Answer to Question #277894 in General Chemistry for James

Question

Calculate the weight of sugar that must be fermented to produce a liter of alcohol (denisty = 0.79 g/mL)

Answer 1

Solution:

Calculate the mass of alcohol (ethanol):

Mass of ethanol = Density × Volume

Mass of ethanol = (0.79 g/mL) × (1L) × (1000 mL / 1L) = 790 g

Calculate the moles of ethanol:

The molar mass of ethanol is 46.07 g/mol

Therefore,

(790 g) × (1 mol / 46.07 g) = 17.148 mol of ethanol

The fermentation process of sugar (sucrose) into alcohol (ethanol):

C₁₂H₂₂O₁₁(sucrose) + H₂O(water) → C₆H₁₂O₆(glucose) + C₆H₁₂O₆(fructose)

C₆H₁₂O₆(glucose) → 2C₂H₅OH(ethanol) + 2CO₂(carbon dioxide)

According to stoichiometry:

Moles of sucrose = Moles of glucose = Moles of ethanol/2

Therefore,

Moles of sucrose = (17.148 mol) / 2 = 8.574 mol

Calculate the mass of sucrose:

The molar mass of sucrose is 342.2965 g/mol

Therefore,

(8.574 mol) × (342.2965 g / 1 mol) = 2934.85 g = 2935 g of sucrose

Mass of sucrose = 2935 g

Answer: 2935 grams of sugar must be fermented