mass fractions of gallium fluoride

gallium fluoride | elemental composition

Find the elemental composition for gallium 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: GaF_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 F (fluorine) | 3 Ga (gallium) | 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 Ga (gallium) | 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% Ga (gallium) | 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 Ga (gallium) | 1 | 25.0% | 69.723 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 Ga (gallium) | 1 | 25.0% | 69.723 | 1 × 69.723 = 69.723 m = 56.995209489 u + 69.723 u = 126.718209489 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% | 56.995209489/126.718209489 Ga (gallium) | 1 | 25.0% | 69.723/126.718209489 Check: 56.995209489/126.718209489 + 69.723/126.718209489 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent F (fluorine) | 3 | 75.0% | 56.995209489/126.718209489 × 100% = 44.98% Ga (gallium) | 1 | 25.0% | 69.723/126.718209489 × 100% = 55.02%

Mass fraction pie chart