Final answer:
The fermentation of grapes produces ethanol and carbon dioxide. For every molecule of glucose that is fully converted, 2 molecules of ethanol and 2 molecules of carbon dioxide are produced. If 200.0 g of glucose is fully converted, the total mass of ethanol and carbon dioxide produced would be 40.8 kg.
Step-by-step explanation:
When grapes undergo fermentation, the carbohydrate glucose is converted to ethanol and carbon dioxide. The balanced chemical equation for this process is:
C6H12O6 (aq) → 2 C2H5OH(aq) + 2 CO2 (aq)
From this equation, we can see that for every molecule of glucose that is fully converted, 2 molecules of ethanol and 2 molecules of carbon dioxide are produced. The molecular masses of glucose, ethanol, and carbon dioxide are 180 g/mol, 46 g/mol, and 44 g/mol, respectively.
Therefore, if 200.0 g of glucose is fully converted, the total mass of ethanol and carbon dioxide produced would be:
(200.0 g glucose) * (2 mol ethanol / 1 mol glucose) * (46.0 g/mol ethanol) + (200.0 g glucose) * (2 mol carbon dioxide / 1 mol glucose) * (44.0 g/mol carbon dioxide)
= 23,200 g of ethanol + 17,600 g of carbon dioxide
= 40,800 g or 40.8 kg of total mass
In an open container, the mass of the container and contents after fermentation would be the same as the mass before fermentation. This is because the carbon dioxide produced during fermentation escapes into the environment, so there is no change in mass.
If 97.7 g of carbon dioxide is produced, the mass of ethanol produced can be calculated as:
(97.7 g carbon dioxide) * (1 mol ethanol / 2 mol carbon dioxide) * (46.0 g/mol ethanol)
= 22.5 g of ethanol