It takes 21.3 days
Given
5 hr = 8 kg Alcohol
Required
Days to consume 1000 kg of glucose
Solution
Alcoholic fermentation⇒ glucose produces ethanol and carbon dioxide,
C₆H₁₂O₆ → 2 C₂H₅OH + 2CO₂
mol ethanol :
[tex]\tt \dfrac{5000~g}{46~g/mol}=108.7~moles[/tex]
moles of glucose to produce 108.7 moles ethanol :
[tex]\tt \dfrac{1}{2}\times 108.7=54.35[/tex]
54.35 moles = 5 hours
moles of 1000 kg of glucose :
[tex]\tt \dfrac{10^6~g}{180~g/mol}=5555.5~moles[/tex]
So for 5555.5 moles, it takes :
[tex]\tt \dfrac{5555.5}{54.35}\times 5~hours=511.085~h=21.3~days[/tex]
