mass fractions of samarium(III) carbonate hydrate

samarium(III) carbonate hydrate | elemental composition

Find the elemental composition for samarium(III) carbonate 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: Sm_2(CO_3)_3·xH_2O Use the chemical formula, Sm_2(CO_3)_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 C (carbon) | 3 H (hydrogen) | 2 O (oxygen) | 10 Sm (samarium) | 2 N_atoms = 3 + 2 + 10 + 2 = 17 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 C (carbon) | 3 | 3/17 H (hydrogen) | 2 | 2/17 O (oxygen) | 10 | 10/17 Sm (samarium) | 2 | 2/17 Check: 3/17 + 2/17 + 10/17 + 2/17 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 3 | 3/17 × 100% = 17.6% H (hydrogen) | 2 | 2/17 × 100% = 11.8% O (oxygen) | 10 | 10/17 × 100% = 58.8% Sm (samarium) | 2 | 2/17 × 100% = 11.8% 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 C (carbon) | 3 | 17.6% | 12.011 H (hydrogen) | 2 | 11.8% | 1.008 O (oxygen) | 10 | 58.8% | 15.999 Sm (samarium) | 2 | 11.8% | 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 C (carbon) | 3 | 17.6% | 12.011 | 3 × 12.011 = 36.033 H (hydrogen) | 2 | 11.8% | 1.008 | 2 × 1.008 = 2.016 O (oxygen) | 10 | 58.8% | 15.999 | 10 × 15.999 = 159.990 Sm (samarium) | 2 | 11.8% | 150.36 | 2 × 150.36 = 300.72 m = 36.033 u + 2.016 u + 159.990 u + 300.72 u = 498.759 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 C (carbon) | 3 | 17.6% | 36.033/498.759 H (hydrogen) | 2 | 11.8% | 2.016/498.759 O (oxygen) | 10 | 58.8% | 159.990/498.759 Sm (samarium) | 2 | 11.8% | 300.72/498.759 Check: 36.033/498.759 + 2.016/498.759 + 159.990/498.759 + 300.72/498.759 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 3 | 17.6% | 36.033/498.759 × 100% = 7.225% H (hydrogen) | 2 | 11.8% | 2.016/498.759 × 100% = 0.4042% O (oxygen) | 10 | 58.8% | 159.990/498.759 × 100% = 32.08% Sm (samarium) | 2 | 11.8% | 300.72/498.759 × 100% = 60.29%

Mass fraction pie chart