Fermintation and respiration If you were poor and had no mon

Fermintation and respiration: If you were poor and had no money for beer, but had a pet goldfish, you could seal your goldfish in a jar and wait for it to use fermentative metabolism to generate the ethanol for you. It wouldn\'t taste like beer, but there would be alcohol in the water all the same. Given the following, how long would it take (in days) for your pet goldfish to make its water have the same alcohol content as a light beer (4.2%)? 5g goldfish in 500ml jar filled to the top with fully aerated water (no airspace) in jar Temperature = 20°C, Oxygen solubility = 1.6 mmol/L Goldfish metabolic rate: 5 µmol ATP/g/min.

Beer = 4.2% alcohol by volume Ethanol density is 0.7893 g/ml, 46 g/mol

HINT: Use the equations for respiration and fermentation to determine ATP generated in each type of metabolic reaction. The correct answer is somewhere between 1 day and 1 month.

Solution

the correct answer is 10 days and 10 minutes

First we must calculate the molar volume of ethanol that is required with the given data

required concentration of ethanol in water is 4.2%

Molarity = percentage *density /(100%*molecular weght)

X = 4.2 *0.7893/10*46

=0.7207 Mol/dm3 =0.7207 Mol/L

thus for 500 mL the volume of ethanol required is 0.36035 Mol

which will correspond to 217007868952500000000000 number of molecules

the metabolic rate of gold fish is 5 µmol/g/min so for

5g of fish it is 25 µmol/min = 15055353750000000000 molecules            

according to respiration equation for anerobic metabolism

C₆H₁₂0₆ ------> 2C₂H₅OH + 2CO₂ +2ATP

15055353750000000000 molecule of ATP = 15055353750000000000 molecule of ethanol per minute

217007868952500000000000 molecule ethanol = X minute = 14414 minutes =240.23 hours = 10 days and 9.7 minutes