mass fractions of oleum

oleum | elemental composition

Find the elemental composition for oleum 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: H_2SO_4SO_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 H (hydrogen) | 2 O (oxygen) | 7 S (sulfur) | 2 N_atoms = 2 + 7 + 2 = 11 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 H (hydrogen) | 2 | 2/11 O (oxygen) | 7 | 7/11 S (sulfur) | 2 | 2/11 Check: 2/11 + 7/11 + 2/11 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 2 | 2/11 × 100% = 18.2% O (oxygen) | 7 | 7/11 × 100% = 63.6% S (sulfur) | 2 | 2/11 × 100% = 18.2% 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 H (hydrogen) | 2 | 18.2% | 1.008 O (oxygen) | 7 | 63.6% | 15.999 S (sulfur) | 2 | 18.2% | 32.06 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 H (hydrogen) | 2 | 18.2% | 1.008 | 2 × 1.008 = 2.016 O (oxygen) | 7 | 63.6% | 15.999 | 7 × 15.999 = 111.993 S (sulfur) | 2 | 18.2% | 32.06 | 2 × 32.06 = 64.12 m = 2.016 u + 111.993 u + 64.12 u = 178.129 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 H (hydrogen) | 2 | 18.2% | 2.016/178.129 O (oxygen) | 7 | 63.6% | 111.993/178.129 S (sulfur) | 2 | 18.2% | 64.12/178.129 Check: 2.016/178.129 + 111.993/178.129 + 64.12/178.129 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 2 | 18.2% | 2.016/178.129 × 100% = 1.132% O (oxygen) | 7 | 63.6% | 111.993/178.129 × 100% = 62.87% S (sulfur) | 2 | 18.2% | 64.12/178.129 × 100% = 36.00%

Mass fraction pie chart