The heat of combustion of ethanol, C₂H₅OH(l), is -1367 kJ/mol. A bottle of stout (dark beer) contains up to 6.0% ethanol by mass. Assuming the density of the beer to be 1.0 g/mL, what is the caloric content due to the alcohol (ethanol) in a bottle of beer (500 mL)?

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Calculate the mass of the beer using its volume and density: \( \text{mass} = \text{volume} \times \text{density} \).

Determine the mass of ethanol in the beer using the percentage by mass: \( \text{mass of ethanol} = \text{mass of beer} \times \frac{6.0}{100} \).

Convert the mass of ethanol to moles using the molar mass of ethanol (C\(_2\)H\(_5\)OH), which is approximately 46.08 g/mol: \( \text{moles of ethanol} = \frac{\text{mass of ethanol}}{46.08} \).

Calculate the total heat of combustion for the ethanol in the beer using the heat of combustion per mole: \( \text{total heat} = \text{moles of ethanol} \times (-1367 \text{ kJ/mol}) \).

Convert the total heat from kJ to calories, knowing that 1 kJ = 239.006 calories.

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주요 개념

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Heat of Combustion

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

Mass Percent Concentration

Mass percent concentration is a way to express the concentration of a component in a mixture, calculated as the mass of the component divided by the total mass of the mixture, multiplied by 100. In this case, the beer contains 6.0% ethanol by mass, which means that in 100 g of beer, there are 6 g of ethanol. This concept is essential for determining the total mass of ethanol in the 500 mL of beer.

Density and Volume Relationship

Density is defined as mass per unit volume, and it allows us to convert between the volume of a liquid and its mass. Given that the density of the beer is 1.0 g/mL, a 500 mL bottle of beer has a mass of 500 g. Understanding this relationship is vital for calculating the total mass of ethanol present in the beer based on its volume.

The heat of combustion of ethanol, C2H5OH(l), is -1367 kJ/mol. A bottle of stout (dark beer) contains up to 6.0% ethanol by mass. Assuming the density of the beer to be 1.0 g/mL, what is the caloric content due to the alcohol (ethanol) in a bottle of beer (500 mL)?