In yeast, ethanol is produced from glucose under anaerobic conditions. What is the maximum amount of ethanol (in millimoles) that could theoretically be produced under the following conditions? A cell-free yeast extract is placed in a solution that contains 2.50 × 102 mmol glucose, 0.40 mmol ADP, 0.40 mmol Pi, 0.80 mmol ATP, 0.20 mmol NAD , and 0.20 mmol NADH. It is kept under anaerobic conditions. Under the same conditions, what is the theoretical minimum amount of glucose (in millimoles) required in the solution to form the maximum amount of ethanol?
Under anaerobic conditions in yeast, glucose is converted into ethanol using the following reactions and stoichiometry:
1) Glycolysis: Glucose + 2 NAD + 2 ADP + 2 Pi → 2 Pyruvate + 2 NADH + 2 H+ + 2 ATP.
2) Alcoholic fermentation: Pyruvate + NADH + H+ → Ethanol + CO2 + NAD+
To calculate the maximum amount of ethanol that could theoretically be produced under the given conditions, we need to identify the limiting reactants in these reactions. Since we have 2.50 × 10² mmol glucose, ATP, ADP, Pi, NAD, and NADH are the main limiting reactants.
Reaction 1:
0.40 mmol ADP + 0.40 mmol Pi can produce 0.40 mmol ATP; since 2 ATP are produced from 1 glucose, 0.40 mmol ATP / 2 = 0.20 mmol glucose can be used in glycolysis.
Reaction 2:
0.20 mmol NAD + 0.20 mmol NADH can drive the formation of 0.20 mmol ethanol since 2 pyruvates will be consumed per glucose to make ethanol (1:1 stoichiometry between glucose and ethanol in this case).
Given that the conditions are anaerobic, we can consider that all the available glycolytic ATP will be used to produce ethanol. In this case, the maximum amount of ethanol that will be produced is the same as the limiting amount of glucose utilized, which is 0.20 mmol.
For the second part of the question, the theoretical minimum amount of glucose required to form the maximum amount of ethanol is also 0.20 mmol, as it is the limiting factor in the anaerobic fermentation process.
To calculate the maximum amount of ethanol that could theoretically be produced, we need to determine the number of moles of ethanol that can be produced per mole of glucose.
The balanced equation for glucose fermentation in yeast is as follows:
C6H12O6 -> 2 C2H5OH + 2 CO2
From the equation, we can see that 1 mole of glucose produces 2 moles of ethanol.
Given that the solution contains 2.5 × 10^2 mmol of glucose, we can convert this to moles:
2.5 × 10^2 mmol = 2.5 × 10^-1 moles
Since 1 mole of glucose produces 2 moles of ethanol, the maximum amount of ethanol that can be produced is:
2.5 × 10^-1 moles glucose × 2 moles ethanol/mole glucose = 5 × 10^-1 moles ethanol
To calculate the theoretical minimum amount of glucose required to form the maximum amount of ethanol, we divide the maximum amount of ethanol by the molar ratio of ethanol to glucose:
5 × 10^-1 moles ethanol ÷ 2 moles ethanol/mole glucose = 2.5 × 10^-1 moles glucose
Therefore, the theoretical minimum amount of glucose required is 2.5 × 10^-1 moles or 2.5 × 10^2 mmol.
To determine the maximum amount of ethanol that could theoretically be produced, we need to calculate the stoichiometry of the reaction between glucose and ethanol.
The overall reaction for the conversion of glucose to ethanol can be represented as:
C6H12O6 → 2C2H5OH + 2CO2
From the balanced equation, we can see that for every molecule of glucose, two molecules of ethanol are produced.
Therefore, the maximum amount of ethanol that could be produced would be twice the amount of glucose available in the solution.
Given that the solution contains 2.50 × 102 mmol of glucose, the maximum amount of ethanol produced would be:
Maximum ethanol produced = 2 × 2.50 × 102 mmol = 5.00 × 102 mmol
To calculate the theoretical minimum amount of glucose required to form the maximum amount of ethanol, we can use the stoichiometry of the reaction.
Since two molecules of ethanol are produced from one molecule of glucose, the minimum amount of glucose required would be half the amount of ethanol produced.
Therefore, the minimum amount of glucose required can be calculated as:
Minimum glucose required = (Maximum ethanol produced) / 2
Minimum glucose required = 5.00 × 102 mmol / 2 = 2.50 × 102 mmol
So, the theoretical minimum amount of glucose required in the solution to form the maximum amount of ethanol is 2.50 × 102 mmol.