You'd have to do it by weight, because the distance between water molecules is going to vary depending on the heat of the water. All chemistry is done using weights rather than measurements like "cups".

A cup is 8 ounces. A gallon of water weighs 8 pounds. You can put "gallons to ounces" in the google search bar and get the converson, and that should get you started.
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(a) One cup of water weighs 0.521 pounds or 236.32 grams
(b) Grams in one mole of water1 = 18
(c) Moles in one cup = (a) / (b) = 13.13
(d) Avogadro number2 = 6.02 x 10^23
(e) Molecules in one cup = (c) x (d) = 13.13 x 6.02 x 10^23 = 7.9 x 10^24

so the answer is 7.9 x 10^24
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If you mean an actual cup of water (as in, 8 fluid ounces) the answer would be roughly 7.5 * 10^24 molecules.

If you meant an arbitrary physical cup: take the amount of water it holds, then multiply the amount of water in ounces by 28 (number of grams in an ounce of water) then multiply that by 6.02 * 10^23 (number of molecules in a mole), and divide all that by 18 (number of grams of water per mole).
Source(s):
http://www.newton.dep.anl.gov/askasci/chem03/chem03149.htm

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Amusing your cup holds exactly 1 cup, convert 1 cup to mL, (1 US cup = 236.588237 mL) 1 mL of water weighs 1 g at 4 C, (if you want a more accurate number you'll have to adjust for the density changes with temperature.) A Water molecule is 18.01528 g per 1 mole, so 236.58 / 18.01528 = 13.1321856 moles of water. There are 6.02 X 10^23 molecules in one mole, which 7.9055242 × 10^24 molecules.

Or you can google "molecules in a cup of water."

Or better yet, you could learn to do your chemistry homework for yourself and receive the benefits of an education.
Source(s):
google.com

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It's is easiest when you use metrics system, so measure and calculate everything is liters, meters, and grams.

1) You need to know how much volume of water is in a cup.

2) Density of water is 1 kg/L (at 4 deg C, or 40F). Use that to figure out how many kilograms of water you have. Then, convert that to grams!

You should get about 250 grams of water in a cup.

3) Find molar mass of water. Molar mass is a mass of one mole of molecules. Mole is like a dozen. It's not 12, but about 6.02x10^23 (6 followed by 23 zeros).

Molar mass of water is 18.0 g/mol. You can get that from periodic table: 16.0 for an Oxigen molecule, 1.0 for each Hydrogen.

4) Now, the hard part ;-) First, calculate how many moles of water molecules you have. Second, multiply that by 6.02x10^23 to get how many molecules you have.


If you have 250 g of water, then:
(250 g) / (18.0 g/mol) = 13.9 mol
13.9 mol = 13.9 mol * (6.02x10^23 / 1 mol) = 83.7x10^23 = 8.37x10^24

That about 8 followed by 24 zeros!
Source(s):
http://en.wikipedia.org/wiki/Hydrogen
http://en.wikipedia.org/wiki/Mole_(chemistry)
http://en.wikipedia.org/wiki/Oxygen
http://en.wikipedia.org/wiki/Water_(molecule)

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