How many molecules of liquid ethanol are in 1.00 ml of ethanol, given its density is 0.789 g/ml?

Mass = volume * density = 1.00 mL * 0.789 g/mL = 0.789 g
The relative molecular mass of ethanol can be calculated by adding the relative atomic masses of all the atoms within its structure (C2H5OH):
(12.011 g/mol *2) + (15.999 g/mol * 1) + (1.0079 g/mol * 6) = 46.068 g/mol
       2 Carbon                1 Oxygen               6 Hydrogen
This can be used to find the number of moles of ethanol:
moles = mass / rmm = 0.789 g / 46.068 g/mol = 0.0171 mol (3 sig. fig.)
Using Avogadro's constant, the number of molecules within 1 mole of substance, the number of molecules within 1 mL of ethanol can be found:
no. molecules = moles * Avogadro constant 
                       = 0.0171 mol * (6.022*10^23 1/mol)
                       = 1.03*10^22 molecules