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

Ethanol, commonly found in alcoholic beverages like wine, has intrinsic energy, which when combusted, releases a specific amount of heat. This heat is termed as the heat of combustion. It is a crucial aspect as it determines the caloric content of a substance, which in the dietary sense, corresponds to the energy that can be obtained from consuming the substance. In relation to the exercise, the heat of combustion for ethanol is given as -1,367 kJ/mol.

When calculating the caloric content of a serving of wine, one must consider not only the heat of combustion of ethanol but also the percentage of ethanol by mass in the wine. Legally, the term 'calories' refer to what scientists call kilocalories, and the conversion factor of 1 kJ = 239.006 calories is used to bridge between these two units. Thus, by applying the given conversion, we convert the energy released during combustion from kilojoules to calories, arriving at the caloric impact of enjoying that seemingly innocent glass of wine. For individuals tracking their caloric intake, understanding this process ensures a more informed approach to dietary choices.

In chemical calculations, particularly when dealing with reactions, the molar mass of a substance is a fundamental measure. The molar mass of ethanol, C2H5OH, is 46.07 g/mol. This property lets us convert grams of ethanol into moles, which is essential for quantitative analysis.

The concept of molar mass is vital because stoichiometry – the calculation of reactants and products in chemical reactions – is based on the mole unit. To find out how much energy is released from burning ethanol in wine, you start by determining how much ethanol there is in grams, and then convert that amount to moles using it's molar mass. One can liken molar mass to a conversion factor, which allows us to bridge the gap between the macroscopic world we live in and the molecular world where chemical reactions take place.

Stoichiometry is like a recipe for chemists. It helps quantify the relationship between reactants and products in a chemical reaction. In a combustion reaction, which is a chemical reaction where a substance combines with oxygen to produce heat and light, stoichiometry helps us understand the amounts of each substance needed and the amount of energy released.

Using the exercise as an example, the combustion of ethanol (C2H5OH) reacts with oxygen (O2) according to a balanced chemical equation. As we saw in the solution, knowing the molar mass of ethanol, the heat of combustion, and the moles of ethanol—determined from the mass of ethanol in the glass of wine using stoichiometry—made it possible to calculate the total energy released. This precise calculation is extremely useful in various fields, from designing engines and fuels to specifying dietary content in food science.