mass fractions of cerussete

cerussete | elemental composition

Find the elemental composition for cerussete 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: PbCO_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 C (carbon) | 1 O (oxygen) | 3 Pb (lead) | 1 N_atoms = 1 + 3 + 1 = 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 C (carbon) | 1 | 1/5 O (oxygen) | 3 | 3/5 Pb (lead) | 1 | 1/5 Check: 1/5 + 3/5 + 1/5 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 1 | 1/5 × 100% = 20.0% O (oxygen) | 3 | 3/5 × 100% = 60.0% Pb (lead) | 1 | 1/5 × 100% = 20.0% 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 C (carbon) | 1 | 20.0% | 12.011 O (oxygen) | 3 | 60.0% | 15.999 Pb (lead) | 1 | 20.0% | 207.2 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) | 1 | 20.0% | 12.011 | 1 × 12.011 = 12.011 O (oxygen) | 3 | 60.0% | 15.999 | 3 × 15.999 = 47.997 Pb (lead) | 1 | 20.0% | 207.2 | 1 × 207.2 = 207.2 m = 12.011 u + 47.997 u + 207.2 u = 267.208 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) | 1 | 20.0% | 12.011/267.208 O (oxygen) | 3 | 60.0% | 47.997/267.208 Pb (lead) | 1 | 20.0% | 207.2/267.208 Check: 12.011/267.208 + 47.997/267.208 + 207.2/267.208 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 1 | 20.0% | 12.011/267.208 × 100% = 4.495% O (oxygen) | 3 | 60.0% | 47.997/267.208 × 100% = 17.96% Pb (lead) | 1 | 20.0% | 207.2/267.208 × 100% = 77.54%

Mass fraction pie chart