mass fractions of terbium(III) oxide

terbium(III) oxide | elemental composition

Find the elemental composition for terbium(III) oxide 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: Tb_2O_3 Use the chemical formula, Tb_2O_3, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms O (oxygen) | 3 Tb (terbium) | 2 N_atoms = 3 + 2 = 5 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 O (oxygen) | 3 | 3/5 Tb (terbium) | 2 | 2/5 Check: 3/5 + 2/5 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent O (oxygen) | 3 | 3/5 × 100% = 60.0% Tb (terbium) | 2 | 2/5 × 100% = 40.0% 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 O (oxygen) | 3 | 60.0% | 15.999 Tb (terbium) | 2 | 40.0% | 158.92535 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 O (oxygen) | 3 | 60.0% | 15.999 | 3 × 15.999 = 47.997 Tb (terbium) | 2 | 40.0% | 158.92535 | 2 × 158.92535 = 317.85070 m = 47.997 u + 317.85070 u = 365.84770 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 O (oxygen) | 3 | 60.0% | 47.997/365.84770 Tb (terbium) | 2 | 40.0% | 317.85070/365.84770 Check: 47.997/365.84770 + 317.85070/365.84770 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent O (oxygen) | 3 | 60.0% | 47.997/365.84770 × 100% = 13.12% Tb (terbium) | 2 | 40.0% | 317.85070/365.84770 × 100% = 86.88%

Mass fraction pie chart