Fermentation rate

Question

If 5.2 X 10¹⁹ molecules of Glucose were metabolized by alcoholic fermentation in 45 minutes, how many

      molecules of ethanol would be produced by the cells in 1.8 hours?

Answer 1

The alcoholic fermentation of glucose can be described by the following balanced equation:

C₆H₁₂O₆ (glucose) --> 2 CH₃CH₂OH (ethanol) + 2CO₂ + energy (2ATP + heat)

In this problem we are given molecules of glucose metabolized per minute and want to find molecules of ethanol produced after a certain amount of hours

We can solve this problem using dimensional analysis...

Start by writing the units you are given (molecules glucose/minute) and stepwise convert them to the units you want to find (molecules ethanol/hour):

1.) Lets first convert molecules of glucose to molecules of ethanol. We know from the principles of stoichiometry that in order to convert from molecules of one compound to molecules of another compound we must use Avogadro's number (1 mol glucose = 6.022 x 10²³ molecules glucose and 1 mol ethanol = 6.022 x 10²³ molecules ethanol) and the molar ratio from the balanced equation (1 mol glucose = 2 mol ethanol)

(5.2 x 10¹⁹ molecules glucose / 45 minutes) x (1 mol glucose / 6.022 x 10²³ molecules glucose) x (2 mol ethanol / 1 mol glucose) x (6.022 x 10²³ molecules ethanol / 1 mol ethanol)

= 2.31 x 10¹⁸ molecules ethanol / minute

*Notice that molecules glucose, mol glucose, and mol ethanol all cancel leaving us with molecules ethanol in the numerator. This is how we set up dimensional analysis problems! (Notice too that Avogadro's number also cancels out which is nice and leaves us with less math to do)

2.) The next step is to convert molecules ethanol per minute to molecules ethanol per hour using the conversion factor (1 hour = 60 min)

(2.31 x 10¹⁸ molecules ethanol / min) x (60 min / 1 hr) = 1.39 x 10²⁰ molecules ethanol / hr

3.) The last step is to use the conversion factor you found (molecules ethanol / hr) to find how many molecules of ethanol are produced in 1.8 hours

(1.39 x 10²⁰ molecules ethanol / hr) x 1.8 hr = 2.5 x 10²⁰ molecules ethanol

That's it! You're done. Hope this helps!