mass fractions of calcium permanganate

calcium permanganate | elemental composition

Find the elemental composition for calcium permanganate 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: CaMn_2O_8 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 Ca (calcium) | 1 Mn (manganese) | 2 O (oxygen) | 8 N_atoms = 1 + 2 + 8 = 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 Ca (calcium) | 1 | 1/11 Mn (manganese) | 2 | 2/11 O (oxygen) | 8 | 8/11 Check: 1/11 + 2/11 + 8/11 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Ca (calcium) | 1 | 1/11 × 100% = 9.09% Mn (manganese) | 2 | 2/11 × 100% = 18.2% O (oxygen) | 8 | 8/11 × 100% = 72.7% 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 Ca (calcium) | 1 | 9.09% | 40.078 Mn (manganese) | 2 | 18.2% | 54.938044 O (oxygen) | 8 | 72.7% | 15.999 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 Ca (calcium) | 1 | 9.09% | 40.078 | 1 × 40.078 = 40.078 Mn (manganese) | 2 | 18.2% | 54.938044 | 2 × 54.938044 = 109.876088 O (oxygen) | 8 | 72.7% | 15.999 | 8 × 15.999 = 127.992 m = 40.078 u + 109.876088 u + 127.992 u = 277.946088 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 Ca (calcium) | 1 | 9.09% | 40.078/277.946088 Mn (manganese) | 2 | 18.2% | 109.876088/277.946088 O (oxygen) | 8 | 72.7% | 127.992/277.946088 Check: 40.078/277.946088 + 109.876088/277.946088 + 127.992/277.946088 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Ca (calcium) | 1 | 9.09% | 40.078/277.946088 × 100% = 14.42% Mn (manganese) | 2 | 18.2% | 109.876088/277.946088 × 100% = 39.53% O (oxygen) | 8 | 72.7% | 127.992/277.946088 × 100% = 46.05%

Mass fraction pie chart