mass fractions of copper(II) vanadate

copper(II) vanadate | elemental composition

Find the elemental composition for copper(II) vanadate 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(VO_3)_2 Use the chemical formula, Cu(VO_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 O (oxygen) | 6 V (vanadium) | 2 N_atoms = 1 + 6 + 2 = 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 O (oxygen) | 6 | 6/9 V (vanadium) | 2 | 2/9 Check: 1/9 + 6/9 + 2/9 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Cu (copper) | 1 | 1/9 × 100% = 11.1% O (oxygen) | 6 | 6/9 × 100% = 66.7% V (vanadium) | 2 | 2/9 × 100% = 22.2% 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 O (oxygen) | 6 | 66.7% | 15.999 V (vanadium) | 2 | 22.2% | 50.9415 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 O (oxygen) | 6 | 66.7% | 15.999 | 6 × 15.999 = 95.994 V (vanadium) | 2 | 22.2% | 50.9415 | 2 × 50.9415 = 101.8830 m = 63.546 u + 95.994 u + 101.8830 u = 261.4230 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% | 63.546/261.4230 O (oxygen) | 6 | 66.7% | 95.994/261.4230 V (vanadium) | 2 | 22.2% | 101.8830/261.4230 Check: 63.546/261.4230 + 95.994/261.4230 + 101.8830/261.4230 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Cu (copper) | 1 | 11.1% | 63.546/261.4230 × 100% = 24.31% O (oxygen) | 6 | 66.7% | 95.994/261.4230 × 100% = 36.72% V (vanadium) | 2 | 22.2% | 101.8830/261.4230 × 100% = 38.97%

Mass fraction pie chart