mass fractions of potassium hexacyanocobaltate(III)

potassium hexacyanocobaltate(III) | elemental composition

Find the elemental composition for potassium hexacyanocobaltate(III) 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: K_3Co(CN)_6 Use the chemical formula, K_3Co(CN)_6, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms C (carbon) | 5 Co (cobalt) | 1 K (potassium) | 3 N (nitrogen) | 6 N_atoms = 5 + 1 + 3 + 6 = 15 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 C (carbon) | 5 | 5/15 Co (cobalt) | 1 | 1/15 K (potassium) | 3 | 3/15 N (nitrogen) | 6 | 6/15 Check: 5/15 + 1/15 + 3/15 + 6/15 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 5 | 5/15 × 100% = 33.3% Co (cobalt) | 1 | 1/15 × 100% = 6.67% K (potassium) | 3 | 3/15 × 100% = 20.0% N (nitrogen) | 6 | 6/15 × 100% = 40.0% 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 C (carbon) | 5 | 33.3% | 12.011 Co (cobalt) | 1 | 6.67% | 58.933194 K (potassium) | 3 | 20.0% | 39.0983 N (nitrogen) | 6 | 40.0% | 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 C (carbon) | 5 | 33.3% | 12.011 | 5 × 12.011 = 60.055 Co (cobalt) | 1 | 6.67% | 58.933194 | 1 × 58.933194 = 58.933194 K (potassium) | 3 | 20.0% | 39.0983 | 3 × 39.0983 = 117.2949 N (nitrogen) | 6 | 40.0% | 14.007 | 6 × 14.007 = 84.042 m = 60.055 u + 58.933194 u + 117.2949 u + 84.042 u = 320.325094 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 C (carbon) | 5 | 33.3% | 60.055/320.325094 Co (cobalt) | 1 | 6.67% | 58.933194/320.325094 K (potassium) | 3 | 20.0% | 117.2949/320.325094 N (nitrogen) | 6 | 40.0% | 84.042/320.325094 Check: 60.055/320.325094 + 58.933194/320.325094 + 117.2949/320.325094 + 84.042/320.325094 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 5 | 33.3% | 60.055/320.325094 × 100% = 18.75% Co (cobalt) | 1 | 6.67% | 58.933194/320.325094 × 100% = 18.40% K (potassium) | 3 | 20.0% | 117.2949/320.325094 × 100% = 36.62% N (nitrogen) | 6 | 40.0% | 84.042/320.325094 × 100% = 26.24%

Mass fraction pie chart