mass fractions of cobalt aluminum oxide

cobalt aluminum oxide | elemental composition

Find the elemental composition for cobalt aluminum oxide in terms of the atom and mass percents: atom percent = N_i/N_atoms × 100% mass percent = (N_im_i)/m × 100% Plan: • Write the chemical formula and gather atomic masses from the periodic table. • Determine values for N_i, m_i, N_atoms and m using these items. • Finally, compute the percents and check the results. Write the chemical formula: CoAl_2O_4 Use the chemical formula to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms, per molecule: | number of atoms Al (aluminum) | 2 Co (cobalt) | 1 O (oxygen) | 4 N_atoms = 2 + 1 + 4 = 7 Divide each N_i by N_atoms to calculate atom fractions. Then use the property that atom fractions must sum to one to check the work: | number of atoms | atom fraction Al (aluminum) | 2 | 2/7 Co (cobalt) | 1 | 1/7 O (oxygen) | 4 | 4/7 Check: 2/7 + 1/7 + 4/7 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Al (aluminum) | 2 | 2/7 × 100% = 28.6% Co (cobalt) | 1 | 1/7 × 100% = 14.3% O (oxygen) | 4 | 4/7 × 100% = 57.1% Look up the atomic mass, m_i, in unified atomic mass units, u, for each element in the periodic table: | number of atoms | atom percent | atomic mass/u Al (aluminum) | 2 | 28.6% | 26.9815385 Co (cobalt) | 1 | 14.3% | 58.933194 O (oxygen) | 4 | 57.1% | 15.999 Multiply N_i by m_i to compute the mass for each element. Then sum those values to compute the molecular mass, m: | number of atoms | atom percent | atomic mass/u | mass/u Al (aluminum) | 2 | 28.6% | 26.9815385 | 2 × 26.9815385 = 53.9630770 Co (cobalt) | 1 | 14.3% | 58.933194 | 1 × 58.933194 = 58.933194 O (oxygen) | 4 | 57.1% | 15.999 | 4 × 15.999 = 63.996 m = 53.9630770 u + 58.933194 u + 63.996 u = 176.8922710 u Divide the mass for each element by m to calculate mass fractions. Then use the property that mass fractions must sum to one to check the work: | number of atoms | atom percent | mass fraction Al (aluminum) | 2 | 28.6% | 53.9630770/176.8922710 Co (cobalt) | 1 | 14.3% | 58.933194/176.8922710 O (oxygen) | 4 | 57.1% | 63.996/176.8922710 Check: 53.9630770/176.8922710 + 58.933194/176.8922710 + 63.996/176.8922710 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Al (aluminum) | 2 | 28.6% | 53.9630770/176.8922710 × 100% = 30.51% Co (cobalt) | 1 | 14.3% | 58.933194/176.8922710 × 100% = 33.32% O (oxygen) | 4 | 57.1% | 63.996/176.8922710 × 100% = 36.18%

Mass fraction pie chart