mass fractions of benzoic acid

benzoic acid | elemental composition

Find the elemental composition for benzoic acid 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: C_6H_5COOH 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 C (carbon) | 7 H (hydrogen) | 6 O (oxygen) | 2 N_atoms = 7 + 6 + 2 = 15 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 C (carbon) | 7 | 7/15 H (hydrogen) | 6 | 6/15 O (oxygen) | 2 | 2/15 Check: 7/15 + 6/15 + 2/15 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 7 | 7/15 × 100% = 46.7% H (hydrogen) | 6 | 6/15 × 100% = 40.0% O (oxygen) | 2 | 2/15 × 100% = 13.3% 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 C (carbon) | 7 | 46.7% | 12.011 H (hydrogen) | 6 | 40.0% | 1.008 O (oxygen) | 2 | 13.3% | 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 C (carbon) | 7 | 46.7% | 12.011 | 7 × 12.011 = 84.077 H (hydrogen) | 6 | 40.0% | 1.008 | 6 × 1.008 = 6.048 O (oxygen) | 2 | 13.3% | 15.999 | 2 × 15.999 = 31.998 m = 84.077 u + 6.048 u + 31.998 u = 122.123 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 C (carbon) | 7 | 46.7% | 84.077/122.123 H (hydrogen) | 6 | 40.0% | 6.048/122.123 O (oxygen) | 2 | 13.3% | 31.998/122.123 Check: 84.077/122.123 + 6.048/122.123 + 31.998/122.123 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 7 | 46.7% | 84.077/122.123 × 100% = 68.85% H (hydrogen) | 6 | 40.0% | 6.048/122.123 × 100% = 4.952% O (oxygen) | 2 | 13.3% | 31.998/122.123 × 100% = 26.20%

Mass fraction pie chart