mass fractions of bentonite

bentonite | elemental composition

Find the elemental composition for bentonite 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: Al_2O_3·(SiO_2)_4·H_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 Al (aluminum) | 2 H (hydrogen) | 2 O (oxygen) | 12 Si (silicon) | 4 N_atoms = 2 + 2 + 12 + 4 = 20 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 Al (aluminum) | 2 | 2/20 H (hydrogen) | 2 | 2/20 O (oxygen) | 12 | 12/20 Si (silicon) | 4 | 4/20 Check: 2/20 + 2/20 + 12/20 + 4/20 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Al (aluminum) | 2 | 2/20 × 100% = 10.00% H (hydrogen) | 2 | 2/20 × 100% = 10.00% O (oxygen) | 12 | 12/20 × 100% = 60.0% Si (silicon) | 4 | 4/20 × 100% = 20.0% 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 Al (aluminum) | 2 | 10.00% | 26.9815385 H (hydrogen) | 2 | 10.00% | 1.008 O (oxygen) | 12 | 60.0% | 15.999 Si (silicon) | 4 | 20.0% | 28.085 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 Al (aluminum) | 2 | 10.00% | 26.9815385 | 2 × 26.9815385 = 53.9630770 H (hydrogen) | 2 | 10.00% | 1.008 | 2 × 1.008 = 2.016 O (oxygen) | 12 | 60.0% | 15.999 | 12 × 15.999 = 191.988 Si (silicon) | 4 | 20.0% | 28.085 | 4 × 28.085 = 112.340 m = 53.9630770 u + 2.016 u + 191.988 u + 112.340 u = 360.3070770 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 Al (aluminum) | 2 | 10.00% | 53.9630770/360.3070770 H (hydrogen) | 2 | 10.00% | 2.016/360.3070770 O (oxygen) | 12 | 60.0% | 191.988/360.3070770 Si (silicon) | 4 | 20.0% | 112.340/360.3070770 Check: 53.9630770/360.3070770 + 2.016/360.3070770 + 191.988/360.3070770 + 112.340/360.3070770 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Al (aluminum) | 2 | 10.00% | 53.9630770/360.3070770 × 100% = 14.98% H (hydrogen) | 2 | 10.00% | 2.016/360.3070770 × 100% = 0.5595% O (oxygen) | 12 | 60.0% | 191.988/360.3070770 × 100% = 53.28% Si (silicon) | 4 | 20.0% | 112.340/360.3070770 × 100% = 31.18%

Mass fraction pie chart