mass fractions of 2-(diethylamino)ethanol

2-(diethylamino)ethanol | elemental composition

Find the elemental composition for 2-(diethylamino)ethanol 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)_2NCH_2CH_2OH Use the chemical formula, (C_2H_5)_2NCH_2CH_2OH, 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) | 6 H (hydrogen) | 15 N (nitrogen) | 1 O (oxygen) | 1 N_atoms = 6 + 15 + 1 + 1 = 23 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) | 6 | 6/23 H (hydrogen) | 15 | 15/23 N (nitrogen) | 1 | 1/23 O (oxygen) | 1 | 1/23 Check: 6/23 + 15/23 + 1/23 + 1/23 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 6 | 6/23 × 100% = 26.1% H (hydrogen) | 15 | 15/23 × 100% = 65.2% N (nitrogen) | 1 | 1/23 × 100% = 4.35% O (oxygen) | 1 | 1/23 × 100% = 4.35% 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) | 6 | 26.1% | 12.011 H (hydrogen) | 15 | 65.2% | 1.008 N (nitrogen) | 1 | 4.35% | 14.007 O (oxygen) | 1 | 4.35% | 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) | 6 | 26.1% | 12.011 | 6 × 12.011 = 72.066 H (hydrogen) | 15 | 65.2% | 1.008 | 15 × 1.008 = 15.120 N (nitrogen) | 1 | 4.35% | 14.007 | 1 × 14.007 = 14.007 O (oxygen) | 1 | 4.35% | 15.999 | 1 × 15.999 = 15.999 m = 72.066 u + 15.120 u + 14.007 u + 15.999 u = 117.192 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) | 6 | 26.1% | 72.066/117.192 H (hydrogen) | 15 | 65.2% | 15.120/117.192 N (nitrogen) | 1 | 4.35% | 14.007/117.192 O (oxygen) | 1 | 4.35% | 15.999/117.192 Check: 72.066/117.192 + 15.120/117.192 + 14.007/117.192 + 15.999/117.192 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 6 | 26.1% | 72.066/117.192 × 100% = 61.49% H (hydrogen) | 15 | 65.2% | 15.120/117.192 × 100% = 12.90% N (nitrogen) | 1 | 4.35% | 14.007/117.192 × 100% = 11.95% O (oxygen) | 1 | 4.35% | 15.999/117.192 × 100% = 13.65%

Mass fraction pie chart