How much does one mole of U.S. Quarters weigh?

Answer 1

We usually are concerned with the gram-mole when we speak of moles. A gram-mole is Avagadro's number of molecules. Avagadro's number is chosen such that the grams in one mole of a substance corresponds to the molecular weight of that substance. Hydrogen gas has an atomic weight of about 2 and a gram-mole of hydrogen gas weighs about 2 grams. Iron has an atomic weight of about 55.845, so a gram-mole of iron weighs about 55.845 grams. If instead of molecules we used the quarter as the unit (defining a "Quarter-mole" as 6.022×1023 quarters, then we could calculate the weight of this new kind of mole. According to the US Mint, one quarter weighs about 5.670 g, so one "Quarter-mole" of quarters would weigh about 5.67x6.022x1023 grams or about 3.41x1024 grams or about 3.41x1021 kg or about 3.41x1018 metric tons. By comparison, the mass of the Earth is about 5.97x1024 kg or 5.97x1021 metric tons (about the same as 1748 "Quarter-moles").

Another way to look at it is to find the total gram-moles of material in one quarter. A quarter weighs 5.67 g and is 8.83% Nickel and 91.17% Copper. Nickel has an atomic weight of 58.6934 while Copper has an atomic weight of 63.546. This means a single quarter has 0.00853 gram-moles of Nickel and 0.081348 gram-moles of Copper. Together, a quarter has 0.089878 moles of metal. It would therefore take 1/0.089878 or about 11.12 quarters to contain one mole of metal. This many quarters would weigh about 63.09 grams.