mass fractions of 2-tricosanone

2-tricosanone | elemental composition

Find the elemental composition for 2-tricosanone 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_23H_46O_1 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) | 23 H (hydrogen) | 46 O (oxygen) | 1 N_atoms = 23 + 46 + 1 = 70 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) | 23 | 23/70 H (hydrogen) | 46 | 46/70 O (oxygen) | 1 | 1/70 Check: 23/70 + 46/70 + 1/70 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 23 | 23/70 × 100% = 32.9% H (hydrogen) | 46 | 46/70 × 100% = 65.7% O (oxygen) | 1 | 1/70 × 100% = 1.43% 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) | 23 | 32.9% | 12.011 H (hydrogen) | 46 | 65.7% | 1.008 O (oxygen) | 1 | 1.43% | 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) | 23 | 32.9% | 12.011 | 23 × 12.011 = 276.253 H (hydrogen) | 46 | 65.7% | 1.008 | 46 × 1.008 = 46.368 O (oxygen) | 1 | 1.43% | 15.999 | 1 × 15.999 = 15.999 m = 276.253 u + 46.368 u + 15.999 u = 338.620 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) | 23 | 32.9% | 276.253/338.620 H (hydrogen) | 46 | 65.7% | 46.368/338.620 O (oxygen) | 1 | 1.43% | 15.999/338.620 Check: 276.253/338.620 + 46.368/338.620 + 15.999/338.620 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 23 | 32.9% | 276.253/338.620 × 100% = 81.58% H (hydrogen) | 46 | 65.7% | 46.368/338.620 × 100% = 13.69% O (oxygen) | 1 | 1.43% | 15.999/338.620 × 100% = 4.725%

Mass fraction pie chart