Question

As we have attempted to lessen our dependence on fossil fuels, the demand for biofuels, such as ethanol, which is produced by the fermentation of the sugars found in corn, has increased. Using Le Châtelier's principle, predict which way the equilibrium will shift during the fermentation of sugar for each of the following changes. $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q) \rightleftharpoons 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+2 \mathrm{CO}_{2}(a q) $$ a. when the concentration of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) is increased b. when the concentration of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) is decreased c. when \(\mathrm{CO}_{2}\) gas is added to the solution d. when the volume of water in the solution is doubled

Short answer

In summary, applying Le Châtelier's principle to the fermentation of sugar equation, the equilibrium will shift as follows: a. Increasing the concentration of \(C_6H_{12}O_6\) will shift the equilibrium to the right, favoring ethanol and carbon dioxide production. b. Decreasing the concentration of \(C_2H_5OH\) will also shift the equilibrium to the right, favoring ethanol and carbon dioxide production. c. Adding \(CO_2\) gas to the solution will shift the equilibrium to the left, reducing the production of ethanol and carbon dioxide. d. Doubling the volume of water in the solution will shift the equilibrium to the right, favoring the production of ethanol and carbon dioxide.

Step-by-step solution

Understand Le Châtelier's Principle

Le Châtelier's principle states that if a change is made to a system at equilibrium, the system will adjust its position to partially counteract the change. In other words, if a change is made to the concentrations of reactants or products in an equilibrium reaction, the equilibrium will shift to either the left or right, favoring either the forward or reverse reactions.

Predict the equilibrium shift for an increase in the concentration of glucose (\(C_6H_{12}O_6\))

According to Le Châtelier's principle, if the concentration of glucose (\(C_6H_{12}O_6\)) is increased, the reaction will shift towards the side with fewer moles of \(C_6H_{12}O_6\), which is the right side. This means that the production of ethanol (\(C_2H_5OH\)) and carbon dioxide (\(CO_2\)) will be favored.

Predict the equilibrium shift for a decrease in the concentration of ethanol (\(C_2H_5OH\))

According to Le Châtelier's principle, if the concentration of ethanol (\(C_2H_5OH\)) is decreased, the reaction will shift towards the side with more moles of \(C_2H_5OH\), which is the right side. This means that the production of ethanol and carbon dioxide will be favored.

Predict the equilibrium shift for an addition of carbon dioxide (\(CO_2\)) gas to the solution

According to Le Châtelier's principle, if the concentration of carbon dioxide (\(CO_2\)) is increased by adding the gas to the solution, the reaction will shift towards the side with fewer moles of \(CO_2\), which is the left side. This means that the consumption of glucose (\(C_6H_{12}O_6\)) to produce more ethanol (\(C_2H_5OH\)) and carbon dioxide will be reduced.

Predict the equilibrium shift when the volume of water in the solution is doubled

If the volume of water in the solution is doubled, it means that the concentration of all species in the reaction is reduced. Since all three components in the reaction are dissolved in water, doubling the volume means that the concentrations are halved. According to Le Châtelier's principle, the reaction will now shift to counteract the change. In this case, the reaction will try to increase the concentrations of both the reactant and products. Hence, the reaction will favor the side with more moles, which is the right side in this specific process. The production of ethanol (\(C_2H_5OH\)) and carbon dioxide (\(CO_2\)) will be favored.

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state in a reversible chemical reaction where the rate of the forward reaction equals the rate of the reverse reaction, and the concentrations of reactants and products remain constant over time. This does not mean the reactants and products are in equal concentrations, but rather that their ratio remains stable. It's important to note that chemical equilibrium can be disturbed by changing conditions such as concentration, pressure, and temperature.

At equilibrium, a change in any of these conditions will result in an equilibrium shift to restore a new state of balance. This balancing act is exemplified in the generation of biofuels through processes such as fermentation, where equilibrium principles are applied to maximize product yields.

Biofuels Fermentation

Fermentation is an anaerobic process used by microorganisms to convert sugars into simpler substances such as ethanol, a type of biofuel. The fermentation of sugars, like those found in corn, is a crucial step in the production of bioethanol. During this biochemical reaction, enzymes from microorganisms catalyze the conversion of glucose into ethanol and carbon dioxide.

Biofuels like ethanol offer a renewable energy source, and their production is carefully monitored and optimized using concepts like chemical equilibrium and Le Châtelier's principle. Understanding how to manipulate conditions to drive the equilibrium toward more product formation is central in making the fermentation process economically viable.

Ethanol Production

Ethanol production through fermentation is highly relevant to developing sustainable energy. In this process, glucose derived from plants such as corn is broken down into ethanol and carbon dioxide. The production of ethanol can be summarized by a chemical equation, with glucose on one side (reactant) and ethanol and carbon dioxide on the other (products).

The reaction is subject to equilibrium dynamics, and maintaining optimal conditions for fermentation is key to maximizing ethanol yield. This includes monitoring temperature, pH levels, and other variables that influence the microbial activity and reaction rate. By managing these factors, producers can enhance the efficiency of ethanol production and contribute to a sustainable energy future.

Equilibrium Shifts

Equilibrium shifts occur when an external change is imposed on a reaction in equilibrium. Le Châtelier's principle helps us predict the direction of this shift. For instance, increasing the reactant concentration typically drives the reaction forward, while removing a product encourages the formation of more product.

In the context of ethanol production, changes in reactant (glucose) or product (ethanol, carbon dioxide) levels will cause the equilibrium to shift in a way that opposes the change. To enhance ethanol output, conditions may be adjusted to shift the equilibrium toward the product side. When applied to industrial biofuel production, understanding equilibrium shifts can lead to more efficient processes and higher yields of ethanol, thus improving the viability of biofuels as alternative energy sources.