mass fractions of cobalt arsenate

cobalt arsenate | elemental composition

Find the elemental composition for cobalt arsenate 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: Co_3(AsO_4)_2 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 As (arsenic) | 2 Co (cobalt) | 3 O (oxygen) | 8 N_atoms = 2 + 3 + 8 = 13 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 As (arsenic) | 2 | 2/13 Co (cobalt) | 3 | 3/13 O (oxygen) | 8 | 8/13 Check: 2/13 + 3/13 + 8/13 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent As (arsenic) | 2 | 2/13 × 100% = 15.4% Co (cobalt) | 3 | 3/13 × 100% = 23.1% O (oxygen) | 8 | 8/13 × 100% = 61.5% 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 As (arsenic) | 2 | 15.4% | 74.921595 Co (cobalt) | 3 | 23.1% | 58.933194 O (oxygen) | 8 | 61.5% | 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 As (arsenic) | 2 | 15.4% | 74.921595 | 2 × 74.921595 = 149.843190 Co (cobalt) | 3 | 23.1% | 58.933194 | 3 × 58.933194 = 176.799582 O (oxygen) | 8 | 61.5% | 15.999 | 8 × 15.999 = 127.992 m = 149.843190 u + 176.799582 u + 127.992 u = 454.634772 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 As (arsenic) | 2 | 15.4% | 149.843190/454.634772 Co (cobalt) | 3 | 23.1% | 176.799582/454.634772 O (oxygen) | 8 | 61.5% | 127.992/454.634772 Check: 149.843190/454.634772 + 176.799582/454.634772 + 127.992/454.634772 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent As (arsenic) | 2 | 15.4% | 149.843190/454.634772 × 100% = 32.96% Co (cobalt) | 3 | 23.1% | 176.799582/454.634772 × 100% = 38.89% O (oxygen) | 8 | 61.5% | 127.992/454.634772 × 100% = 28.15%

Mass fraction pie chart