element mass fraction of gallium(III) perchlorate hexahydrate

gallium(III) perchlorate hexahydrate | elemental composition

Find the elemental composition for gallium(III) perchlorate hexahydrate 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: Ga(ClO_4)_3·6H_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 Cl (chlorine) | 3 Ga (gallium) | 1 H (hydrogen) | 12 O (oxygen) | 18 N_atoms = 3 + 1 + 12 + 18 = 34 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 Cl (chlorine) | 3 | 3/34 Ga (gallium) | 1 | 1/34 H (hydrogen) | 12 | 12/34 O (oxygen) | 18 | 18/34 Check: 3/34 + 1/34 + 12/34 + 18/34 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Cl (chlorine) | 3 | 3/34 × 100% = 8.82% Ga (gallium) | 1 | 1/34 × 100% = 2.94% H (hydrogen) | 12 | 12/34 × 100% = 35.3% O (oxygen) | 18 | 18/34 × 100% = 52.9% 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 Cl (chlorine) | 3 | 8.82% | 35.45 Ga (gallium) | 1 | 2.94% | 69.723 H (hydrogen) | 12 | 35.3% | 1.008 O (oxygen) | 18 | 52.9% | 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 Cl (chlorine) | 3 | 8.82% | 35.45 | 3 × 35.45 = 106.35 Ga (gallium) | 1 | 2.94% | 69.723 | 1 × 69.723 = 69.723 H (hydrogen) | 12 | 35.3% | 1.008 | 12 × 1.008 = 12.096 O (oxygen) | 18 | 52.9% | 15.999 | 18 × 15.999 = 287.982 m = 106.35 u + 69.723 u + 12.096 u + 287.982 u = 476.151 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 Cl (chlorine) | 3 | 8.82% | 106.35/476.151 Ga (gallium) | 1 | 2.94% | 69.723/476.151 H (hydrogen) | 12 | 35.3% | 12.096/476.151 O (oxygen) | 18 | 52.9% | 287.982/476.151 Check: 106.35/476.151 + 69.723/476.151 + 12.096/476.151 + 287.982/476.151 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Cl (chlorine) | 3 | 8.82% | 106.35/476.151 × 100% = 22.34% Ga (gallium) | 1 | 2.94% | 69.723/476.151 × 100% = 14.64% H (hydrogen) | 12 | 35.3% | 12.096/476.151 × 100% = 2.540% O (oxygen) | 18 | 52.9% | 287.982/476.151 × 100% = 60.48%

Mass fraction pie chart