Chapter 14 The Ideal Gas Law and Kinetic Theory 14 1 Molecular Mass the Mole and Avogadro s Number To facilitate comparison of the mass of one atom with another a mass scale know as the atomic mass scale has been established The unit is called the atomic mass unit symbol u The reference element is chosen to be the most abundant isotope of carbon which is called carbon 12 1 u 1 6605 10 27 kg The atomic mass is given in atomic mass units For example a Li atom has a mass of 6 941u 14 1 Molecular Mass the Mole and Avogadro s Number One mole of a substance contains as many particles as there are atoms in 12 grams of the isotope cabron 12 The number of atoms per mole is known as Avogadro s number NA N A 6 022 10 23 mol 1 N n NA number of moles number of atoms 14 1 Molecular Mass the Mole and Avogadro s Number mparticle N m n mparticle N A Mass per mole The mass per mole in g mol of a substance has the same numerical value as the atomic or molecular mass of the substance in atomic mass units For example Hydrogen has an atomic mass of 1 00794 g mol while the mass of a single hydrogen atom is 1 00794 u 14 1 Molecular Mass the Mole and Avogadro s Number Example 1 The Hope Diamond and the Rosser Reeves Ruby The Hope diamond 44 5 carats is almost pure carbon The Rosser Reeves ruby 138 carats is primarily aluminum oxide Al2O3 One carat is equivalent to a mass of 0 200 g Determine a the number of carbon atoms in the Hope diamond and b the number of Al 2O3 molecules in the ruby 14 1 Molecular Mass the Mole and Avogadro s Number a n 44 5 carats 0 200 g 1 carat 0 741 mol m Mass per mole 12 011 g mol N nN A 0 741 mol 6 022 1023 mol 1 4 46 1023 atoms b m 138 carats 0 200 g 1 carat n 0 271 mol Mass per mole 101 96 g mol 2 26 98 3 15 99 N nN A 0 271 mol 6 022 1023 mol 1 1 63 1023 atoms