The volume of carbon dioxide produced when 375 mL of a 75.0% ethanol solution by mass with a density of 1.22 g/mL reacts with excess oxygen is 667.52 L.
We are told in the question that the solution contains 75.0% ethanol solution by mass.
Hence;
Density of solution = mass/volume
mass = Density × volume = 1.22 g/mL × 375 mL = 457.5 g
Mass% = mass of solute/ mass of solution × 100
Mass of solute = x
Mass of solution = 457.5 g
Mass percent = 75.0%
Substituting values;
75 = x/457.5 + x × 100
75/100 = x/457.5 + x
0.75(457.5 + x) = x
343.125 + 0.75x = x
343.125 = x - 0.75x
x = 343.125/0.25
x = 1372.5 g
The equation of the reaction is;
C2H6O(l) + 3O2(g) → 2CO2(g) + 3H2O(l)
Number of moles of ethanol = 1372.5 g/46 g/mol = 29.8 moles
From the reaction equation;
2 moles of ethanol produces 2 moles of carbon dioxide
29.8 moles of ethanol also produces 29.8 moles of carbon dioxide
If 1 mole of carbon dioxide occupies 22.4 L
29.8 moles of carbon dioxide occupies 29.8 moles × 22.4 L/ 1 mole
= 667.52 L
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