mass fractions of neodymium(III) sulfate octahydrate

neodymium(III) sulfate octahydrate | elemental composition

Find the elemental composition for neodymium(III) sulfate octahydrate 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: Nd_2(SO_4)_3·8H_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) | 16 Nd (neodymium) | 2 O (oxygen) | 20 S (sulfur) | 3 N_atoms = 16 + 2 + 20 + 3 = 41 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) | 16 | 16/41 Nd (neodymium) | 2 | 2/41 O (oxygen) | 20 | 20/41 S (sulfur) | 3 | 3/41 Check: 16/41 + 2/41 + 20/41 + 3/41 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 16 | 16/41 × 100% = 39.0% Nd (neodymium) | 2 | 2/41 × 100% = 4.88% O (oxygen) | 20 | 20/41 × 100% = 48.8% S (sulfur) | 3 | 3/41 × 100% = 7.32% 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) | 16 | 39.0% | 1.008 Nd (neodymium) | 2 | 4.88% | 144.242 O (oxygen) | 20 | 48.8% | 15.999 S (sulfur) | 3 | 7.32% | 32.06 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) | 16 | 39.0% | 1.008 | 16 × 1.008 = 16.128 Nd (neodymium) | 2 | 4.88% | 144.242 | 2 × 144.242 = 288.484 O (oxygen) | 20 | 48.8% | 15.999 | 20 × 15.999 = 319.980 S (sulfur) | 3 | 7.32% | 32.06 | 3 × 32.06 = 96.18 m = 16.128 u + 288.484 u + 319.980 u + 96.18 u = 720.772 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) | 16 | 39.0% | 16.128/720.772 Nd (neodymium) | 2 | 4.88% | 288.484/720.772 O (oxygen) | 20 | 48.8% | 319.980/720.772 S (sulfur) | 3 | 7.32% | 96.18/720.772 Check: 16.128/720.772 + 288.484/720.772 + 319.980/720.772 + 96.18/720.772 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 16 | 39.0% | 16.128/720.772 × 100% = 2.238% Nd (neodymium) | 2 | 4.88% | 288.484/720.772 × 100% = 40.02% O (oxygen) | 20 | 48.8% | 319.980/720.772 × 100% = 44.39% S (sulfur) | 3 | 7.32% | 96.18/720.772 × 100% = 13.34%

Mass fraction pie chart