mass fractions of pyrophosphoric acid

pyrophosphoric acid | elemental composition

Find the elemental composition for pyrophosphoric acid 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: (HO)_2P(O)OP(O)(OH)_2 Use the chemical formula, (HO)_2P(O)OP(O)(OH)_2, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms H (hydrogen) | 4 O (oxygen) | 7 P (phosphorus) | 2 N_atoms = 4 + 7 + 2 = 13 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 | 4/13 O (oxygen) | 7 | 7/13 P (phosphorus) | 2 | 2/13 Check: 4/13 + 7/13 + 2/13 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 4 | 4/13 × 100% = 30.8% O (oxygen) | 7 | 7/13 × 100% = 53.8% P (phosphorus) | 2 | 2/13 × 100% = 15.4% 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 | 30.8% | 1.008 O (oxygen) | 7 | 53.8% | 15.999 P (phosphorus) | 2 | 15.4% | 30.973761998 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 | 30.8% | 1.008 | 4 × 1.008 = 4.032 O (oxygen) | 7 | 53.8% | 15.999 | 7 × 15.999 = 111.993 P (phosphorus) | 2 | 15.4% | 30.973761998 | 2 × 30.973761998 = 61.947523996 m = 4.032 u + 111.993 u + 61.947523996 u = 177.972523996 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 | 30.8% | 4.032/177.972523996 O (oxygen) | 7 | 53.8% | 111.993/177.972523996 P (phosphorus) | 2 | 15.4% | 61.947523996/177.972523996 Check: 4.032/177.972523996 + 111.993/177.972523996 + 61.947523996/177.972523996 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 4 | 30.8% | 4.032/177.972523996 × 100% = 2.266% O (oxygen) | 7 | 53.8% | 111.993/177.972523996 × 100% = 62.93% P (phosphorus) | 2 | 15.4% | 61.947523996/177.972523996 × 100% = 34.81%

Mass fraction pie chart