mass fractions of ammonium metavanadate

ammonium metavanadate | elemental composition

Find the elemental composition for ammonium metavanadate 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: NH_4VO_3 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 H (hydrogen) | 4 N (nitrogen) | 1 O (oxygen) | 3 V (vanadium) | 1 N_atoms = 4 + 1 + 3 + 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 H (hydrogen) | 4 | 4/9 N (nitrogen) | 1 | 1/9 O (oxygen) | 3 | 3/9 V (vanadium) | 1 | 1/9 Check: 4/9 + 1/9 + 3/9 + 1/9 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 4 | 4/9 × 100% = 44.4% N (nitrogen) | 1 | 1/9 × 100% = 11.1% O (oxygen) | 3 | 3/9 × 100% = 33.3% V (vanadium) | 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 H (hydrogen) | 4 | 44.4% | 1.008 N (nitrogen) | 1 | 11.1% | 14.007 O (oxygen) | 3 | 33.3% | 15.999 V (vanadium) | 1 | 11.1% | 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 H (hydrogen) | 4 | 44.4% | 1.008 | 4 × 1.008 = 4.032 N (nitrogen) | 1 | 11.1% | 14.007 | 1 × 14.007 = 14.007 O (oxygen) | 3 | 33.3% | 15.999 | 3 × 15.999 = 47.997 V (vanadium) | 1 | 11.1% | 50.9415 | 1 × 50.9415 = 50.9415 m = 4.032 u + 14.007 u + 47.997 u + 50.9415 u = 116.9775 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 H (hydrogen) | 4 | 44.4% | 4.032/116.9775 N (nitrogen) | 1 | 11.1% | 14.007/116.9775 O (oxygen) | 3 | 33.3% | 47.997/116.9775 V (vanadium) | 1 | 11.1% | 50.9415/116.9775 Check: 4.032/116.9775 + 14.007/116.9775 + 47.997/116.9775 + 50.9415/116.9775 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 4 | 44.4% | 4.032/116.9775 × 100% = 3.447% N (nitrogen) | 1 | 11.1% | 14.007/116.9775 × 100% = 11.97% O (oxygen) | 3 | 33.3% | 47.997/116.9775 × 100% = 41.03% V (vanadium) | 1 | 11.1% | 50.9415/116.9775 × 100% = 43.55%

Mass fraction pie chart