Equation of Fermentation of Glucose:
C6H1206 --> C2H505 + CO2
When we balance this equation we get 1 mole of glucose producing 2 moles of ethanol and 2 moles of carbon dioxide:
C6H12O6 --> 2 C2H5OH + 2 CO2
We know that 6.5g of Glucose was used, so to convert this to moles we divide the mass by it's molar mass.
[C6H12O6] = 6.5/180.156 = 0.036moles
We know from the equation that 1 mole of glucose produces 2 moles of Carbon dioxide, therefore 0.036 moles of glucose produces 0.072 moles of carbon dioxide.
Now we know that 0.072 moles of carbon dioxide is produced, we find the mass by using the equation, moles=mass/molar mass
0.072 = mass/44.01
mass = 0.072*44.01 = 3.16872grams