mass fractions of gadolinium(III) fluoride

gadolinium(III) fluoride | elemental composition

Find the elemental composition for gadolinium(III) fluoride 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: GdF_3 Use the chemical formula, GdF_3, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms F (fluorine) | 3 Gd (gadolinium) | 1 N_atoms = 3 + 1 = 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 F (fluorine) | 3 | 3/4 Gd (gadolinium) | 1 | 1/4 Check: 3/4 + 1/4 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent F (fluorine) | 3 | 3/4 × 100% = 75.0% Gd (gadolinium) | 1 | 1/4 × 100% = 25.0% 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 F (fluorine) | 3 | 75.0% | 18.998403163 Gd (gadolinium) | 1 | 25.0% | 157.25 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 F (fluorine) | 3 | 75.0% | 18.998403163 | 3 × 18.998403163 = 56.995209489 Gd (gadolinium) | 1 | 25.0% | 157.25 | 1 × 157.25 = 157.25 m = 56.995209489 u + 157.25 u = 214.245209489 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 F (fluorine) | 3 | 75.0% | 56.995209489/214.245209489 Gd (gadolinium) | 1 | 25.0% | 157.25/214.245209489 Check: 56.995209489/214.245209489 + 157.25/214.245209489 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent F (fluorine) | 3 | 75.0% | 56.995209489/214.245209489 × 100% = 26.60% Gd (gadolinium) | 1 | 25.0% | 157.25/214.245209489 × 100% = 73.40%

Mass fraction pie chart