#### Input interpretation

potassium hydrogen tartrate | elemental composition

#### Result

Find the elemental composition for potassium hydrogen tartrate 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: KO_2CCH(OH)CH(OH)CO_2H Use the chemical formula, KO_2CCH(OH)CH(OH)CO_2H, 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) | 4 H (hydrogen) | 5 K (potassium) | 1 O (oxygen) | 6 N_atoms = 4 + 5 + 1 + 6 = 16 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) | 4 | 4/16 H (hydrogen) | 5 | 5/16 K (potassium) | 1 | 1/16 O (oxygen) | 6 | 6/16 Check: 4/16 + 5/16 + 1/16 + 6/16 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 4 | 4/16 × 100% = 25.0% H (hydrogen) | 5 | 5/16 × 100% = 31.3% K (potassium) | 1 | 1/16 × 100% = 6.25% O (oxygen) | 6 | 6/16 × 100% = 37.5% 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) | 4 | 25.0% | 12.011 H (hydrogen) | 5 | 31.3% | 1.008 K (potassium) | 1 | 6.25% | 39.0983 O (oxygen) | 6 | 37.5% | 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) | 4 | 25.0% | 12.011 | 4 × 12.011 = 48.044 H (hydrogen) | 5 | 31.3% | 1.008 | 5 × 1.008 = 5.040 K (potassium) | 1 | 6.25% | 39.0983 | 1 × 39.0983 = 39.0983 O (oxygen) | 6 | 37.5% | 15.999 | 6 × 15.999 = 95.994 m = 48.044 u + 5.040 u + 39.0983 u + 95.994 u = 188.1763 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) | 4 | 25.0% | 48.044/188.1763 H (hydrogen) | 5 | 31.3% | 5.040/188.1763 K (potassium) | 1 | 6.25% | 39.0983/188.1763 O (oxygen) | 6 | 37.5% | 95.994/188.1763 Check: 48.044/188.1763 + 5.040/188.1763 + 39.0983/188.1763 + 95.994/188.1763 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 4 | 25.0% | 48.044/188.1763 × 100% = 25.53% H (hydrogen) | 5 | 31.3% | 5.040/188.1763 × 100% = 2.678% K (potassium) | 1 | 6.25% | 39.0983/188.1763 × 100% = 20.78% O (oxygen) | 6 | 37.5% | 95.994/188.1763 × 100% = 51.01%

#### Mass fraction pie chart

Mass fraction pie chart