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Chapter 5: Problem 94

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 \((177 \mathrm{mL})\) ?

Short Answer

Expert verified
The caloric content due to the ethanol in a 6-oz glass of Sauvignon Blanc wine is approximately 133,050.5 calories.

Step by step solution

01

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
02

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
03

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.
04

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.

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Most popular questions from this chapter

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