mass fractions of 3-(diethylamino)phenol

3-(diethylamino)phenol | elemental composition

Find the elemental composition for 3-(diethylamino)phenol 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_2H_5)_2NC_6H_4OH Use the chemical formula, (C_2H_5)_2NC_6H_4OH, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms C (carbon) | 10 H (hydrogen) | 15 N (nitrogen) | 1 O (oxygen) | 1 N_atoms = 10 + 15 + 1 + 1 = 27 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) | 10 | 10/27 H (hydrogen) | 15 | 15/27 N (nitrogen) | 1 | 1/27 O (oxygen) | 1 | 1/27 Check: 10/27 + 15/27 + 1/27 + 1/27 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 10 | 10/27 × 100% = 37.0% H (hydrogen) | 15 | 15/27 × 100% = 55.6% N (nitrogen) | 1 | 1/27 × 100% = 3.70% O (oxygen) | 1 | 1/27 × 100% = 3.70% 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) | 10 | 37.0% | 12.011 H (hydrogen) | 15 | 55.6% | 1.008 N (nitrogen) | 1 | 3.70% | 14.007 O (oxygen) | 1 | 3.70% | 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) | 10 | 37.0% | 12.011 | 10 × 12.011 = 120.110 H (hydrogen) | 15 | 55.6% | 1.008 | 15 × 1.008 = 15.120 N (nitrogen) | 1 | 3.70% | 14.007 | 1 × 14.007 = 14.007 O (oxygen) | 1 | 3.70% | 15.999 | 1 × 15.999 = 15.999 m = 120.110 u + 15.120 u + 14.007 u + 15.999 u = 165.236 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) | 10 | 37.0% | 120.110/165.236 H (hydrogen) | 15 | 55.6% | 15.120/165.236 N (nitrogen) | 1 | 3.70% | 14.007/165.236 O (oxygen) | 1 | 3.70% | 15.999/165.236 Check: 120.110/165.236 + 15.120/165.236 + 14.007/165.236 + 15.999/165.236 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 10 | 37.0% | 120.110/165.236 × 100% = 72.69% H (hydrogen) | 15 | 55.6% | 15.120/165.236 × 100% = 9.151% N (nitrogen) | 1 | 3.70% | 14.007/165.236 × 100% = 8.477% O (oxygen) | 1 | 3.70% | 15.999/165.236 × 100% = 9.683%

Mass fraction pie chart