mass fractions of titanium(IV) nitrate

titanium(IV) nitrate | elemental composition

Find the elemental composition for titanium(IV) nitrate 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: Ti(NO_3)_4 Use the chemical formula, Ti(NO_3)_4, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms N (nitrogen) | 4 O (oxygen) | 12 Ti (titanium) | 1 N_atoms = 4 + 12 + 1 = 17 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 N (nitrogen) | 4 | 4/17 O (oxygen) | 12 | 12/17 Ti (titanium) | 1 | 1/17 Check: 4/17 + 12/17 + 1/17 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent N (nitrogen) | 4 | 4/17 × 100% = 23.5% O (oxygen) | 12 | 12/17 × 100% = 70.6% Ti (titanium) | 1 | 1/17 × 100% = 5.88% 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 N (nitrogen) | 4 | 23.5% | 14.007 O (oxygen) | 12 | 70.6% | 15.999 Ti (titanium) | 1 | 5.88% | 47.867 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 N (nitrogen) | 4 | 23.5% | 14.007 | 4 × 14.007 = 56.028 O (oxygen) | 12 | 70.6% | 15.999 | 12 × 15.999 = 191.988 Ti (titanium) | 1 | 5.88% | 47.867 | 1 × 47.867 = 47.867 m = 56.028 u + 191.988 u + 47.867 u = 295.883 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 N (nitrogen) | 4 | 23.5% | 56.028/295.883 O (oxygen) | 12 | 70.6% | 191.988/295.883 Ti (titanium) | 1 | 5.88% | 47.867/295.883 Check: 56.028/295.883 + 191.988/295.883 + 47.867/295.883 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent N (nitrogen) | 4 | 23.5% | 56.028/295.883 × 100% = 18.94% O (oxygen) | 12 | 70.6% | 191.988/295.883 × 100% = 64.89% Ti (titanium) | 1 | 5.88% | 47.867/295.883 × 100% = 16.18%

Mass fraction pie chart