element mass fraction of cobalt(II) cyanide

cobalt(II) cyanide | elemental composition

Find the elemental composition for cobalt(II) 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: C_2CoN_2 Use the chemical formula, C_2CoN_2, 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) | 2 Co (cobalt) | 1 N (nitrogen) | 2 N_atoms = 2 + 1 + 2 = 5 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) | 2 | 2/5 Co (cobalt) | 1 | 1/5 N (nitrogen) | 2 | 2/5 Check: 2/5 + 1/5 + 2/5 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 2 | 2/5 × 100% = 40.0% Co (cobalt) | 1 | 1/5 × 100% = 20.0% N (nitrogen) | 2 | 2/5 × 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) | 2 | 40.0% | 12.011 Co (cobalt) | 1 | 20.0% | 58.933194 N (nitrogen) | 2 | 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) | 2 | 40.0% | 12.011 | 2 × 12.011 = 24.022 Co (cobalt) | 1 | 20.0% | 58.933194 | 1 × 58.933194 = 58.933194 N (nitrogen) | 2 | 40.0% | 14.007 | 2 × 14.007 = 28.014 m = 24.022 u + 58.933194 u + 28.014 u = 110.969194 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) | 2 | 40.0% | 24.022/110.969194 Co (cobalt) | 1 | 20.0% | 58.933194/110.969194 N (nitrogen) | 2 | 40.0% | 28.014/110.969194 Check: 24.022/110.969194 + 58.933194/110.969194 + 28.014/110.969194 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 2 | 40.0% | 24.022/110.969194 × 100% = 21.65% Co (cobalt) | 1 | 20.0% | 58.933194/110.969194 × 100% = 53.11% N (nitrogen) | 2 | 40.0% | 28.014/110.969194 × 100% = 25.24%

Mass fraction pie chart