Problem 94 - 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 ethanol in a 6-oz glass of Sauvignon Blanc wine is approximately 133,050.5 calories.

Step 1: Calculate the mass of ethanol in the glass of wine

First, we need to determine the mass of ethanol in the glass of wine. We know the volume of wine (177 mL) and its density (1.0 g/mL). We can use these values to determine the mass of the wine: mass of wine = volume × density mass of wine = 177 mL × 1.0 g/mL = 177 g Now, we can find the mass of ethanol, knowing that it makes up 10.6% of the wine: mass of ethanol = mass of wine × percentage of ethanol mass of ethanol = 177 g × 0.106 = 18.762 g

Step 2: Calculate the moles of ethanol

Next, we need to determine the moles of ethanol present in the wine. The molecular formula of ethanol is C2H5OH, with a molar mass of approximately: \[12.01\,(\text{C}) × 2 + 1.01\,(\text{H}) × 6 + 16.00\,(\text{O}) = 46.07 \,\text{g/mol}\] Using this molar mass, we can calculate the moles of ethanol: moles of ethanol = mass of ethanol / molar mass of ethanol moles of ethanol = 18.762 g / 46.07 g/mol = 0.407 mol

Step 3: Determine the heat released by the combustion of the ethanol

We know that the heat of combustion of ethanol is -1367 kJ/mol. To find the heat released by the combustion of 0.407 mol of ethanol, we need to multiply the moles by the heat of combustion: heat released = moles of ethanol × heat of combustion of ethanol heat released = 0.407 mol × (-1367 kJ/mol) = -556.5 kJ The heat released is negative because combustion liberates heat.

Step 4: Convert the heat released to calories

Finally, we need to convert the heat released from kJ to calories. We know that 1 kJ = 239 cal: caloric content due to ethanol = heat released × caloric conversion factor caloric content due to ethanol = -556.5 kJ × 239 cal/kJ = -133050.5 cal Therefore, the caloric content due to the ethanol in a 6-oz glass of Sauvignon Blanc wine is approximately 133,050.5 calories.

Key Concepts

Heat of Combustion

The heat of combustion is a crucial concept in understanding how energy is released when a substance burns. This is the energy that is released as heat when a specific amount of substance undergoes complete combustion with oxygen. In the context of ethanol (commonly found in alcoholic beverages like wine), the heat of combustion is

• 1367 kJ/mol, indicating that burning one mole of ethanol releases this amount of energy.

This value is usually negative because it represents an exothermic process – one where heat is released rather than absorbed. Knowing the heat of combustion allows us to calculate the energy output from fuels, compare different fuels, or in this case, understand the caloric impact of ethanol in wine.

Ethanol

Ethanol, also known as ethyl alcohol, is a common type of alcohol found in alcoholic beverages. Its chemical formula is

• \( ext{C}_2 ext{H}_5 ext{OH}\) and it is composed of two carbon atoms, six hydrogen atoms, and one oxygen atom.

Ethanol is known for its ability to act as a psychoactive drug, but in terms of chemistry, it is a very important compound due to its combustibility and energy content. When burned, ethanol releases energy, which is crucial for calculations like the caloric content in beverages. Understanding ethanol's properties helps in determining its effect on the caloric content in drinks like wine.

Density Calculation

Density is a measure of how much mass is contained in a given volume. It is calculated using the formula

• \( ext{Density} = \frac{\text{mass}}{\text{volume}}\).

For the wine in the exercise, the assumed density is 1.0 g/mL. This means every milliliter of the wine has a mass of 1.0 gram. Using this value, it is simple to determine the total mass of a liquid when its volume is known.

• For example, in the 6-ounce glass of wine (equivalent to 177 mL), the mass can be calculated as \(177 \,\text{mL} \times 1.0 \,\text{g/mL} = 177 \,\text{g}\).

Thus, density is a practical way to convert between volume and mass, which is essential in chemistry for precise measurements.

Mole Conversion

Moles are a fundamental unit in chemistry used to quantify the amount of a substance. When dealing with the mass of a substance, it can help to know the number of moles because it simplifies the calculation of chemical reactions. This is done via

• \( ext{moles} = \frac{\text{mass}}{\text{molar mass}}\).

In the exercise provided, the conversion from mass to moles involves ethanol, whose molar mass is 46.07 g/mol. For the 18.762 grams of ethanol, converting to moles is straightforward:

• \(\frac{18.762 \,\text{g}}{46.07 \,\text{g/mol}} = 0.407 \,\text{mol}\).

Knowing the number of moles allows you to engage in more precise and accurate calculations, especially when assessing the energy changes in reaction processes like combustion.

Molar Mass

Molar mass is the mass of one mole of a given substance, usually expressed in grams per mole (g/mol). It is essential for converting between grams of a substance and moles. Calculating the molar mass of a compound involves adding up the atomic masses of each constituent atom. For ethanol,

• the breakdown is \(12.01 \times 2 + 1.01 \times 6 + 16.00 = 46.07\)

g/mol. The molar mass serves as a bridge between the mass of a sample and the amount in moles, a fundamental concept in stoichiometry. With the molar mass known, determining how many moles are in a specific mass becomes a simple division problem.