mass fractions of diammonium sulfide

diammonium sulfide | elemental composition

Find the elemental composition for diammonium sulfide 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 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 S (sulfur) | 1 N_atoms = 8 + 2 + 1 = 11 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 | 8/11 N (nitrogen) | 2 | 2/11 S (sulfur) | 1 | 1/11 Check: 8/11 + 2/11 + 1/11 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 8 | 8/11 × 100% = 72.7% N (nitrogen) | 2 | 2/11 × 100% = 18.2% S (sulfur) | 1 | 1/11 × 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 H (hydrogen) | 8 | 72.7% | 1.008 N (nitrogen) | 2 | 18.2% | 14.007 S (sulfur) | 1 | 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 H (hydrogen) | 8 | 72.7% | 1.008 | 8 × 1.008 = 8.064 N (nitrogen) | 2 | 18.2% | 14.007 | 2 × 14.007 = 28.014 S (sulfur) | 1 | 9.09% | 32.06 | 1 × 32.06 = 32.06 m = 8.064 u + 28.014 u + 32.06 u = 68.138 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 | 72.7% | 8.064/68.138 N (nitrogen) | 2 | 18.2% | 28.014/68.138 S (sulfur) | 1 | 9.09% | 32.06/68.138 Check: 8.064/68.138 + 28.014/68.138 + 32.06/68.138 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 8 | 72.7% | 8.064/68.138 × 100% = 11.83% N (nitrogen) | 2 | 18.2% | 28.014/68.138 × 100% = 41.11% S (sulfur) | 1 | 9.09% | 32.06/68.138 × 100% = 47.05%

Mass fraction pie chart