Question

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?

Short answer

Answer: 983.14 kJ of heat is released during the fermentation of grape juice to produce 750.0 mL of wine containing 12.0% ethyl alcohol by volume.

Step-by-step solution

Calculate the mass of ethyl alcohol in the wine

We are given the volume and the percentage of ethyl alcohol (by volume) in the wine. We can use this information to find the volume of ethyl alcohol: Volume of ethyl alcohol = total volume of wine × percentage of ethyl alcohol = 750.0 mL × 0.12 = 90.0 mL We are given the density of ethyl alcohol (0.789 g/cm³). We can convert the volume of ethyl alcohol to its mass using the density: Mass of ethyl alcohol = volume × density = 90.0 mL × 0.789 g/cm³ = 71.01 g

Calculate the moles of ethyl alcohol produced

Next, we have to find the moles of ethyl alcohol produced, using its molar mass (C2H5OH: M = 46.07 g/mol): Moles of ethyl alcohol = mass / molar mass = 71.01 g / 46.07 g/mol = 1.541 mol

Find the balanced reaction equation for glucose fermentation

We need to find the balanced equation for the fermentation of glucose to ethyl alcohol and carbon dioxide. The balanced equation is: C6H12O6(s) → 2 C2H5OH(l) + 2 CO2(g) According to the balanced equation, 1 mole of glucose produces 2 moles of ethyl alcohol.

Calculate the moles of glucose required

Since 1 mole of glucose produces 2 moles of ethyl alcohol, we can calculate the moles of glucose needed to produce the 1.541 mol of ethyl alcohol: Moles of glucose required = moles of ethyl alcohol produced / 2 = 1.541 mol / 2 = 0.7705 mol

Calculate the heat liberated during the reaction

We are given the heat of formation of glucose (-1275.2 kJ/mol). The negative sign indicates that the reaction is exothermic, and heat is released. To calculate the heat liberated during the fermentation of grape juice, we can use the following formula: Heat liberated = moles of glucose × heat of formation of glucose = 0.7705 mol × (-1275.2 kJ/mol) = -983.14 kJ Since the heat liberated has a negative sign, this indicates that 983.14 kJ of heat is released during the fermentation of grape juice to produce 750.0 mL of wine containing 12.0% ethyl alcohol by volume.

Key concepts

Heat of Reaction

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

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

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.