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A US Gallon of ethanol contains 3.785 liters and each liter weighs 0.789 kg. A Mole weight of ethanol is 46.06 g.

So...

Moles/gallon ethanol= (3.785 L)x(789g/L)/(46.06g/mole) = 63.84

Assuming you need to show how the units cancel out I've indicated what they are.

The answer is not quite correct in the real world as ethanol is produced at about 96% purity if not denatured. The 4% or so is water.

Added:

The last addition is correct and can be easily re-calculated knowing two things:

1. the density of 96% ethanol + 4% water is a bit higher: 799 g/L

2. 96% means 96% by volume (0.960 L per 1.00 Litre)

Newly calculated:

(0.960L/1.00L)(3.785 L)x(799g/L)/(46.06g/mole) = 63.03 mol ethanol in a gallon 96% alcohol

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