element mass fraction of methyl (2e,6e)-(10r,11s)-10,11-epoxy-3,7,11-trimethyltrideca-2,6-dienoate

methyl (2e, 6e)-(10r, 11s)-10, 11-epoxy-3, 7, 11-trimethyltrideca-2, 6-dienoate | elemental composition

Find the elemental composition for methyl (2e, 6e)-(10r, 11s)-10, 11-epoxy-3, 7, 11-trimethyltrideca-2, 6-dienoate 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_17H_28O_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 C (carbon) | 17 H (hydrogen) | 28 O (oxygen) | 3 N_atoms = 17 + 28 + 3 = 48 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) | 17 | 17/48 H (hydrogen) | 28 | 28/48 O (oxygen) | 3 | 3/48 Check: 17/48 + 28/48 + 3/48 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 17 | 17/48 × 100% = 35.4% H (hydrogen) | 28 | 28/48 × 100% = 58.3% O (oxygen) | 3 | 3/48 × 100% = 6.25% 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) | 17 | 35.4% | 12.011 H (hydrogen) | 28 | 58.3% | 1.008 O (oxygen) | 3 | 6.25% | 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) | 17 | 35.4% | 12.011 | 17 × 12.011 = 204.187 H (hydrogen) | 28 | 58.3% | 1.008 | 28 × 1.008 = 28.224 O (oxygen) | 3 | 6.25% | 15.999 | 3 × 15.999 = 47.997 m = 204.187 u + 28.224 u + 47.997 u = 280.408 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) | 17 | 35.4% | 204.187/280.408 H (hydrogen) | 28 | 58.3% | 28.224/280.408 O (oxygen) | 3 | 6.25% | 47.997/280.408 Check: 204.187/280.408 + 28.224/280.408 + 47.997/280.408 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 17 | 35.4% | 204.187/280.408 × 100% = 72.82% H (hydrogen) | 28 | 58.3% | 28.224/280.408 × 100% = 10.07% O (oxygen) | 3 | 6.25% | 47.997/280.408 × 100% = 17.12%

Mass fraction pie chart