mass fractions of ammonium persulfate

ammonium persulfate | elemental composition

Find the elemental composition for ammonium persulfate 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: (NH_4)_2S_2O_8 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 H (hydrogen) | 8 N (nitrogen) | 2 O (oxygen) | 8 S (sulfur) | 2 N_atoms = 8 + 2 + 8 + 2 = 20 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 H (hydrogen) | 8 | 8/20 N (nitrogen) | 2 | 2/20 O (oxygen) | 8 | 8/20 S (sulfur) | 2 | 2/20 Check: 8/20 + 2/20 + 8/20 + 2/20 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 8 | 8/20 × 100% = 40.0% N (nitrogen) | 2 | 2/20 × 100% = 10.00% O (oxygen) | 8 | 8/20 × 100% = 40.0% S (sulfur) | 2 | 2/20 × 100% = 10.00% 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 H (hydrogen) | 8 | 40.0% | 1.008 N (nitrogen) | 2 | 10.00% | 14.007 O (oxygen) | 8 | 40.0% | 15.999 S (sulfur) | 2 | 10.00% | 32.06 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 H (hydrogen) | 8 | 40.0% | 1.008 | 8 × 1.008 = 8.064 N (nitrogen) | 2 | 10.00% | 14.007 | 2 × 14.007 = 28.014 O (oxygen) | 8 | 40.0% | 15.999 | 8 × 15.999 = 127.992 S (sulfur) | 2 | 10.00% | 32.06 | 2 × 32.06 = 64.12 m = 8.064 u + 28.014 u + 127.992 u + 64.12 u = 228.190 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 H (hydrogen) | 8 | 40.0% | 8.064/228.190 N (nitrogen) | 2 | 10.00% | 28.014/228.190 O (oxygen) | 8 | 40.0% | 127.992/228.190 S (sulfur) | 2 | 10.00% | 64.12/228.190 Check: 8.064/228.190 + 28.014/228.190 + 127.992/228.190 + 64.12/228.190 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 8 | 40.0% | 8.064/228.190 × 100% = 3.534% N (nitrogen) | 2 | 10.00% | 28.014/228.190 × 100% = 12.28% O (oxygen) | 8 | 40.0% | 127.992/228.190 × 100% = 56.09% S (sulfur) | 2 | 10.00% | 64.12/228.190 × 100% = 28.10%

Mass fraction pie chart