mass fractions of 1,13-tetradecadiene

1, 13-tetradecadiene | elemental composition

Find the elemental composition for 1, 13-tetradecadiene 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: CH_2=CH(CH_2)_10CH=CH_2 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) | 14 H (hydrogen) | 26 N_atoms = 14 + 26 = 40 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) | 14 | 14/40 H (hydrogen) | 26 | 26/40 Check: 14/40 + 26/40 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 14 | 14/40 × 100% = 35.0% H (hydrogen) | 26 | 26/40 × 100% = 65.0% 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) | 14 | 35.0% | 12.011 H (hydrogen) | 26 | 65.0% | 1.008 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) | 14 | 35.0% | 12.011 | 14 × 12.011 = 168.154 H (hydrogen) | 26 | 65.0% | 1.008 | 26 × 1.008 = 26.208 m = 168.154 u + 26.208 u = 194.362 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) | 14 | 35.0% | 168.154/194.362 H (hydrogen) | 26 | 65.0% | 26.208/194.362 Check: 168.154/194.362 + 26.208/194.362 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 14 | 35.0% | 168.154/194.362 × 100% = 86.52% H (hydrogen) | 26 | 65.0% | 26.208/194.362 × 100% = 13.48%

Mass fraction pie chart