Question

You are the brewmaster at a local craft brewery. In an effort to cut costs, you have been tasked to develop a procedure to recover the carbon dioxide generated during the fermentation process. This recovered carbon dioxide will be used to later carbonate the beer before it is bottled. During fermentation, sucrose (C12H22O11) dissolved in water is broken down into ethanol (CH3CH2OH) and carbon dioxide by yeast. The carbon dioxide is then released into the space above the reaction where it is then captured using your novel device. To test your recovery method, you sprinkle 22 g of dry yeast into a rigid glass container that contains 10 gallons of water (1 gallon=3.78 liters). Then you add 4.5 kg of sucrose to simulate the wort (the sugary liquid that will be fermented into beer). The volume of the rigid glass container is 10.5 gallons and the fermentation temperature is controlled using a water bath set to 25°C.

a) Write a balanced equation for the fermentation process, including phases of each compound.

b) Calculate the volume of carbon dioxide that is released by the fermentation of 4.5 kg of sucrose. You can assume that the carbon dioxide is collected and kept at a constant pressure of 1 atm in a storage tank.

c) To properly carbonate your 10 gallon batch of beer, you need approximately 100 L of carbon dioxide at 1 atm. How many batches of beer can you carbonate with the amount of carbon dioxide generated by your experiment?

d) How much ethanol is produced during the fermentation of 4.5 kg sucrose. Express your answer in gallons.

e) Calculate the amount of heat generated by the fermentation of 4.5 kg sucrose. Express your answer in kJ.

Answer 1

a) Write a balanced equation for the fermentation process, including phases of each compound.

C12H22O11(l) + H2O(l) = 4CH3CH2OH(l) + 4 CO2(g)

b) Calculate the volume of carbon dioxide that is released by the fermentation of 4.5 kg of sucrose. You can assume that the carbon dioxide is collected and kept at a constant pressure of 1 atm in a storage tank.

CO2 if

m = 4.5 kg of sucrse are fermented... assume P = 1 atm at T = 25 °C

mol of sucrose = mass/MW = 4500/342.2965 = 13.146 mol of sucrose

then... 1 mol of sucrose --> 4 mol of CO2

mol of CO2 = 13.146*4 = 52.584 mol of CO2

then...

assume at std. condition 1 mol of gas --< 22.L

52.584 mol --> 52.584*22.4 = 1177.8816 L of CO2

c) To properly carbonate your 10 gallon batch of beer, you need approximately 100 L of carbon dioxide at 1 atm. How many batches of beer can you carbonate with the amount of carbon dioxide generated by your experiment?

10 gal --> 100 L

x gal --> 1177.8816 L

x = 1177.8816 /100 = 11.77 --> about 12 batches (of 10 gallons each)

d) How much ethanol is produced during the fermentation of 4.5 kg sucrose. Express your answer in gallons.

1 mol of sucrose --> 4 mol of ethanol

mol of ethanol= 13.146*4 = 52.584 mol of ethanol

mass = mol*MW = 52.584 *46 = 2418.864 g of ethanol

D = 0.789 g/mL

V = mass/D = 2418.864 /0.789 = 3065.733 mL = 3.06 L

1 gal = 3.78 L

then

3.06 /3.78

gallons = 0.809523