Question

In alcohol fermentation, yeast converts glucose to ethanol and carbon dioxide: $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+2 \mathrm{CO}_{2}(g) $$ If \(5.97 \mathrm{~g}\) of glucose reacts and \(1.44 \mathrm{~L}\) of \(\mathrm{CO}_{2}\) gas is collected at \(293 \mathrm{~K}\) and \(0.984 \mathrm{~atm},\) what is the percent yield of the reaction?

Short answer

The percent yield of the reaction is 88.9%.

Step-by-step solution

Calculate Moles of Glucose

First, determine the moles of glucose. The molecular weight of glucose (C₆H₁₂O₆) is approximately 180.18 g/mol. Use the formula:\[\text{Moles of Glucose} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{5.97 \text{ g}}{180.18 \text{ g/mol}} = 0.0331 \text{ mol}\]

Use Stoichiometry to Find Moles of CO₂ Formed Theoretically

From the balanced chemical equation, 1 mole of glucose produces 2 moles of CO₂. Thus, calculate the theoretical moles of CO₂:\[\text{Moles of CO₂} = 0.0331 \text{ mol of glucose} \times \frac{2 \text{ mol CO₂}}{1 \text{ mol glucose}} = 0.0662 \text{ mol CO₂}\]

Calculate the Volume of CO₂ Formed Theoretically

Use the ideal gas law to find the theoretical volume of CO₂ produced under the given conditions:\[PV = nRT \rightarrow V = \frac{nRT}{P}\]Where:- \(n = 0.0662 \text{ mol}\)- \(R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}\)- \(T = 293 \text{ K}\)- \(P = 0.984 \text{ atm}\)Calculate \(V\):\[V = \frac{(0.0662 \text{ mol})(0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1})(293 \text{ K})}{0.984 \text{ atm}} = 1.62 \text{ L}\]

Calculate Percent Yield

Use the actual volume of CO₂ collected to find the percent yield using:\[\text{Percent Yield} = \frac{\text{Actual Volume}}{\text{Theoretical Volume}} \times 100t= \frac{1.44 \text{ L}}{1.62 \text{ L}} \times 100 = 88.9\%\]

Conclusion: Percent Yield

The percent yield of the reaction is calculated to assess efficiency.

Key concepts

Alcohol Fermentation

Alcohol fermentation is a biological process where yeast converts glucose into ethanol and carbon dioxide. This process is essential in brewing and winemaking. During alcohol fermentation, yeast utilizes glucose as a food source, transforming it using enzymes into ethanol and carbon dioxide gas.
This conversion is crucial because it allows yeast to generate energy in environments lacking oxygen, a characteristic known as anaerobic respiration.

• The main equation for alcohol fermentation is: \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH} + 2 \mathrm{CO}_{2}\).
• Yeast is the microorganism responsible for this conversion.
• The process results in the production of two important by-products: ethanol and \(\mathrm{CO}_{2}\).

The efficiency of alcohol fermentation is often measured by how closely the actual production matches the theoretical prediction, as seen in the percent yield calculation.

Stoichiometry

Stoichiometry is a section of chemistry that involves the calculation of reactants and products in chemical reactions.
In the context of alcohol fermentation, stoichiometry helps us understand the relationship between glucose and the products, ethanol and carbon dioxide. By using the balanced chemical equation, one can determine how much of a product is expected from a given amount of reactant.

• 1 mole of glucose yields 2 moles of ethanol and 2 moles of carbon dioxide.
• Stoichiometry helps in predicting the theoretical yield of products.

Applying stoichiometry to the given reaction, given the moles of glucose, allows the computation of the amount of \(\mathrm{CO}_{2}\) produced. This approach is essential to identify any deviation from the expected yield, such as in the case of the percent yield calculations.

Ideal Gas Law

The ideal gas law is a fundamental equation that relates the pressure, volume, temperature, and amount of gas for a perfect gas. The equation is expressed as \( PV = nRT \). In the exercise, we use it to calculate the expected volume of gas collected from the fermentation process.

• \(P\) represents the pressure of the gas.
• \(V\) is the volume of the gas.
• \(n\) signifies the number of moles of gas.
• \(R\) is the ideal gas constant, 0.0821 \(\text{L atm K}^{-1} \text{ mol}^{-1}\).
• \(T\) is the temperature in Kelvin.

In this reaction, we calculate the theoretical volume of \(\mathrm{CO}_{2}\) produced using the ideal gas law and compare it with the actual volume measured. This comparison helps provide the percent yield, which indicates the efficiency of the alcohol fermentation process under actual conditions.

Glucose Conversion

Glucose conversion is a term that describes the transformation of glucose into other chemical substances through chemical reactions. In alcohol fermentation, glucose is converted into ethanol and carbon dioxide. This is effectively glucose's role as a starting material in the biochemical process.

• Glucose serves as the primary reactant in alcohol fermentation.
• Each molecule of glucose produces two molecules of both ethanol and carbon dioxide.

The efficiency of glucose conversion is critical for industries relying on fermentation, such as alcohol production and biofuels. Understanding how glucose converts aids in optimizing conditions to maximize product yield and ensure the process runs efficiently. Knowing the percent yield and the efficiency of conversion helps producers refine their processes to reduce waste and improve outcomes.