mass fractions of cerium(III) sulfide

cerium(III) sulfide | elemental composition

Find the elemental composition for cerium(III) sulfide 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: Ce_2S_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 Ce (cerium) | 2 S (sulfur) | 3 N_atoms = 2 + 3 = 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 Ce (cerium) | 2 | 2/5 S (sulfur) | 3 | 3/5 Check: 2/5 + 3/5 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Ce (cerium) | 2 | 2/5 × 100% = 40.0% S (sulfur) | 3 | 3/5 × 100% = 60.0% 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 Ce (cerium) | 2 | 40.0% | 140.116 S (sulfur) | 3 | 60.0% | 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 Ce (cerium) | 2 | 40.0% | 140.116 | 2 × 140.116 = 280.232 S (sulfur) | 3 | 60.0% | 32.06 | 3 × 32.06 = 96.18 m = 280.232 u + 96.18 u = 376.412 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 Ce (cerium) | 2 | 40.0% | 280.232/376.412 S (sulfur) | 3 | 60.0% | 96.18/376.412 Check: 280.232/376.412 + 96.18/376.412 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Ce (cerium) | 2 | 40.0% | 280.232/376.412 × 100% = 74.45% S (sulfur) | 3 | 60.0% | 96.18/376.412 × 100% = 25.55%

Mass fraction pie chart