mass fractions of silver cyanide

silver cyanide | elemental composition

Find the elemental composition for silver cyanide 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: AgCN Use the chemical formula, AgCN, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms Ag (silver) | 1 C (carbon) | 1 N (nitrogen) | 1 N_atoms = 1 + 1 + 1 = 3 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 Ag (silver) | 1 | 1/3 C (carbon) | 1 | 1/3 N (nitrogen) | 1 | 1/3 Check: 1/3 + 1/3 + 1/3 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Ag (silver) | 1 | 1/3 × 100% = 33.3% C (carbon) | 1 | 1/3 × 100% = 33.3% N (nitrogen) | 1 | 1/3 × 100% = 33.3% 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 Ag (silver) | 1 | 33.3% | 107.8682 C (carbon) | 1 | 33.3% | 12.011 N (nitrogen) | 1 | 33.3% | 14.007 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 Ag (silver) | 1 | 33.3% | 107.8682 | 1 × 107.8682 = 107.8682 C (carbon) | 1 | 33.3% | 12.011 | 1 × 12.011 = 12.011 N (nitrogen) | 1 | 33.3% | 14.007 | 1 × 14.007 = 14.007 m = 107.8682 u + 12.011 u + 14.007 u = 133.8862 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 Ag (silver) | 1 | 33.3% | 107.8682/133.8862 C (carbon) | 1 | 33.3% | 12.011/133.8862 N (nitrogen) | 1 | 33.3% | 14.007/133.8862 Check: 107.8682/133.8862 + 12.011/133.8862 + 14.007/133.8862 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Ag (silver) | 1 | 33.3% | 107.8682/133.8862 × 100% = 80.57% C (carbon) | 1 | 33.3% | 12.011/133.8862 × 100% = 8.971% N (nitrogen) | 1 | 33.3% | 14.007/133.8862 × 100% = 10.46%

Mass fraction pie chart