mass fractions of aluminum oxide

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aluminum oxide | elemental composition

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$Find the elemental composition for aluminum oxide 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 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 O (oxygen) | 3 N_atoms = 2 + 3 = 5 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 | 2/5 O (oxygen) | 3 | 3/5 Check: 2/5 + 3/5 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Al (aluminum) | 2 | 2/5 × 100% = 40.0% O (oxygen) | 3 | 3/5 × 100% = 60.0% 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 | 40.0% | 26.9815385 O (oxygen) | 3 | 60.0% | 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 Al (aluminum) | 2 | 40.0% | 26.9815385 | 2 × 26.9815385 = 53.9630770 O (oxygen) | 3 | 60.0% | 15.999 | 3 × 15.999 = 47.997 m = 53.9630770 u + 47.997 u = 101.9600770 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 | 40.0% | 53.9630770/101.9600770 O (oxygen) | 3 | 60.0% | 47.997/101.9600770 Check: 53.9630770/101.9600770 + 47.997/101.9600770 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Al (aluminum) | 2 | 40.0% | 53.9630770/101.9600770 × 100% = 52.93% O (oxygen) | 3 | 60.0% | 47.997/101.9600770 × 100% = 47.07%$

Find the elemental composition for aluminum oxide 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 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 O (oxygen) | 3 N_atoms = 2 + 3 = 5 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 | 2/5 O (oxygen) | 3 | 3/5 Check: 2/5 + 3/5 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Al (aluminum) | 2 | 2/5 × 100% = 40.0% O (oxygen) | 3 | 3/5 × 100% = 60.0% 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 | 40.0% | 26.9815385 O (oxygen) | 3 | 60.0% | 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 Al (aluminum) | 2 | 40.0% | 26.9815385 | 2 × 26.9815385 = 53.9630770 O (oxygen) | 3 | 60.0% | 15.999 | 3 × 15.999 = 47.997 m = 53.9630770 u + 47.997 u = 101.9600770 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 | 40.0% | 53.9630770/101.9600770 O (oxygen) | 3 | 60.0% | 47.997/101.9600770 Check: 53.9630770/101.9600770 + 47.997/101.9600770 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Al (aluminum) | 2 | 40.0% | 53.9630770/101.9600770 × 100% = 52.93% O (oxygen) | 3 | 60.0% | 47.997/101.9600770 × 100% = 47.07%