element mass fraction of trans-decahydronaphthalene

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trans-decahydronaphthalene | elemental composition

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$Find the elemental composition for trans-decahydronaphthalene 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_10H_18 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) | 10 H (hydrogen) | 18 N_atoms = 10 + 18 = 28 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) | 10 | 10/28 H (hydrogen) | 18 | 18/28 Check: 10/28 + 18/28 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 10 | 10/28 × 100% = 35.7% H (hydrogen) | 18 | 18/28 × 100% = 64.3% 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) | 10 | 35.7% | 12.011 H (hydrogen) | 18 | 64.3% | 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) | 10 | 35.7% | 12.011 | 10 × 12.011 = 120.110 H (hydrogen) | 18 | 64.3% | 1.008 | 18 × 1.008 = 18.144 m = 120.110 u + 18.144 u = 138.254 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) | 10 | 35.7% | 120.110/138.254 H (hydrogen) | 18 | 64.3% | 18.144/138.254 Check: 120.110/138.254 + 18.144/138.254 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 10 | 35.7% | 120.110/138.254 × 100% = 86.88% H (hydrogen) | 18 | 64.3% | 18.144/138.254 × 100% = 13.12%$

Find the elemental composition for trans-decahydronaphthalene 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_10H_18 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) | 10 H (hydrogen) | 18 N_atoms = 10 + 18 = 28 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) | 10 | 10/28 H (hydrogen) | 18 | 18/28 Check: 10/28 + 18/28 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 10 | 10/28 × 100% = 35.7% H (hydrogen) | 18 | 18/28 × 100% = 64.3% 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) | 10 | 35.7% | 12.011 H (hydrogen) | 18 | 64.3% | 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) | 10 | 35.7% | 12.011 | 10 × 12.011 = 120.110 H (hydrogen) | 18 | 64.3% | 1.008 | 18 × 1.008 = 18.144 m = 120.110 u + 18.144 u = 138.254 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) | 10 | 35.7% | 120.110/138.254 H (hydrogen) | 18 | 64.3% | 18.144/138.254 Check: 120.110/138.254 + 18.144/138.254 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 10 | 35.7% | 120.110/138.254 × 100% = 86.88% H (hydrogen) | 18 | 64.3% | 18.144/138.254 × 100% = 13.12%