mass fractions of titanium disulfide

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titanium disulfide | elemental composition

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$Find the elemental composition for titanium disulfide 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: TiS_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 S (sulfur) | 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 S (sulfur) | 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 S (sulfur) | 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 S (sulfur) | 2 | 66.7% | 32.06 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 S (sulfur) | 2 | 66.7% | 32.06 | 2 × 32.06 = 64.12 Ti (titanium) | 1 | 33.3% | 47.867 | 1 × 47.867 = 47.867 m = 64.12 u + 47.867 u = 111.987 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 S (sulfur) | 2 | 66.7% | 64.12/111.987 Ti (titanium) | 1 | 33.3% | 47.867/111.987 Check: 64.12/111.987 + 47.867/111.987 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent S (sulfur) | 2 | 66.7% | 64.12/111.987 × 100% = 57.26% Ti (titanium) | 1 | 33.3% | 47.867/111.987 × 100% = 42.74%$

Find the elemental composition for titanium disulfide 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: TiS_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 S (sulfur) | 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 S (sulfur) | 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 S (sulfur) | 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 S (sulfur) | 2 | 66.7% | 32.06 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 S (sulfur) | 2 | 66.7% | 32.06 | 2 × 32.06 = 64.12 Ti (titanium) | 1 | 33.3% | 47.867 | 1 × 47.867 = 47.867 m = 64.12 u + 47.867 u = 111.987 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 S (sulfur) | 2 | 66.7% | 64.12/111.987 Ti (titanium) | 1 | 33.3% | 47.867/111.987 Check: 64.12/111.987 + 47.867/111.987 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent S (sulfur) | 2 | 66.7% | 64.12/111.987 × 100% = 57.26% Ti (titanium) | 1 | 33.3% | 47.867/111.987 × 100% = 42.74%