Avogadros Number To Calculate Mass of a Single Atom

Avogadro's Number To Calculate Mass of a Single Atom Avogadros number is one of the most important constants used in chemistry. It is the number of particles in a single mole of a material, based on the number of atoms in exactly 12 grams of the isotope carbon-12. Although this number is a constant, its experimentally determined, so we use an approximate value of 6.022 x 1023. So, you know how many atoms are in a mole. Heres how to use the information to determine the mass of a single atom. Avogadro's Number Example Problem: Mass of a Single Atom Question: Calculate the mass in grams of a single carbon (C) atom. Solution To calculate the mass of a single atom, first look up the atomic mass of carbon from the periodic table.This number, 12.01, is the mass in grams of one mole of carbon. One mole of carbon is 6.022 x 1023 atoms of carbon (Avogadros number). This relation is then used to convert a carbon atom to grams by the ratio: mass of 1 atom / 1 atom mass of a mole of atoms / 6.022 x 1023 atoms Plug in the atomic mass of carbon to solve for the mass of 1 atom: mass of 1 atom mass of a mole of atoms / 6.022 x 1023 mass of 1 C atom 12.01 g / 6.022 x 1023 C atomsmass of 1 C atom 1.994 x 10-23 g Answer The mass of a single carbon atom is 1.994 x 10-23 g. Applying the Formula to Solve for Other Atoms and Molecules Although the problem was worked using carbon (the element upon which Avogadros number is based), you can use the same method to solve for the mass of an atom or molecule. If youre finding the mass of an atom of a different element, just use that elements atomic mass. If you want to use the relation to solve for the mass of a single molecule, theres an extra step. You need to add up the masses of all of the atoms in that one molecule and use them instead. Lets say, for example, you want to know the mass of a single atom of water. From the formula (H2O), you know there are two hydrogen atoms and one oxygen atom. You use the periodic table to look up the mass of each atom (H is 1.01 and O is 16.00). Forming a water molecule gives you a mass of: 1.01 1.01 16.00 18.02 grams per mole of water and you solve with: mass of 1 molecule mass of one mole of molecules / 6.022 x 1023 mass of 1 water molecule 18.02 grams per mole / 6.022 x 1023 molecules per mole mass of 1 water molecule 2.992 x 10-23 grams