mass fractions of potassium hexacyanomanganate(III)

potassium hexacyanomanganate(III) | elemental composition

Find the elemental composition for potassium hexacyanomanganate(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_3Mn(CN)_6 Use the chemical formula, K_3Mn(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) | 6 K (potassium) | 3 Mn (manganese) | 1 N (nitrogen) | 6 N_atoms = 6 + 3 + 1 + 6 = 16 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) | 6 | 6/16 K (potassium) | 3 | 3/16 Mn (manganese) | 1 | 1/16 N (nitrogen) | 6 | 6/16 Check: 6/16 + 3/16 + 1/16 + 6/16 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 6 | 6/16 × 100% = 37.5% K (potassium) | 3 | 3/16 × 100% = 18.8% Mn (manganese) | 1 | 1/16 × 100% = 6.25% N (nitrogen) | 6 | 6/16 × 100% = 37.5% 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) | 6 | 37.5% | 12.011 K (potassium) | 3 | 18.8% | 39.0983 Mn (manganese) | 1 | 6.25% | 54.938044 N (nitrogen) | 6 | 37.5% | 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) | 6 | 37.5% | 12.011 | 6 × 12.011 = 72.066 K (potassium) | 3 | 18.8% | 39.0983 | 3 × 39.0983 = 117.2949 Mn (manganese) | 1 | 6.25% | 54.938044 | 1 × 54.938044 = 54.938044 N (nitrogen) | 6 | 37.5% | 14.007 | 6 × 14.007 = 84.042 m = 72.066 u + 117.2949 u + 54.938044 u + 84.042 u = 328.340944 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) | 6 | 37.5% | 72.066/328.340944 K (potassium) | 3 | 18.8% | 117.2949/328.340944 Mn (manganese) | 1 | 6.25% | 54.938044/328.340944 N (nitrogen) | 6 | 37.5% | 84.042/328.340944 Check: 72.066/328.340944 + 117.2949/328.340944 + 54.938044/328.340944 + 84.042/328.340944 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 6 | 37.5% | 72.066/328.340944 × 100% = 21.95% K (potassium) | 3 | 18.8% | 117.2949/328.340944 × 100% = 35.72% Mn (manganese) | 1 | 6.25% | 54.938044/328.340944 × 100% = 16.73% N (nitrogen) | 6 | 37.5% | 84.042/328.340944 × 100% = 25.60%

Mass fraction pie chart