mass fractions of metaphosphoric acid

metaphosphoric acid | elemental composition

Find the elemental composition for metaphosphoric 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: HPO_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) | 1 O (oxygen) | 3 P (phosphorus) | 1 N_atoms = 1 + 3 + 1 = 5 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) | 1 | 1/5 O (oxygen) | 3 | 3/5 P (phosphorus) | 1 | 1/5 Check: 1/5 + 3/5 + 1/5 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 1 | 1/5 × 100% = 20.0% O (oxygen) | 3 | 3/5 × 100% = 60.0% P (phosphorus) | 1 | 1/5 × 100% = 20.0% 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) | 1 | 20.0% | 1.008 O (oxygen) | 3 | 60.0% | 15.999 P (phosphorus) | 1 | 20.0% | 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) | 1 | 20.0% | 1.008 | 1 × 1.008 = 1.008 O (oxygen) | 3 | 60.0% | 15.999 | 3 × 15.999 = 47.997 P (phosphorus) | 1 | 20.0% | 30.973761998 | 1 × 30.973761998 = 30.973761998 m = 1.008 u + 47.997 u + 30.973761998 u = 79.978761998 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) | 1 | 20.0% | 1.008/79.978761998 O (oxygen) | 3 | 60.0% | 47.997/79.978761998 P (phosphorus) | 1 | 20.0% | 30.973761998/79.978761998 Check: 1.008/79.978761998 + 47.997/79.978761998 + 30.973761998/79.978761998 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 1 | 20.0% | 1.008/79.978761998 × 100% = 1.260% O (oxygen) | 3 | 60.0% | 47.997/79.978761998 × 100% = 60.01% P (phosphorus) | 1 | 20.0% | 30.973761998/79.978761998 × 100% = 38.73%

Mass fraction pie chart