mass fractions of ammonium cerium(IV) sulfate hydrate

ammonium cerium(IV) sulfate hydrate | elemental composition

Find the elemental composition for ammonium cerium(IV) sulfate hydrate 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: Ce(NH_4)_4(SO_4)_4·xH_2O 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 Ce (cerium) | 1 H (hydrogen) | 18 N (nitrogen) | 4 O (oxygen) | 17 S (sulfur) | 4 N_atoms = 1 + 18 + 4 + 17 + 4 = 44 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 Ce (cerium) | 1 | 1/44 H (hydrogen) | 18 | 18/44 N (nitrogen) | 4 | 4/44 O (oxygen) | 17 | 17/44 S (sulfur) | 4 | 4/44 Check: 1/44 + 18/44 + 4/44 + 17/44 + 4/44 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Ce (cerium) | 1 | 1/44 × 100% = 2.27% H (hydrogen) | 18 | 18/44 × 100% = 40.9% N (nitrogen) | 4 | 4/44 × 100% = 9.09% O (oxygen) | 17 | 17/44 × 100% = 38.6% S (sulfur) | 4 | 4/44 × 100% = 9.09% 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 Ce (cerium) | 1 | 2.27% | 140.116 H (hydrogen) | 18 | 40.9% | 1.008 N (nitrogen) | 4 | 9.09% | 14.007 O (oxygen) | 17 | 38.6% | 15.999 S (sulfur) | 4 | 9.09% | 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 Ce (cerium) | 1 | 2.27% | 140.116 | 1 × 140.116 = 140.116 H (hydrogen) | 18 | 40.9% | 1.008 | 18 × 1.008 = 18.144 N (nitrogen) | 4 | 9.09% | 14.007 | 4 × 14.007 = 56.028 O (oxygen) | 17 | 38.6% | 15.999 | 17 × 15.999 = 271.983 S (sulfur) | 4 | 9.09% | 32.06 | 4 × 32.06 = 128.24 m = 140.116 u + 18.144 u + 56.028 u + 271.983 u + 128.24 u = 614.511 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 Ce (cerium) | 1 | 2.27% | 140.116/614.511 H (hydrogen) | 18 | 40.9% | 18.144/614.511 N (nitrogen) | 4 | 9.09% | 56.028/614.511 O (oxygen) | 17 | 38.6% | 271.983/614.511 S (sulfur) | 4 | 9.09% | 128.24/614.511 Check: 140.116/614.511 + 18.144/614.511 + 56.028/614.511 + 271.983/614.511 + 128.24/614.511 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Ce (cerium) | 1 | 2.27% | 140.116/614.511 × 100% = 22.80% H (hydrogen) | 18 | 40.9% | 18.144/614.511 × 100% = 2.953% N (nitrogen) | 4 | 9.09% | 56.028/614.511 × 100% = 9.117% O (oxygen) | 17 | 38.6% | 271.983/614.511 × 100% = 44.26% S (sulfur) | 4 | 9.09% | 128.24/614.511 × 100% = 20.87%

Mass fraction pie chart