism of ethanol releases 349.4 Calories. However, comparing this to the given 110 Calories for the serving, approximately 317.6% of the Calories come from ethanol. This may seem paradoxical, but it is important to note that this calculation does not account for other biochemical processes involved in the metabolism of ethanol, or other components contributing to the calorie count.

Step-by-step solution

Write the balanced chemical equation for the metabolism of ethanol

The metabolism of ethanol (\(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}\)) involves its reaction with oxygen (\(\mathrm{O}_{2}\)) to produce carbon dioxide (\(\mathrm{CO}_{2}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)). The balanced chemical equation for this reaction is: \[\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH} + \mathrm{O}_{2} \rightarrow 2\mathrm{CO}_{2} + 3\mathrm{H}_{2}\mathrm{O}\]

Calculate the enthalpy change (\(\Delta H\)) for the reaction

Using the enthalpies of formation from Appendix C, we can find the \(\Delta H\) for the reaction. We do this by calculating the difference between the sum of the enthalpies of formation of the products and the sum of the enthalpies of formation of the reactants: \(\Delta H = [2\Delta H_f(\mathrm{CO}_{2}) + 3\Delta H_f(\mathrm{H}_{2}\mathrm{O})] - [\Delta H_f(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}) + \Delta H_f(\mathrm{O}_{2})]\) Since the enthalpy of formation of elemental oxygen is zero, the equation becomes: \(\Delta H = [2\Delta H_f(\mathrm{CO}_{2}) + 3\Delta H_f(\mathrm{H}_{2}\mathrm{O})] - \Delta H_f(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH})\) Using the enthalpies of formation from Appendix C: \(\Delta H = [2(-393.5 \,\mathrm{kcal/mol}) + 3(-285.8\, \mathrm{kcal/mol})] - (-277.0\, \mathrm{kcal/mol})\) \(\Delta H = -1370.2\, \mathrm{kcal/mol}\)

Calculate the mass of ethanol in 12 oz of light beer

Given the 4.2% alcohol content by volume and the density of ethanol, we can calculate the mass of ethanol in a 12-oz serving of light beer. First, convert 12 oz to mL (1 oz = 29.5735 mL): \(12\,\mathrm{oz} \times \frac{29.5735\,\mathrm{mL}}{1\,\mathrm{oz}} = 354.88\, \mathrm{mL}\) Next, find the volume of ethanol in the beer: \(354.88\,\mathrm{mL} \times 0.042 = 14.905\, \mathrm{mL}\) Now, calculate the mass of ethanol using its density (0.789 g/mL): \(14.905\, \mathrm{mL} \times \frac{0.789\, \mathrm{g}}{1\, \mathrm{mL}} = 11.75\, \mathrm{g}\)

Calculate the calories released by the metabolism of ethanol

We have the enthalpy change per mol (\(\Delta H\)) and the mass of ethanol. To find the calories released, first calculate the moles of ethanol: \(11.75\, \mathrm{g} \times \frac{1\,\mathrm{mol}}{46.07\, \mathrm{g}} = 0.255\, \mathrm{mol}\) Now, multiply the moles of ethanol by the enthalpy change per mol: \(0.255\, \mathrm{mol} \times -1370.2\, \mathrm{kcal/mol} = -349.4\, \mathrm{kcal}\) To convert kcal to Calories: \(-349.4\, \mathrm{kcal} \times \frac{1\, \mathrm{Calorie}}{1\, \mathrm{kcal}} = -349.4\, \mathrm{Calories}\) The metabolism of ethanol releases 349.4 Calories.

Determine the percentage of calories coming from the ethanol

Now that we have the Calories released from the metabolism of ethanol, we can find the percentage of calories coming from ethanol compared to the total Calories in a 12-oz serving of light beer: \(\frac{349.4\, \mathrm{Calories}}{110\, \mathrm{Calories}} \times 100\% \approx 317.6\%\) The percentage of calories coming from the ethanol is roughly 317.6%. This may seem paradoxical, but it is important to note that this calculation does not account for other biochemical processes involved in the metabolism of ethanol. It is also possible that the 110 Calories stated for the light beer includes other components (such as carbohydrates) contributing to the calorie count.

Key concepts

Understanding Ethanol Metabolism

Ethanol, commonly found in alcoholic beverages, is metabolized in our bodies through a series of chemical reactions. The primary pathway involves the enzyme alcohol dehydrogenase (ADH), which transforms ethanol into acetaldehyde. This toxic compound is then converted to acetate by another enzyme, aldehyde dehydrogenase (ALDH). The acetate ultimately turns into water and carbon dioxide, which the body can expel. Ethanol metabolism can be summarized by a chemical equation where ethanol (\(\mathrm{C}_2\mathrm{H}_5\mathrm{OH}\)) reacts with oxygen (\(\mathrm{O}_2\)) to produce carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2\mathrm{O}\)). This entire process releases energy in the form of Calories.

• Step 1: Ethanol is converted into acetaldehyde.
• Step 2: Acetaldehyde further converts into acetate.
• Step 3: Finally, acetate is metabolized to water and carbon dioxide.

Overall, this chemical reaction not only breaks down ethanol but also releases energy, a key aspect of why alcohol has caloric content.

Exploring the Chemical Reaction Process

Chemical reactions are central to understanding metabolism, including that of ethanol. When ethanol (\(\mathrm{C}_2\mathrm{H}_5\mathrm{OH}\)) undergoes metabolism, it reacts with oxygen (\(\mathrm{O}_2\)) to yield carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2\mathrm{O}\)). This reaction can be expressed as:\[\mathrm{C}_2\mathrm{H}_5\mathrm{OH} + 3\mathrm{O}_2 \rightarrow 2\mathrm{CO}_2 + 3\mathrm{H}_2\mathrm{O} \]Balanced chemical equations ensure that matter is conserved in a chemical reaction, meaning the same number of each type of atom is present on both sides of the equation.
In this reaction, ethanol combines with oxygen, breaking down to form carbon dioxide and water. It is also important to consider enthalpy (\(\Delta H\)), which measures the heat change during the reaction. A negative \(\Delta H\) value indicates that the reaction releases energy, making it exothermic. This released energy is crucial when calculating caloric content, as metabolism converts this chemical energy into usable energy for our bodies.

Calories Calculation from Ethanol

Calculating the calories from ethanol involves understanding the amount of energy released during its metabolism. Let's explore how we determine the caloric content from ethanol in a light beer scenario:

• Calculate the mass of ethanol: Knowing the beer's alcohol content and ethanol's density helps us find how much ethanol is in a given volume of beer.
• Convert to moles: Using ethanol's molar mass, we convert the mass into moles, which is essential for energy calculations.
• Determine released energy: The enthalpy change (\(\Delta H\)) per mole of ethanol tells us how much energy is released. Multiplying by the number of moles gives the total energy released during metabolism.
• Convert to Calories: Since metabolism results in energy release, we translate this energy into Calories to represent the caloric content.

For example, using a mass of 11.75 g of ethanol:

• We find the energy released: \(-349.4\, \mathrm{Calories}\).
• Next, calculate the percentage contribution: Compare the energy from ethanol to the beer's total Calories to get an idea of how much of the caloric intake comes from ethanol.

This calculation can reveal insights into the dietary impact of ethanol and the significance of its presence as a calorie source in beverages.