mass fractions of bismuth chloride

bismuth chloride | elemental composition

Find the elemental composition for bismuth chloride 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: BiCl_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 Bi (bismuth) | 1 Cl (chlorine) | 3 N_atoms = 1 + 3 = 4 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 Bi (bismuth) | 1 | 1/4 Cl (chlorine) | 3 | 3/4 Check: 1/4 + 3/4 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Bi (bismuth) | 1 | 1/4 × 100% = 25.0% Cl (chlorine) | 3 | 3/4 × 100% = 75.0% 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 Bi (bismuth) | 1 | 25.0% | 208.98040 Cl (chlorine) | 3 | 75.0% | 35.45 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 Bi (bismuth) | 1 | 25.0% | 208.98040 | 1 × 208.98040 = 208.98040 Cl (chlorine) | 3 | 75.0% | 35.45 | 3 × 35.45 = 106.35 m = 208.98040 u + 106.35 u = 315.33040 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 Bi (bismuth) | 1 | 25.0% | 208.98040/315.33040 Cl (chlorine) | 3 | 75.0% | 106.35/315.33040 Check: 208.98040/315.33040 + 106.35/315.33040 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Bi (bismuth) | 1 | 25.0% | 208.98040/315.33040 × 100% = 66.27% Cl (chlorine) | 3 | 75.0% | 106.35/315.33040 × 100% = 33.73%

Mass fraction pie chart