mass fractions of copper(II) niobate

copper(II) niobate | elemental composition

Find the elemental composition for copper(II) 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: Cu(NbO_3)_2 Use the chemical formula, Cu(NbO_3)_2, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms Cu (copper) | 1 Nb (niobium) | 2 O (oxygen) | 6 N_atoms = 1 + 2 + 6 = 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 Cu (copper) | 1 | 1/9 Nb (niobium) | 2 | 2/9 O (oxygen) | 6 | 6/9 Check: 1/9 + 2/9 + 6/9 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Cu (copper) | 1 | 1/9 × 100% = 11.1% Nb (niobium) | 2 | 2/9 × 100% = 22.2% O (oxygen) | 6 | 6/9 × 100% = 66.7% 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 Cu (copper) | 1 | 11.1% | 63.546 Nb (niobium) | 2 | 22.2% | 92.90637 O (oxygen) | 6 | 66.7% | 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 Cu (copper) | 1 | 11.1% | 63.546 | 1 × 63.546 = 63.546 Nb (niobium) | 2 | 22.2% | 92.90637 | 2 × 92.90637 = 185.81274 O (oxygen) | 6 | 66.7% | 15.999 | 6 × 15.999 = 95.994 m = 63.546 u + 185.81274 u + 95.994 u = 345.35274 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 Cu (copper) | 1 | 11.1% | 63.546/345.35274 Nb (niobium) | 2 | 22.2% | 185.81274/345.35274 O (oxygen) | 6 | 66.7% | 95.994/345.35274 Check: 63.546/345.35274 + 185.81274/345.35274 + 95.994/345.35274 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Cu (copper) | 1 | 11.1% | 63.546/345.35274 × 100% = 18.40% Nb (niobium) | 2 | 22.2% | 185.81274/345.35274 × 100% = 53.80% O (oxygen) | 6 | 66.7% | 95.994/345.35274 × 100% = 27.80%

Mass fraction pie chart