mass fractions of gadoversetamide

gadoversetamide | elemental composition

Find the elemental composition for gadoversetamide 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_20H_34GdN_5O_10 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) | 20 Gd (gadolinium) | 1 H (hydrogen) | 34 N (nitrogen) | 5 O (oxygen) | 10 N_atoms = 20 + 1 + 34 + 5 + 10 = 70 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) | 20 | 20/70 Gd (gadolinium) | 1 | 1/70 H (hydrogen) | 34 | 34/70 N (nitrogen) | 5 | 5/70 O (oxygen) | 10 | 10/70 Check: 20/70 + 1/70 + 34/70 + 5/70 + 10/70 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 20 | 20/70 × 100% = 28.6% Gd (gadolinium) | 1 | 1/70 × 100% = 1.43% H (hydrogen) | 34 | 34/70 × 100% = 48.6% N (nitrogen) | 5 | 5/70 × 100% = 7.14% O (oxygen) | 10 | 10/70 × 100% = 14.3% 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) | 20 | 28.6% | 12.011 Gd (gadolinium) | 1 | 1.43% | 157.25 H (hydrogen) | 34 | 48.6% | 1.008 N (nitrogen) | 5 | 7.14% | 14.007 O (oxygen) | 10 | 14.3% | 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) | 20 | 28.6% | 12.011 | 20 × 12.011 = 240.220 Gd (gadolinium) | 1 | 1.43% | 157.25 | 1 × 157.25 = 157.25 H (hydrogen) | 34 | 48.6% | 1.008 | 34 × 1.008 = 34.272 N (nitrogen) | 5 | 7.14% | 14.007 | 5 × 14.007 = 70.035 O (oxygen) | 10 | 14.3% | 15.999 | 10 × 15.999 = 159.990 m = 240.220 u + 157.25 u + 34.272 u + 70.035 u + 159.990 u = 661.767 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) | 20 | 28.6% | 240.220/661.767 Gd (gadolinium) | 1 | 1.43% | 157.25/661.767 H (hydrogen) | 34 | 48.6% | 34.272/661.767 N (nitrogen) | 5 | 7.14% | 70.035/661.767 O (oxygen) | 10 | 14.3% | 159.990/661.767 Check: 240.220/661.767 + 157.25/661.767 + 34.272/661.767 + 70.035/661.767 + 159.990/661.767 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 20 | 28.6% | 240.220/661.767 × 100% = 36.30% Gd (gadolinium) | 1 | 1.43% | 157.25/661.767 × 100% = 23.76% H (hydrogen) | 34 | 48.6% | 34.272/661.767 × 100% = 5.179% N (nitrogen) | 5 | 7.14% | 70.035/661.767 × 100% = 10.58% O (oxygen) | 10 | 14.3% | 159.990/661.767 × 100% = 24.18%

Mass fraction pie chart