mass fractions of samarium(III) phosphate hydrate

samarium(III) phosphate hydrate | elemental composition

Find the elemental composition for samarium(III) phosphate hydrate 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: O_4PSm·xH_2O 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) | 2 O (oxygen) | 5 P (phosphorus) | 1 Sm (samarium) | 1 N_atoms = 2 + 5 + 1 + 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) | 2 | 2/9 O (oxygen) | 5 | 5/9 P (phosphorus) | 1 | 1/9 Sm (samarium) | 1 | 1/9 Check: 2/9 + 5/9 + 1/9 + 1/9 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 2 | 2/9 × 100% = 22.2% O (oxygen) | 5 | 5/9 × 100% = 55.6% P (phosphorus) | 1 | 1/9 × 100% = 11.1% Sm (samarium) | 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) | 2 | 22.2% | 1.008 O (oxygen) | 5 | 55.6% | 15.999 P (phosphorus) | 1 | 11.1% | 30.973761998 Sm (samarium) | 1 | 11.1% | 150.36 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) | 2 | 22.2% | 1.008 | 2 × 1.008 = 2.016 O (oxygen) | 5 | 55.6% | 15.999 | 5 × 15.999 = 79.995 P (phosphorus) | 1 | 11.1% | 30.973761998 | 1 × 30.973761998 = 30.973761998 Sm (samarium) | 1 | 11.1% | 150.36 | 1 × 150.36 = 150.36 m = 2.016 u + 79.995 u + 30.973761998 u + 150.36 u = 263.344761998 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) | 2 | 22.2% | 2.016/263.344761998 O (oxygen) | 5 | 55.6% | 79.995/263.344761998 P (phosphorus) | 1 | 11.1% | 30.973761998/263.344761998 Sm (samarium) | 1 | 11.1% | 150.36/263.344761998 Check: 2.016/263.344761998 + 79.995/263.344761998 + 30.973761998/263.344761998 + 150.36/263.344761998 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 2 | 22.2% | 2.016/263.344761998 × 100% = 0.7655% O (oxygen) | 5 | 55.6% | 79.995/263.344761998 × 100% = 30.38% P (phosphorus) | 1 | 11.1% | 30.973761998/263.344761998 × 100% = 11.76% Sm (samarium) | 1 | 11.1% | 150.36/263.344761998 × 100% = 57.10%

Mass fraction pie chart