element mass fraction of bismuth(III) nitrate pentahydrate

bismuth(III) nitrate pentahydrate | elemental composition

Find the elemental composition for bismuth(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: Bi(NO_3)_3·5H_2O 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 Bi (bismuth) | 1 H (hydrogen) | 10 N (nitrogen) | 3 O (oxygen) | 14 N_atoms = 1 + 10 + 3 + 14 = 28 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 Bi (bismuth) | 1 | 1/28 H (hydrogen) | 10 | 10/28 N (nitrogen) | 3 | 3/28 O (oxygen) | 14 | 14/28 Check: 1/28 + 10/28 + 3/28 + 14/28 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Bi (bismuth) | 1 | 1/28 × 100% = 3.57% H (hydrogen) | 10 | 10/28 × 100% = 35.7% N (nitrogen) | 3 | 3/28 × 100% = 10.7% O (oxygen) | 14 | 14/28 × 100% = 50.0% 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 Bi (bismuth) | 1 | 3.57% | 208.98040 H (hydrogen) | 10 | 35.7% | 1.008 N (nitrogen) | 3 | 10.7% | 14.007 O (oxygen) | 14 | 50.0% | 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 Bi (bismuth) | 1 | 3.57% | 208.98040 | 1 × 208.98040 = 208.98040 H (hydrogen) | 10 | 35.7% | 1.008 | 10 × 1.008 = 10.080 N (nitrogen) | 3 | 10.7% | 14.007 | 3 × 14.007 = 42.021 O (oxygen) | 14 | 50.0% | 15.999 | 14 × 15.999 = 223.986 m = 208.98040 u + 10.080 u + 42.021 u + 223.986 u = 485.06740 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 Bi (bismuth) | 1 | 3.57% | 208.98040/485.06740 H (hydrogen) | 10 | 35.7% | 10.080/485.06740 N (nitrogen) | 3 | 10.7% | 42.021/485.06740 O (oxygen) | 14 | 50.0% | 223.986/485.06740 Check: 208.98040/485.06740 + 10.080/485.06740 + 42.021/485.06740 + 223.986/485.06740 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Bi (bismuth) | 1 | 3.57% | 208.98040/485.06740 × 100% = 43.08% H (hydrogen) | 10 | 35.7% | 10.080/485.06740 × 100% = 2.078% N (nitrogen) | 3 | 10.7% | 42.021/485.06740 × 100% = 8.663% O (oxygen) | 14 | 50.0% | 223.986/485.06740 × 100% = 46.18%

Mass fraction pie chart