The heat of combustion of ethanol, C₂H₅OH(l), is -1367 kJ/mol. A batch of Sauvignon Blanc wine contains 10.6% ethanol by mass. Assuming the density of the wine to be 1.0 g/mL, what is the caloric content due to the alcohol (ethanol) in a 6-oz glass of wine (177 mL)?

Verified step by step guidance

1. Convert the volume of wine from mL to grams using the density: \( \text{mass} = \text{volume} \times \text{density} \).
2. Calculate the mass of ethanol in the wine using the percentage by mass: \( \text{mass of ethanol} = \text{total mass of wine} \times \frac{10.6}{100} \).
3. Convert the mass of ethanol to moles using the molar mass of ethanol \( C_2H_5OH \), which is approximately 46.08 g/mol: \( \text{moles of ethanol} = \frac{\text{mass of ethanol}}{\text{molar mass of ethanol}} \).
4. Calculate the total heat of combustion for the ethanol using the heat of combustion per mole: \( \text{total heat} = \text{moles of ethanol} \times (-1367 \text{ kJ/mol}) \).
5. Convert the total heat from kJ to calories, knowing that 1 kJ = 239.006 calories.

Key Concepts

Heat of Combustion

The heat of combustion is the amount of energy released when a substance undergoes complete combustion with oxygen. For ethanol, this value is -1367 kJ/mol, indicating that this amount of energy is released per mole of ethanol burned. Understanding this concept is crucial for calculating the energy content of ethanol in wine.

Mass Percent Concentration

Mass percent concentration refers to the mass of a solute divided by the total mass of the solution, expressed as a percentage. In this case, the wine contains 10.6% ethanol by mass, meaning that in 100 grams of wine, there are 10.6 grams of ethanol. This concept is essential for determining the amount of ethanol in a specific volume of wine.

Density and Volume Conversion

Density is defined as mass per unit volume, and it allows for the conversion between mass and volume. Given that the density of the wine is 1.0 g/mL, this means that 1 mL of wine has a mass of 1 gram. This concept is important for converting the volume of wine (177 mL) into mass, which is necessary for calculating the caloric content from the ethanol present.