Question

Fermentation is a complex chemical process of winemaking in which glucose is converted into ethanol and carbon dioxide: $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+2 \mathrm{CO}_{2} $$ glucose ethanol Starting with \(500.4 \mathrm{~g}\) of glucose, what is the maximum amount of ethanol in grams and in liters that can be obtained by this process (density of ethanol \(=0.789 \mathrm{~g} / \mathrm{mL}\) )?

Short answer

255.84 g of ethanol, which is 0.324 L.

Step-by-step solution

Calculate Molar Masses

Determine the molar mass of glucose \(\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6\) and ethanol \(\mathrm{C}_2\mathrm{H}_5\mathrm{OH}\). - Glucose: \(6(12.01) + 12(1.01) + 6(16.00) = 180.18\text{ g/mol}\).- Ethanol: \(2(12.01) + 6(1.01) + 16.00 = 46.08\text{ g/mol}\).

Determine Moles of Glucose

Use the given mass of glucose to find the number of moles \(n\) of glucose available.\[ n = \frac{500.4\text{ g}}{180.18\text{ g/mol}} = \,2.777\text{ mol} \].

Moles to Mass of Ethanol

Based on the stoichiometry of the reaction, each mole of glucose produces two moles of ethanol. Calculate the moles of ethanol produced:\(2.777\text{ mol glucose} \times 2 = 5.554\text{ mol ethanol} \).Now convert moles of ethanol to grams:\[ 5.554\,\text{mol} \times 46.08\text{ g/mol} = 255.84\text{ g} \].

Convert Ethanol Mass to Volume

Use the density of ethanol to convert mass to volume.\[ \text{Volume} = \frac{255.84\text{ g}}{0.789\text{ g/mL}} = 324.29\text{ mL} \].Since the question asks for liters, divide by 1,000:\(324.29\text{ mL} = 0.324\text{ L}\).

Key concepts

Chemical Process

Fermentation is among the most famous chemical processes, especially within winemaking and brewing. Fermentation involves the transformation of glucose into ethanol and carbon dioxide. The process begins with yeast enzymes breaking down sugars into smaller compounds. These smaller compounds, namely ethanol and carbon dioxide, emerge as by-products of metabolism.
The chemical reaction can be expressed simply with the equation:

• \( \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \rightarrow 2 \mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH} + 2\mathrm{CO}_{2} \)

This equation highlights the conversion process occurring inside yeast cells, where complex organic reactions break down glucose molecules. Without involving complicated laboratory setups, fermentation offers a biological and straightforward means of transforming sugar into alcohol.

Glucose Conversion

Glucose conversion refers to the transformation of glucose, a simple sugar, into different substances like ethanol. In the context of fermentation, yeast plays a crucial role in converting glucose. Yeast acts as a natural catalyst, facilitating the breakdown of glucose into smaller molecules.
During this conversion, glucose \( \mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6 \) serves as the substrate, undergoing fermentation to yield ethanol \( \mathrm{C}_2\mathrm{H}_5\mathrm{OH} \) and carbon dioxide \( \mathrm{CO}_2 \).

• Each glucose molecule breaks down into two molecules of ethanol.
• This biological conversion is energy-efficient and environmentally friendly, unlike many other chemical transformations that require external energy and resources.
• Understanding this conversion helps illustrate why glucose is fundamental in brewing and biofuel productions.

Ethanol Production

The production of ethanol is a key outcome of the fermentation chemical process. Ethanol, also known as ethyl alcohol, is a type of alcohol that appears in alcoholic beverages and is used as a clean biofuel alternative. Its creation involves the anaerobic processes that yeast undergo, where they convert organic substances without oxygen.
To calculate ethanol yield, you need to know the stoichiometry of the reaction, which determines that each glucose molecule produces two ethanol molecules. This information allows chemists to predict theoretical production quantities from known glucose amounts.
For example, starting with 500.4 grams of glucose, the maximum ethanol produced can be determined by calculating moles of glucose and thereby determining moles of ethanol, ultimately converting this to mass and volume with the knowledge of ethanol's density for practical purposes.

Carbon Dioxide

Carbon dioxide (\( \mathrm{CO}_2 \)) is another major by-product of the fermentation process, released alongside ethanol. This gas plays an essential role in several biological and industrial contexts. For instance, the bubbles in sparkling beverages and the leavening action in breadmaking are due to \( \mathrm{CO}_2 \) produced during fermentation.

• During the fermentation of glucose by yeast, each glucose molecule results in two \( \mathrm{CO}_2 \) molecules.
• Even though \( \mathrm{CO}_2 \) is not the primary product in ethanol production, it is essential for creating the airy structure in baked goods.

Its presence and release are crucial indicators of the progression in fermentation, effectively illustrating the active conversion of glucose when a visible fizz or foam manifests.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It is essential for predicting how much product will be formed in chemical processes, like fermentation.The stoichiometric coefficients in the fermentation equation play a significant role:

• For every mole of glucose \( \mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6 \), two moles of ethanol \( \mathrm{C}_2\mathrm{H}_5\mathrm{OH} \) are produced.
• This understanding allows scientists and chemists to calculate the theoretical yields of products based on starting amounts of reactants, just like determining the mass and volume of ethanol possible from a given mass of glucose.

It involves performing calculations that help in understanding both product outputs and reactant needs, pivotal in industries like winemaking, pharmaceuticals, and biofuel production.