mass fractions of zirconium(IV) carbonate hydroxide oxide

zirconium(IV) carbonate hydroxide oxide | elemental composition

Find the elemental composition for zirconium(IV) carbonate hydroxide 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: Zr(OH)_2CO_3·ZrO_2 Use the chemical formula, Zr(OH)_2CO_3·ZrO_2, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms C (carbon) | 1 H (hydrogen) | 4 O (oxygen) | 7 Zr (zirconium) | 2 N_atoms = 1 + 4 + 7 + 2 = 14 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 C (carbon) | 1 | 1/14 H (hydrogen) | 4 | 4/14 O (oxygen) | 7 | 7/14 Zr (zirconium) | 2 | 2/14 Check: 1/14 + 4/14 + 7/14 + 2/14 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 1 | 1/14 × 100% = 7.14% H (hydrogen) | 4 | 4/14 × 100% = 28.6% O (oxygen) | 7 | 7/14 × 100% = 50.0% Zr (zirconium) | 2 | 2/14 × 100% = 14.3% 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 C (carbon) | 1 | 7.14% | 12.011 H (hydrogen) | 4 | 28.6% | 1.008 O (oxygen) | 7 | 50.0% | 15.999 Zr (zirconium) | 2 | 14.3% | 91.224 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 C (carbon) | 1 | 7.14% | 12.011 | 1 × 12.011 = 12.011 H (hydrogen) | 4 | 28.6% | 1.008 | 4 × 1.008 = 4.032 O (oxygen) | 7 | 50.0% | 15.999 | 7 × 15.999 = 111.993 Zr (zirconium) | 2 | 14.3% | 91.224 | 2 × 91.224 = 182.448 m = 12.011 u + 4.032 u + 111.993 u + 182.448 u = 310.484 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 C (carbon) | 1 | 7.14% | 12.011/310.484 H (hydrogen) | 4 | 28.6% | 4.032/310.484 O (oxygen) | 7 | 50.0% | 111.993/310.484 Zr (zirconium) | 2 | 14.3% | 182.448/310.484 Check: 12.011/310.484 + 4.032/310.484 + 111.993/310.484 + 182.448/310.484 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 1 | 7.14% | 12.011/310.484 × 100% = 3.868% H (hydrogen) | 4 | 28.6% | 4.032/310.484 × 100% = 1.299% O (oxygen) | 7 | 50.0% | 111.993/310.484 × 100% = 36.07% Zr (zirconium) | 2 | 14.3% | 182.448/310.484 × 100% = 58.76%

Mass fraction pie chart