Question

The heat of combustion of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\), is \(-1367 \mathrm{~kJ} / \mathrm{mol}\). A batch of Sauvignon Blanc wine contains \(10.6 \%\) ethanol by mass. Assuming the density of the wine to be \(1.0 \mathrm{~g} / \mathrm{mL}\), what caloric content does the alcohol (ethanol) in a 6-oz glass of wine (177 mL) have?

Short answer

The caloric content of the ethanol in a 6-oz glass of Sauvignon Blanc wine is approximately 132,917 calories.

Step-by-step solution

Find the mass of ethanol in the glass of wine

Since the density of the wine is given as 1.0 g/mL, the mass of the wine in a 177 mL glass can be found by multiplying its volume (177 mL) and density. Next, using the given 10.6% ethanol content by mass, find the mass of ethanol in the wine. Mass of wine = Density × Volume = 1.0 g/mL × 177 mL = 177 g Mass of ethanol = (Percentage of ethanol by mass) × (Mass of wine) = 0.106 × 177 g ≈ 18.76 g

Convert the mass of ethanol to moles using its molar mass

The molar mass of ethanol (\(C_2H_5OH\)) can be calculated as: Molar mass of ethanol = 2 × Molar mass of Carbon + 6 × Molar mass of Hydrogen + 1 × Molar mass of Oxygen = 2 × 12.01 g/mol + 6 × 1.01 g/mol + 16.00 g/mol ≈ 46.07 g/mol Now, we can find the moles of ethanol present in the wine using the mass of ethanol and its molar mass: Moles of ethanol = Mass of ethanol / Molar mass of ethanol = 18.76 g / 46.07 g/mol ≈ 0.407 mol

Find the energy released when the ethanol is combusted

Given that the heat of combustion of ethanol is -1367 kJ/mol, we now find the energy released upon combusting the moles of ethanol present in the wine: Energy released = Heat of combustion × Moles of ethanol = (-1367 kJ/mol) × 0.407 mol ≈ -556.10 kJ (Note that the value is negative as heat is being released, not absorbed.)

Convert the energy released in kJ to calories

To convert the energy in kJ to calories, we can use the following conversion factor: 1 cal ≈ 4.184 J First, convert kJ to J: Energy released = -556.10 kJ × (1000 J / 1 kJ) ≈ -556,100 J Now, convert J to calories: Energy released = -556,100 J × (1 cal / 4.184 J) ≈ -132,917 cal The caloric content of the ethanol in a 6-oz glass of Sauvignon Blanc wine is approximately 132,917 calories.

Key concepts

Caloric Content Calculation

Understanding the caloric content of foods and beverages is crucial for nutritional science and for individuals monitoring their dietary intake. Essentially, the caloric content represents the amount of energy that a substance can release during its metabolism.

In the context of ethanol, which is present in alcoholic beverages like wine, calculating the caloric content involves determining the energy released when ethanol is combusted. The combustion of ethanol is an exothermic reaction, meaning it releases energy, measured in joules (J) or kilojoules (kJ), or in the dietary context, in calories or kilocalories. To calculate the calories provided by the ethanol in a glass of wine, one must first find the mass of ethanol, convert it into moles, and then use the heat of combustion (in kJ) to know the energy yielded. The final step is to convert this energy into calories since the calorie is the common unit of energy used in nutritional contexts. Remember that 1 calorie is approximately 4.184 joules.

It's important for students to note that while the concept is straightforward, precision in these calculations is key. Factors like the density of the liquid, the ethanol content by mass, and the accurate conversion factors must be considered to yield a correct value.

Molar Mass of Ethanol

The molar mass of a compound is a fundamental concept in chemistry that refers to the mass of one mole of its molecules, measured in grams per mole (g/mol). It is equivalent to the sum of the atomic masses of all atoms present in the molecule.

For ethanol (\(C_2H_5OH\)), you need to know the atomic masses of carbon (C), hydrogen (H), and oxygen (O) to calculate its molar mass. With carbon having an atomic mass of approximately 12.01 g/mol, hydrogen 1.01 g/mol, and oxygen 16.00 g/mol, it's a matter of multiplying these by the number of each type of atom in an ethanol molecule and summing the values.

Understanding and accurately calculating molar mass is essential. It acts as a conversion factor between the mass of a substance and the amount of substance (moles). In this case, molar mass helps us translate the mass of ethanol from grams to moles, an essential step to connect the mass of ethanol consumed to its energetic value in terms of calories.

Combustion Reactions in Chemistry

Combustion reactions are a type of chemical reaction where a substance combines with oxygen, releasing energy in the form of light or heat. In chemistry classrooms and textbooks, the classic example is the burning of hydrocarbons, like the ethanol found in wine, to produce carbon dioxide and water.

The equation \( C_2H_5OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 3H_2O(l) \) represents the combustion of ethanol. This reaction is exothermic, and the heat of combustion (-1367 kJ/mol for ethanol) gives us information about the amount of energy released per mole of ethanol when it completely reacts with oxygen.

Understanding combustion reactions is not just about the reaction itself but also involves the concept of stoichiometry, which relates the quantitative relationship between reactants and products in a chemical reaction, and thermochemistry, which focuses on the heat exchange associated with chemical reactions. In terms of practical applications, combustion reactions are central to energy production, various industrial processes, and even calculating the caloric content of food and beverages, as this influences dietary decisions and health considerations.