Problem 86 - Chemistry The Central Science

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 is the caloric content due to the alcohol (ethanol) in a 6 -oz glass of wine \((177 \mathrm{~mL}) ?\)

Step-by-Step Solution

Answer

The caloric content due to the alcohol (ethanol) in a 6-oz glass of wine is approximately 132,967 calories.

Step 1: Convert volume of wine to mass

Since we are given the density of wine as \(1.0 \mathrm{~g} / \mathrm{mL}\), we can easily convert the volume of wine (177 mL) into its mass by multiplying volume by the density: Mass of wine = Volume of wine × Density of wine Mass of wine = \(177 \mathrm{~mL} × 1.0 \mathrm{~g} / \mathrm{mL}\) Mass of wine = 177 g

Step 2: Find the mass of ethanol in the wine

We are given that \(10.6\%\) of the wine is ethanol by mass. To find the mass of ethanol, we can simply multiply the mass of wine by this percentage: Mass of ethanol = Mass of wine × Percentage of ethanol Mass of ethanol = \(177 \mathrm{~g} × 0.106\) Mass of ethanol = 18.762 g

Step 3: Calculate the moles of ethanol

We now have the mass of ethanol present in the 6-oz glass of wine. To calculate the energy released from the combustion of this mass, we first need to find the number of moles of ethanol, using the molar mass of ethanol which is 46.07 g/mol. Moles of ethanol = Mass of ethanol / Molar mass of ethanol Moles of ethanol = \(18.762 \mathrm{~g} / 46.07 \mathrm{~g} / \mathrm{mol}\) Moles of ethanol = 0.407 mol

Step 4: Calculate the energy released during combustion

We are given the heat of combustion of ethanol as \(-1367 \mathrm{~kJ} / \mathrm{mol}\). Multiplying the moles of ethanol by the heat of combustion, we can find the total energy released when this ethanol is combusted: Energy released = Moles of ethanol × Heat of combustion Energy released = \(0.407 \mathrm{~mol} × -1367 \mathrm{~kJ} / \mathrm{mol}\) Energy released = -556.5 kJ

Step 5: Convert the energy to calories

Finally, we need to convert the energy released from kJ to calories, using the conversion factor: 1 kJ = 239.006 calories. Caloric content = Energy released × Conversion factor Caloric content = \(-556.5 \mathrm{~kJ} × 239.006 \mathrm{~cal} / \mathrm{kJ}\) Caloric content = -132966.83 cal The caloric content due to the alcohol (ethanol) in a 6-oz glass of wine is approximately 132,967 calories.

Key Concepts

Caloric Content of Ethanol

Ethanol, commonly found in alcoholic beverages like wine, has intrinsic energy, which when combusted, releases a specific amount of heat. This heat is termed as the heat of combustion. It is a crucial aspect as it determines the caloric content of a substance, which in the dietary sense, corresponds to the energy that can be obtained from consuming the substance. In relation to the exercise, the heat of combustion for ethanol is given as -1,367 kJ/mol.

When calculating the caloric content of a serving of wine, one must consider not only the heat of combustion of ethanol but also the percentage of ethanol by mass in the wine. Legally, the term 'calories' refer to what scientists call kilocalories, and the conversion factor of 1 kJ = 239.006 calories is used to bridge between these two units. Thus, by applying the given conversion, we convert the energy released during combustion from kilojoules to calories, arriving at the caloric impact of enjoying that seemingly innocent glass of wine. For individuals tracking their caloric intake, understanding this process ensures a more informed approach to dietary choices.

Molar Mass of Ethanol

In chemical calculations, particularly when dealing with reactions, the molar mass of a substance is a fundamental measure. The molar mass of ethanol, C2H5OH, is 46.07 g/mol. This property lets us convert grams of ethanol into moles, which is essential for quantitative analysis.

The concept of molar mass is vital because stoichiometry – the calculation of reactants and products in chemical reactions – is based on the mole unit. To find out how much energy is released from burning ethanol in wine, you start by determining how much ethanol there is in grams, and then convert that amount to moles using it's molar mass. One can liken molar mass to a conversion factor, which allows us to bridge the gap between the macroscopic world we live in and the molecular world where chemical reactions take place.

Stoichiometry in Combustion Reactions

Stoichiometry is like a recipe for chemists. It helps quantify the relationship between reactants and products in a chemical reaction. In a combustion reaction, which is a chemical reaction where a substance combines with oxygen to produce heat and light, stoichiometry helps us understand the amounts of each substance needed and the amount of energy released.

Using the exercise as an example, the combustion of ethanol (C2H5OH) reacts with oxygen (O2) according to a balanced chemical equation. As we saw in the solution, knowing the molar mass of ethanol, the heat of combustion, and the moles of ethanol—determined from the mass of ethanol in the glass of wine using stoichiometry—made it possible to calculate the total energy released. This precise calculation is extremely useful in various fields, from designing engines and fuels to specifying dietary content in food science.