element counts of 2,4-dicyclohexyl-2-methylpentane

2, 4-dicyclohexyl-2-methylpentane | elemental composition

Find the elemental composition for 2, 4-dicyclohexyl-2-methylpentane 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_6H_11CH(CH_3)CH_2C(CH_3)_2C_6H_11 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) | 18 H (hydrogen) | 34 N_atoms = 18 + 34 = 52 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) | 18 | 18/52 H (hydrogen) | 34 | 34/52 Check: 18/52 + 34/52 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 18 | 18/52 × 100% = 34.6% H (hydrogen) | 34 | 34/52 × 100% = 65.4% 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) | 18 | 34.6% | 12.011 H (hydrogen) | 34 | 65.4% | 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) | 18 | 34.6% | 12.011 | 18 × 12.011 = 216.198 H (hydrogen) | 34 | 65.4% | 1.008 | 34 × 1.008 = 34.272 m = 216.198 u + 34.272 u = 250.470 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) | 18 | 34.6% | 216.198/250.470 H (hydrogen) | 34 | 65.4% | 34.272/250.470 Check: 216.198/250.470 + 34.272/250.470 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 18 | 34.6% | 216.198/250.470 × 100% = 86.32% H (hydrogen) | 34 | 65.4% | 34.272/250.470 × 100% = 13.68%

Mass fraction pie chart