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Ch.5 - Thermochemistry
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Capitolo 5, Problema 94

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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1
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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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.
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Combustion Apparatus

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.
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Mass Percent Calculation

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.
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Relationship of Volume and Moles Example