Problem 56 - Chemistry

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 are reacted and \(1.44 \mathrm{~L}\) of \(\mathrm{CO}_{2}\) gas are collected at \(293 \mathrm{~K}\) and \(0.984 \mathrm{~atm},\) what is the percent yield of the reaction?

Step-by-Step Solution

Answer

The percent yield of the reaction is 90.94%.

Step 1: Determine theoretical yield

The balanced chemical reaction indicates that one molecule of glucose (\(C_{6}H_{12}O_{6}\)) reacts to form two molecules of carbon dioxide (\(CO_{2}\)). Therefore, the molar ratio of glucose to carbon dioxide is 1:2. This means that the mass of glucose (5.97g) needs to be converted into moles using glucose's molar mass (180.156g/mol): \[\frac{5.97g}{180.156g/mol} = 0.0331mol\] The theoretical number of moles of carbon dioxide that should be formed from this reaction is therefore: \(0.0331mol \times 2 = 0.0662mol\)

Step 2: Calculate actual yield

Using the ideal gas law, the moles of carbon dioxide can be converted from the given volume. Given: pressure, \(P = 0.984 atm\); temperature, \(T = 293K\); volume, \(V = 1.44L\) and R (ideal gas constant) = 0.0821 L·atm/K·mol. The ideal gas law is: \(PV = nRT\) Solving for n (moles of gas): \[n = \frac{PV}{RT} = \frac{(0.984 atm) (1.44 L)}{(0.0821 L·atm/K·mol) (293 K)} = 0.0602mol\]

Step 3: Determine percent yield

Percent yield of a reaction can be calculated using the following formula: \[(percent yield) = \frac{(actual yield)}{(theoretical yield)} \times 100\% \rightarrow (percent yield) = \frac{0.0602mol}{0.0662mol} \times 100\% = 90.94\%\]

Key Concepts

Alcohol Fermentation

Alcohol fermentation is a metabolic process used by yeast to produce ethanol and carbon dioxide from sugars like glucose. This process occurs in the absence of oxygen, making it an example of anaerobic respiration. The reaction not only generates ethanol for beverages like beer and wine but also releases carbon dioxide, which can impact the texture of the product.

• The equation for alcohol fermentation is: \[\text{C}_{6}\text{H}_{12}\text{O}_{6}(s) \rightarrow 2\text{C}_{2}\text{H}_{5}\text{OH}(l) + 2 \text{CO}_{2}(g)\]
• Yeast consumes glucose and, through glycolysis and fermentation pathways, produces ethanol and carbon dioxide.
• This process is vital in various industries, not only for brewing and winemaking but also in biofuel production, where ethanol is used as a renewable energy source.

Understanding this chemical process helps us appreciate how yeast contributes to both food science and renewable energy sectors.

Ideal Gas Law

The ideal gas law is a fundamental principle in chemistry that relates the properties of gases. It is represented by the equation \(PV = nRT\), where:

• \(P\) is the pressure of the gas in atmospheres (atm).
• \(V\) is the volume of the gas in liters (L).
• \(n\) is the number of moles of the gas.
• \(R\) is the ideal gas constant (approximately 0.0821 L·atm/K·mol).
• \(T\) is the temperature in Kelvin (K).

In our solution, the ideal gas law is used to determine how many moles of carbon dioxide gas were produced during the fermentation. By rearranging the equation to solve for \(n\), we find the number of moles of a gas when its pressure, volume, and temperature are known. The ideal gas law assumes gases behave ideally, meaning they follow certain theoretical conditions without deviation. This assumption works well for many gases under a wide range of conditions, making it exceptionally useful in stoichiometry calculations and determining gas behavior in chemical reactions.

Percent Yield

Percent yield is a metric used in chemistry to assess the efficiency of a chemical reaction. It compares the amount of product actually obtained from a reaction to the amount theoretically possible if everything were perfect.To calculate percent yield, use the formula:\[\text{Percent Yield} = \left(\frac{\text{Actual Yield}}{\text{Theoretical Yield}}\right) \times 100\%\]

• The actual yield is the amount of product obtained from the reaction experimentally.
• The theoretical yield is the amount of product expected based on stoichiometric calculations from the balanced equation.

In our problem, the percent yield was calculated to be 90.94%, indicating that nearly all of the potential product was obtained, which suggests an efficient reaction. Percent yield could be less than 100% due to factors such as incomplete reactions, side reactions, or loss of product during the process. Knowing how to calculate and interpret percent yield is crucial for evaluating ongoing industrial processes and in quality control.

Chemical Reactions

Chemical reactions are processes where reactants are transformed into products. They are described by chemical equations which provide the quantitative relationships between the substances involved.

• A balanced chemical equation ensures that the number of atoms for each element is the same on both sides, adhering to the law of conservation of mass.
• In the context of alcohol fermentation, the balanced equation shows that one mole of glucose produces two moles of ethanol and two moles of carbon dioxide.
• Understanding chemical reactions involves grasping stoichiometry, which is the calculation of reactants and products in chemical reactions. It is essential in predicting yields, calculating reactant needs, and ensuring safety in chemical processes.

Chemical reactions drive countless processes in both biological systems and industrial applications. They are often leveraged to innovate and improve upon existing methods for producing everything from food to pharmaceuticals.