mass fractions of 1,1-diphenylethylene

1, 1-diphenylethylene | elemental composition

Find the elemental composition for 1, 1-diphenylethylene 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_5)_2C=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) | 12 N_atoms = 14 + 12 = 26 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 | 14/26 H (hydrogen) | 12 | 12/26 Check: 14/26 + 12/26 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 14 | 14/26 × 100% = 53.8% H (hydrogen) | 12 | 12/26 × 100% = 46.2% 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 | 53.8% | 12.011 H (hydrogen) | 12 | 46.2% | 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 | 53.8% | 12.011 | 14 × 12.011 = 168.154 H (hydrogen) | 12 | 46.2% | 1.008 | 12 × 1.008 = 12.096 m = 168.154 u + 12.096 u = 180.250 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 | 53.8% | 168.154/180.250 H (hydrogen) | 12 | 46.2% | 12.096/180.250 Check: 168.154/180.250 + 12.096/180.250 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 14 | 53.8% | 168.154/180.250 × 100% = 93.29% H (hydrogen) | 12 | 46.2% | 12.096/180.250 × 100% = 6.711%

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