element mass fraction of lanthanum(III) chloride hydrate

lanthanum(III) chloride hydrate | elemental composition

Find the elemental composition for lanthanum(III) chloride 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: LaCl_3·xH_2O Use the chemical formula, LaCl_3·xH_2O, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms Cl (chlorine) | 3 H (hydrogen) | 2 La (lanthanum) | 1 O (oxygen) | 1 N_atoms = 3 + 2 + 1 + 1 = 7 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 Cl (chlorine) | 3 | 3/7 H (hydrogen) | 2 | 2/7 La (lanthanum) | 1 | 1/7 O (oxygen) | 1 | 1/7 Check: 3/7 + 2/7 + 1/7 + 1/7 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Cl (chlorine) | 3 | 3/7 × 100% = 42.9% H (hydrogen) | 2 | 2/7 × 100% = 28.6% La (lanthanum) | 1 | 1/7 × 100% = 14.3% O (oxygen) | 1 | 1/7 × 100% = 14.3% 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 Cl (chlorine) | 3 | 42.9% | 35.45 H (hydrogen) | 2 | 28.6% | 1.008 La (lanthanum) | 1 | 14.3% | 138.90547 O (oxygen) | 1 | 14.3% | 15.999 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 Cl (chlorine) | 3 | 42.9% | 35.45 | 3 × 35.45 = 106.35 H (hydrogen) | 2 | 28.6% | 1.008 | 2 × 1.008 = 2.016 La (lanthanum) | 1 | 14.3% | 138.90547 | 1 × 138.90547 = 138.90547 O (oxygen) | 1 | 14.3% | 15.999 | 1 × 15.999 = 15.999 m = 106.35 u + 2.016 u + 138.90547 u + 15.999 u = 263.27047 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 Cl (chlorine) | 3 | 42.9% | 106.35/263.27047 H (hydrogen) | 2 | 28.6% | 2.016/263.27047 La (lanthanum) | 1 | 14.3% | 138.90547/263.27047 O (oxygen) | 1 | 14.3% | 15.999/263.27047 Check: 106.35/263.27047 + 2.016/263.27047 + 138.90547/263.27047 + 15.999/263.27047 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Cl (chlorine) | 3 | 42.9% | 106.35/263.27047 × 100% = 40.40% H (hydrogen) | 2 | 28.6% | 2.016/263.27047 × 100% = 0.7658% La (lanthanum) | 1 | 14.3% | 138.90547/263.27047 × 100% = 52.76% O (oxygen) | 1 | 14.3% | 15.999/263.27047 × 100% = 6.077%

Mass fraction pie chart