mass fractions of cyclohexane, 1,1'-(1,5-pentanediyl)bis-

cyclohexane, 1, 1'-(1, 5-pentanediyl)bis- | elemental composition

Find the elemental composition for cyclohexane, 1, 1'-(1, 5-pentanediyl)bis- 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_32 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) | 32 N_atoms = 17 + 32 = 49 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 | 17/49 H (hydrogen) | 32 | 32/49 Check: 17/49 + 32/49 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 17 | 17/49 × 100% = 34.7% H (hydrogen) | 32 | 32/49 × 100% = 65.3% 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 | 34.7% | 12.011 H (hydrogen) | 32 | 65.3% | 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) | 17 | 34.7% | 12.011 | 17 × 12.011 = 204.187 H (hydrogen) | 32 | 65.3% | 1.008 | 32 × 1.008 = 32.256 m = 204.187 u + 32.256 u = 236.443 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 | 34.7% | 204.187/236.443 H (hydrogen) | 32 | 65.3% | 32.256/236.443 Check: 204.187/236.443 + 32.256/236.443 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 17 | 34.7% | 204.187/236.443 × 100% = 86.36% H (hydrogen) | 32 | 65.3% | 32.256/236.443 × 100% = 13.64%

Mass fraction pie chart