mass fractions of gallium(III) fluoride trihydrate

gallium(III) fluoride trihydrate | elemental composition

Find the elemental composition for gallium(III) fluoride trihydrate 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_3·3H_2O 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 H (hydrogen) | 6 O (oxygen) | 3 N_atoms = 3 + 1 + 6 + 3 = 13 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 | 3/13 Ga (gallium) | 1 | 1/13 H (hydrogen) | 6 | 6/13 O (oxygen) | 3 | 3/13 Check: 3/13 + 1/13 + 6/13 + 3/13 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent F (fluorine) | 3 | 3/13 × 100% = 23.1% Ga (gallium) | 1 | 1/13 × 100% = 7.69% H (hydrogen) | 6 | 6/13 × 100% = 46.2% O (oxygen) | 3 | 3/13 × 100% = 23.1% 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 | 23.1% | 18.998403163 Ga (gallium) | 1 | 7.69% | 69.723 H (hydrogen) | 6 | 46.2% | 1.008 O (oxygen) | 3 | 23.1% | 15.999 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 | 23.1% | 18.998403163 | 3 × 18.998403163 = 56.995209489 Ga (gallium) | 1 | 7.69% | 69.723 | 1 × 69.723 = 69.723 H (hydrogen) | 6 | 46.2% | 1.008 | 6 × 1.008 = 6.048 O (oxygen) | 3 | 23.1% | 15.999 | 3 × 15.999 = 47.997 m = 56.995209489 u + 69.723 u + 6.048 u + 47.997 u = 180.763209489 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 | 23.1% | 56.995209489/180.763209489 Ga (gallium) | 1 | 7.69% | 69.723/180.763209489 H (hydrogen) | 6 | 46.2% | 6.048/180.763209489 O (oxygen) | 3 | 23.1% | 47.997/180.763209489 Check: 56.995209489/180.763209489 + 69.723/180.763209489 + 6.048/180.763209489 + 47.997/180.763209489 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent F (fluorine) | 3 | 23.1% | 56.995209489/180.763209489 × 100% = 31.53% Ga (gallium) | 1 | 7.69% | 69.723/180.763209489 × 100% = 38.57% H (hydrogen) | 6 | 46.2% | 6.048/180.763209489 × 100% = 3.346% O (oxygen) | 3 | 23.1% | 47.997/180.763209489 × 100% = 26.55%

Mass fraction pie chart