mass fractions of methane

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methane | elemental composition

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$Find the elemental composition for methane 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_4 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) | 1 H (hydrogen) | 4 N_atoms = 1 + 4 = 5 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) | 1 | 1/5 H (hydrogen) | 4 | 4/5 Check: 1/5 + 4/5 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 1 | 1/5 × 100% = 20.0% H (hydrogen) | 4 | 4/5 × 100% = 80.0% 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) | 1 | 20.0% | 12.011 H (hydrogen) | 4 | 80.0% | 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) | 1 | 20.0% | 12.011 | 1 × 12.011 = 12.011 H (hydrogen) | 4 | 80.0% | 1.008 | 4 × 1.008 = 4.032 m = 12.011 u + 4.032 u = 16.043 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) | 1 | 20.0% | 12.011/16.043 H (hydrogen) | 4 | 80.0% | 4.032/16.043 Check: 12.011/16.043 + 4.032/16.043 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 1 | 20.0% | 12.011/16.043 × 100% = 74.87% H (hydrogen) | 4 | 80.0% | 4.032/16.043 × 100% = 25.13%$

Find the elemental composition for methane 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_4 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) | 1 H (hydrogen) | 4 N_atoms = 1 + 4 = 5 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) | 1 | 1/5 H (hydrogen) | 4 | 4/5 Check: 1/5 + 4/5 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 1 | 1/5 × 100% = 20.0% H (hydrogen) | 4 | 4/5 × 100% = 80.0% 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) | 1 | 20.0% | 12.011 H (hydrogen) | 4 | 80.0% | 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) | 1 | 20.0% | 12.011 | 1 × 12.011 = 12.011 H (hydrogen) | 4 | 80.0% | 1.008 | 4 × 1.008 = 4.032 m = 12.011 u + 4.032 u = 16.043 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) | 1 | 20.0% | 12.011/16.043 H (hydrogen) | 4 | 80.0% | 4.032/16.043 Check: 12.011/16.043 + 4.032/16.043 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 1 | 20.0% | 12.011/16.043 × 100% = 74.87% H (hydrogen) | 4 | 80.0% | 4.032/16.043 × 100% = 25.13%