mass fractions of zinc niobate

zinc niobate | elemental composition

Find the elemental composition for zinc niobate 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: Zn(NbO_3)_2 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 Nb (niobium) | 2 O (oxygen) | 6 Zn (zinc) | 1 N_atoms = 2 + 6 + 1 = 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 Nb (niobium) | 2 | 2/9 O (oxygen) | 6 | 6/9 Zn (zinc) | 1 | 1/9 Check: 2/9 + 6/9 + 1/9 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Nb (niobium) | 2 | 2/9 × 100% = 22.2% O (oxygen) | 6 | 6/9 × 100% = 66.7% Zn (zinc) | 1 | 1/9 × 100% = 11.1% 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 Nb (niobium) | 2 | 22.2% | 92.90637 O (oxygen) | 6 | 66.7% | 15.999 Zn (zinc) | 1 | 11.1% | 65.38 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 Nb (niobium) | 2 | 22.2% | 92.90637 | 2 × 92.90637 = 185.81274 O (oxygen) | 6 | 66.7% | 15.999 | 6 × 15.999 = 95.994 Zn (zinc) | 1 | 11.1% | 65.38 | 1 × 65.38 = 65.38 m = 185.81274 u + 95.994 u + 65.38 u = 347.18674 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 Nb (niobium) | 2 | 22.2% | 185.81274/347.18674 O (oxygen) | 6 | 66.7% | 95.994/347.18674 Zn (zinc) | 1 | 11.1% | 65.38/347.18674 Check: 185.81274/347.18674 + 95.994/347.18674 + 65.38/347.18674 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Nb (niobium) | 2 | 22.2% | 185.81274/347.18674 × 100% = 53.52% O (oxygen) | 6 | 66.7% | 95.994/347.18674 × 100% = 27.65% Zn (zinc) | 1 | 11.1% | 65.38/347.18674 × 100% = 18.83%

Mass fraction pie chart