The difference between mass and weight is pretty straightforward so then how can we WEIGH a substance then ask how many Daltons (atomic MASS units) are in that substance without a conversion in there for gravity? Or vice versa. For example:
Question: How many moles of potassium are in 156.4 grams?
Answer: Atomic mass of potassium, K = 39.1 Amount of potassium is 156.4g, sample = 156.4/39.1 = 4.00mol. There are 4 moles of potassium in 156.4 grams of potassium.
Nowhere is there any sort of conversion for earth's gravity even though we are weighing out a substance that is obviously high enough to deserve one. I am assuming the amu of all elements is the same in the universe.