mass fractions of sucrose

sucrose | elemental composition

Find the elemental composition for sucrose 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_12H_22O_11 Use the chemical formula, C_12H_22O_11, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms C (carbon) | 12 H (hydrogen) | 22 O (oxygen) | 11 N_atoms = 12 + 22 + 11 = 45 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) | 12 | 12/45 H (hydrogen) | 22 | 22/45 O (oxygen) | 11 | 11/45 Check: 12/45 + 22/45 + 11/45 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 12 | 12/45 × 100% = 26.7% H (hydrogen) | 22 | 22/45 × 100% = 48.9% O (oxygen) | 11 | 11/45 × 100% = 24.4% 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) | 12 | 26.7% | 12.011 H (hydrogen) | 22 | 48.9% | 1.008 O (oxygen) | 11 | 24.4% | 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) | 12 | 26.7% | 12.011 | 12 × 12.011 = 144.132 H (hydrogen) | 22 | 48.9% | 1.008 | 22 × 1.008 = 22.176 O (oxygen) | 11 | 24.4% | 15.999 | 11 × 15.999 = 175.989 m = 144.132 u + 22.176 u + 175.989 u = 342.297 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) | 12 | 26.7% | 144.132/342.297 H (hydrogen) | 22 | 48.9% | 22.176/342.297 O (oxygen) | 11 | 24.4% | 175.989/342.297 Check: 144.132/342.297 + 22.176/342.297 + 175.989/342.297 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 12 | 26.7% | 144.132/342.297 × 100% = 42.11% H (hydrogen) | 22 | 48.9% | 22.176/342.297 × 100% = 6.479% O (oxygen) | 11 | 24.4% | 175.989/342.297 × 100% = 51.41%

Mass fraction pie chart