mass fractions of holmium(III) nitrate pentahydrate

holmium(III) nitrate pentahydrate | elemental composition

Find the elemental composition for holmium(III) nitrate pentahydrate 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: Ho(NO_3)_3·5H_2O Use the chemical formula, Ho(NO_3)_3·5H_2O, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms H (hydrogen) | 3 Ho (holmium) | 1 N (nitrogen) | 1 O (oxygen) | 4 N_atoms = 3 + 1 + 1 + 4 = 9 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 H (hydrogen) | 3 | 3/9 Ho (holmium) | 1 | 1/9 N (nitrogen) | 1 | 1/9 O (oxygen) | 4 | 4/9 Check: 3/9 + 1/9 + 1/9 + 4/9 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 3 | 3/9 × 100% = 33.3% Ho (holmium) | 1 | 1/9 × 100% = 11.1% N (nitrogen) | 1 | 1/9 × 100% = 11.1% O (oxygen) | 4 | 4/9 × 100% = 44.4% 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 H (hydrogen) | 3 | 33.3% | 1.008 Ho (holmium) | 1 | 11.1% | 164.93033 N (nitrogen) | 1 | 11.1% | 14.007 O (oxygen) | 4 | 44.4% | 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 H (hydrogen) | 3 | 33.3% | 1.008 | 3 × 1.008 = 3.024 Ho (holmium) | 1 | 11.1% | 164.93033 | 1 × 164.93033 = 164.93033 N (nitrogen) | 1 | 11.1% | 14.007 | 1 × 14.007 = 14.007 O (oxygen) | 4 | 44.4% | 15.999 | 4 × 15.999 = 63.996 m = 3.024 u + 164.93033 u + 14.007 u + 63.996 u = 245.95733 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 H (hydrogen) | 3 | 33.3% | 3.024/245.95733 Ho (holmium) | 1 | 11.1% | 164.93033/245.95733 N (nitrogen) | 1 | 11.1% | 14.007/245.95733 O (oxygen) | 4 | 44.4% | 63.996/245.95733 Check: 3.024/245.95733 + 164.93033/245.95733 + 14.007/245.95733 + 63.996/245.95733 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 3 | 33.3% | 3.024/245.95733 × 100% = 1.229% Ho (holmium) | 1 | 11.1% | 164.93033/245.95733 × 100% = 67.06% N (nitrogen) | 1 | 11.1% | 14.007/245.95733 × 100% = 5.695% O (oxygen) | 4 | 44.4% | 63.996/245.95733 × 100% = 26.02%

Mass fraction pie chart