mass fractions of carbon dioxide

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carbon dioxide | elemental composition

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$Find the elemental composition for carbon dioxide 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: CO_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) | 1 O (oxygen) | 2 N_atoms = 1 + 2 = 3 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 | 1/3 O (oxygen) | 2 | 2/3 Check: 1/3 + 2/3 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 1 | 1/3 × 100% = 33.3% O (oxygen) | 2 | 2/3 × 100% = 66.7% 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 | 33.3% | 12.011 O (oxygen) | 2 | 66.7% | 15.999 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 | 33.3% | 12.011 | 1 × 12.011 = 12.011 O (oxygen) | 2 | 66.7% | 15.999 | 2 × 15.999 = 31.998 m = 12.011 u + 31.998 u = 44.009 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 | 33.3% | 12.011/44.009 O (oxygen) | 2 | 66.7% | 31.998/44.009 Check: 12.011/44.009 + 31.998/44.009 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 1 | 33.3% | 12.011/44.009 × 100% = 27.29% O (oxygen) | 2 | 66.7% | 31.998/44.009 × 100% = 72.71%$

Find the elemental composition for carbon dioxide 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: CO_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) | 1 O (oxygen) | 2 N_atoms = 1 + 2 = 3 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 | 1/3 O (oxygen) | 2 | 2/3 Check: 1/3 + 2/3 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 1 | 1/3 × 100% = 33.3% O (oxygen) | 2 | 2/3 × 100% = 66.7% 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 | 33.3% | 12.011 O (oxygen) | 2 | 66.7% | 15.999 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 | 33.3% | 12.011 | 1 × 12.011 = 12.011 O (oxygen) | 2 | 66.7% | 15.999 | 2 × 15.999 = 31.998 m = 12.011 u + 31.998 u = 44.009 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 | 33.3% | 12.011/44.009 O (oxygen) | 2 | 66.7% | 31.998/44.009 Check: 12.011/44.009 + 31.998/44.009 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 1 | 33.3% | 12.011/44.009 × 100% = 27.29% O (oxygen) | 2 | 66.7% | 31.998/44.009 × 100% = 72.71%