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 \(\left(d=0.789 \mathrm{~g} / \mathrm{cm}^{3}\right)\) are produced by the fermentation of grape juice?

Short answer

Answer: Approximately -1964.7 kJ of heat is liberated during the process.

Step-by-step solution

Determine the amount of ethyl alcohol

Given 750.0 mL wine containing 12.0% ethyl alcohol by volume, we can calculate the volume of ethyl alcohol present: Ethyl alcohol volume = Total wine volume × (Percentage of ethyl alcohol / 100) = 750.0 × (12.0 / 100)

Find the mass of ethyl alcohol

Using the density of ethyl alcohol (d = 0.789 g/cm³), we can now find the mass of the ethyl alcohol: Mass = Density × Volume Note that 1 mL = 1 cm³, so we can leave the volume in milliliters.

Convert the mass into moles

To find the number of moles of ethyl alcohol, we'll use the molecular weight of ethyl alcohol, which is \(C_2H_5OH \approx(2 × 12.01) + (6 × 1.01) + (1 × 16.00) = 46.07 \mathrm{~g/mol}\). Divide the mass of ethyl alcohol by its molecular weight: Moles of ethyl alcohol = Mass / Molecular weight

Find the enthalpy change of the fermentation process

The heat liberated from the conversion process can be determined by multiplying the moles of ethyl alcohol and the molar enthalpy change of formation for glucose (given as -1275.2 kJ/mol): Heat liberated = Moles of ethyl alcohol × \(\Delta H_{f}^{\circ}\) Now, we have determined all intermediate values, and we can plug them into the formulas to get the final answer. Step 1: Ethyl alcohol volume = 750.0 × (12.0 / 100) = 90.0 mL Step 2: Mass = 0.789 g/cm³ × 90.0 mL = 71.01 g Step 3: Moles of ethyl alcohol = 71.01 g / 46.07 g/mol ≈ 1.541 moles Step 4: Heat liberated = 1.541 moles × (-1275.2 kJ/mol) ≈ -1964.7 kJ The amount of heat liberated when 750.0 mL of wine containing 12.0% ethyl alcohol by volume is produced by the fermentation of grape juice is approximately -1964.7 kJ.

Key concepts

Enthalpy Change of Fermentation

The enthalpy change of fermentation is a vital concept in thermochemistry. Fermentation is a biochemical process where glucose turns into products like ethanol and carbon dioxide. During this transformation, energy is released or absorbed, measured as the enthalpy change. This quantity of heat is typically given per mole of substance, symbolized as \( \Delta H \) and expressed in joules or kilojoules.

For our case, the enthalpy change is given for the conversion of glucose to ethanol, symbolized by the formula \( \Delta H_{f}^{\circ} = -1275.2 \text{kJ/mol} \). The negative sign indicates an exothermic reaction—meaning heat is released during the fermentation process. Calculating the total heat change involves using the moles of the product, ethanol, in this example, and the known enthalpy change per mole of reactant, glucose. Accurate calculation of this value is crucial for understanding energy release in biochemical and industrial processes.

Mole Concept in Chemistry

The mole concept is fundamental to stoichiometry in chemistry, serving as the bridge between the macroscopic world we observe and the microscopic world of atoms and molecules. One mole is Avogadro's number of entities, approximately \(6.022 \times 10^{23}\) particles, be it atoms, ions, or molecules. In fermentation, we're concerned with moles of substances because chemical reactions occur in proportion to the moles of reactants and products involved.

To find the number of moles, you divide the mass of the compound by its molar mass. The molar mass is the sum of all atomic masses in a molecule, measured in grams per mole (g/mol). For example, ethanol \(C_2H_5OH\) has a molar mass of about 46.07 g/mol. If you have 71.01 grams of ethanol, you can find the moles of ethanol by dividing mass by molar mass. This calculation is essential in predicting the amount of products and byproducts in chemical reactions like fermentation.

Density and Volume Calculations

Density is a fundamental concept linking an object's mass and its volume. Defined as mass per unit volume, the density of a substance is unique and can be used to identify it. In chemical processes like fermentation, knowing the density of a liquid allows us to convert between the volume of the liquid and its mass, a necessary step in stoichiometric calculations.

The formula to find the mass using density is: \( \text{Mass} = \text{Density} \times \text{Volume} \). For liquids, volume is often measured in milliliters (mL), corresponding to cubic centimeters \( (cm^3) \). By multiplying the density of ethanol (0.789 g/cm³) by the volume of ethanol (in mL), we determine the mass required to find the number of moles. Accurate volume measurements are crucial, hence the use of precise instruments like volumetric flasks or pipettes.