mass fractions of titanium(IV) oxide (rutile)

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titanium(IV) oxide (rutile) | elemental composition

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$Find the elemental composition for titanium(IV) oxide (rutile) 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: TiO_2 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 O (oxygen) | 2 Ti (titanium) | 1 N_atoms = 2 + 1 = 3 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 O (oxygen) | 2 | 2/3 Ti (titanium) | 1 | 1/3 Check: 2/3 + 1/3 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent O (oxygen) | 2 | 2/3 × 100% = 66.7% Ti (titanium) | 1 | 1/3 × 100% = 33.3% 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 O (oxygen) | 2 | 66.7% | 15.999 Ti (titanium) | 1 | 33.3% | 47.867 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 O (oxygen) | 2 | 66.7% | 15.999 | 2 × 15.999 = 31.998 Ti (titanium) | 1 | 33.3% | 47.867 | 1 × 47.867 = 47.867 m = 31.998 u + 47.867 u = 79.865 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 O (oxygen) | 2 | 66.7% | 31.998/79.865 Ti (titanium) | 1 | 33.3% | 47.867/79.865 Check: 31.998/79.865 + 47.867/79.865 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent O (oxygen) | 2 | 66.7% | 31.998/79.865 × 100% = 40.07% Ti (titanium) | 1 | 33.3% | 47.867/79.865 × 100% = 59.93%$

Find the elemental composition for titanium(IV) oxide (rutile) 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: TiO_2 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 O (oxygen) | 2 Ti (titanium) | 1 N_atoms = 2 + 1 = 3 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 O (oxygen) | 2 | 2/3 Ti (titanium) | 1 | 1/3 Check: 2/3 + 1/3 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent O (oxygen) | 2 | 2/3 × 100% = 66.7% Ti (titanium) | 1 | 1/3 × 100% = 33.3% 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 O (oxygen) | 2 | 66.7% | 15.999 Ti (titanium) | 1 | 33.3% | 47.867 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 O (oxygen) | 2 | 66.7% | 15.999 | 2 × 15.999 = 31.998 Ti (titanium) | 1 | 33.3% | 47.867 | 1 × 47.867 = 47.867 m = 31.998 u + 47.867 u = 79.865 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 O (oxygen) | 2 | 66.7% | 31.998/79.865 Ti (titanium) | 1 | 33.3% | 47.867/79.865 Check: 31.998/79.865 + 47.867/79.865 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent O (oxygen) | 2 | 66.7% | 31.998/79.865 × 100% = 40.07% Ti (titanium) | 1 | 33.3% | 47.867/79.865 × 100% = 59.93%