Glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s),\left(\Delta H_{\mathrm{f}}^{\circ}=-1275.2 \mathrm{~kJ} / \mathrm{mol}\right)\) is converted to ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)\), and carbon dioxide in the fermentation of grape juice. What quantity of heat is liberated when \(750.0 \mathrm{~mL}\) of wine containing \(12.0 \%\) ethyl alcohol by volume \(\left(d=0.789 \mathrm{~g} / \mathrm{cm}^{3}\right)\) is produced by the fermentation of grape juice?

The concept of the 'heat of reaction', also known as enthalpy change, plays a crucial role in understanding chemical thermodynamics. It refers to the amount of heat released or absorbed during a chemical reaction. If the process is exothermic, such as the fermentation of glucose to produce ethyl alcohol and carbon dioxide, heat is released, and the enthalpy change has a negative value. This is what happens during the fermentation of grape juice.

To determine the total heat of reaction when making wine, we start by finding out how much glucose is transformed and then applying the stoichiometry of the reaction. The heat of formation for glucose is given as \( -1275.2 \text{kj/mol} \), and by multiplying this with the number of moles of glucose that react, we find the total heat released. In the example, the fermentation liberates 983.14 kJ of energy, indicating a significant release of heat which could potentially be harnessed for other processes or require management to ensure product quality.

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It relies on the balanced chemical equation, which provides the mole ratio of the substances involved. In the context of the fermentation of grape juice, the balanced equation indicates that one mole of glucose (\(C_6H_{12}O_6(s)\)) produces two moles of ethyl alcohol (\(C_2H_5OH(l)\)) and two moles of carbon dioxide (\(CO_2(g)\)).

When calculating the quantity of heat released, we must consider this ratio to determine how much glucose is required to produce a certain amount of ethyl alcohol. In our problem, we calculated the amount of alcohol and then used stoichiometry to find the corresponding amount of glucose needed to produce this alcohol. Understanding stoichiometry is essential, as it helps us connect the quantities of reactants used to the energy changes during a reaction and is widely used in steps to improve efficiency and yield in various industrial processes including winemaking.

Molar mass is a fundamental concept in chemistry that represents the mass of one mole of a substance. It is expressed in grams per mole (g/mol) and is calculated as the sum of the atomic masses of all atoms in a molecule. For ethyl alcohol (\(C_2H_5OH\)), the molar mass is 46.07 g/mol.

In the fermentation example, the molar mass of ethyl alcohol helps us to convert the mass of alcohol in grams to moles, which is a necessary step for using stoichiometry to relate the reactants to the products. After finding the volume of ethyl alcohol in the wine, which was 90.0 mL, the density is used to calculate the mass, and then using the molar mass, the mass is converted to moles. The molar mass is a critical piece in the puzzle that allows us to transition from the macroscopic world we can measure (like mass and volume) to the microscopic world of molecules and atoms that chemical reactions operate on.