element mass fraction of cobalt(III) nitrate

cobalt(III) nitrate | elemental composition

Find the elemental composition for cobalt(III) nitrate 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(NO_3)_3 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 Co (cobalt) | 1 N (nitrogen) | 3 O (oxygen) | 9 N_atoms = 1 + 3 + 9 = 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 Co (cobalt) | 1 | 1/13 N (nitrogen) | 3 | 3/13 O (oxygen) | 9 | 9/13 Check: 1/13 + 3/13 + 9/13 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Co (cobalt) | 1 | 1/13 × 100% = 7.69% N (nitrogen) | 3 | 3/13 × 100% = 23.1% O (oxygen) | 9 | 9/13 × 100% = 69.2% 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 Co (cobalt) | 1 | 7.69% | 58.933194 N (nitrogen) | 3 | 23.1% | 14.007 O (oxygen) | 9 | 69.2% | 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 Co (cobalt) | 1 | 7.69% | 58.933194 | 1 × 58.933194 = 58.933194 N (nitrogen) | 3 | 23.1% | 14.007 | 3 × 14.007 = 42.021 O (oxygen) | 9 | 69.2% | 15.999 | 9 × 15.999 = 143.991 m = 58.933194 u + 42.021 u + 143.991 u = 244.945194 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 Co (cobalt) | 1 | 7.69% | 58.933194/244.945194 N (nitrogen) | 3 | 23.1% | 42.021/244.945194 O (oxygen) | 9 | 69.2% | 143.991/244.945194 Check: 58.933194/244.945194 + 42.021/244.945194 + 143.991/244.945194 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Co (cobalt) | 1 | 7.69% | 58.933194/244.945194 × 100% = 24.06% N (nitrogen) | 3 | 23.1% | 42.021/244.945194 × 100% = 17.16% O (oxygen) | 9 | 69.2% | 143.991/244.945194 × 100% = 58.78%

Mass fraction pie chart