Question

Yeast make alcohol in the absence of oxygen by a process called fermentation (i.e., anaerobic respiration). Complete fermentation of one of the sugar glucose (C₆ H₁₂ O₆) will generate two moles of ethanol (C₂ H₆ O), two moles of carbon dioxide (CO₂) gas, and tow moles of the important molecule ATP (C₁₀ H₁₆ N₅ O₁₃ P₃), using in cellular transfers. You perform an experiment to make alcohol, so you set up an anaerobic fermentation system using yeast. You add 135 grams of glucose to your system and allow the sugar to be fermented to completion, trapping all fermentation products. (a) How many molecules of ATP were produced in your experiment? What is the total mass of the ATP. (b) The volume of the fermenation tank was 15 Liters, and the temperature was kept constant during the experiment at 25 ⁰C. Is it possible to determine the final tank pressure of the CO₂ gas produced by this experiment? Will the Ideal Gas Law work here? (c) What was the total volume of ethanol produced in this experiment? The density of ethanol is 0.789g/mL.

Answer 1

(a) Molar mass of Gucose is 180 g/ mole

135 grams of Glucose contains 135 g / ( 180 g/ mole) = 0.75 mole of glucose

1 mole glucose produces 2 moles of ATP

So, 0.75 moles of glucose will produce 2 * 0.75 moles = 1.5 moles ATP

Number of molecules of ATP = 1.5 moles * 6.023 * 10²³ moles/ 1 mole = 9.03 * 10 ²³ molesules

Mass of ATP = moles of ATP produced * Molar mass of ATP = 1.5 mole * 507 g/ mole = 760.5 g

(b) The pressure can be calculated.

The volume of the CO2 (gas) produced = 15 Liters

Moles of CO2 produced = 2 * 0.75 moles = 1.5 moles

Temperature = 25 ⁰ C = ( 25 +273) K = 298 K

The ideal gas equation is:

P * V = n * R *T

So, P * 15 L = 1.5 moles * 0.082 lit atm mole^-1 K^-1 * 298 K

SO, P = 1.5* 0.082* 298/ 15 atm = 2.44 atm

(c) Moles of ethanol produced = 2 * moles of glucose = 2 * 0.75 = 1.5 moles

So, mass of ethanol = moes * molar mass of ethanol = 1.5 moles * 46 g/ mole = 69 grams

Volume = mass/ density = 69 grams/ 0.789 g/ mL = 87.5 ml