mass fractions of chrome potash alum

chrome potash alum | elemental composition

Find the elemental composition for chrome potash alum 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: CrKO_8S_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 Cr (chromium) | 1 K (potassium) | 1 O (oxygen) | 8 S (sulfur) | 2 N_atoms = 1 + 1 + 8 + 2 = 12 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 Cr (chromium) | 1 | 1/12 K (potassium) | 1 | 1/12 O (oxygen) | 8 | 8/12 S (sulfur) | 2 | 2/12 Check: 1/12 + 1/12 + 8/12 + 2/12 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Cr (chromium) | 1 | 1/12 × 100% = 8.33% K (potassium) | 1 | 1/12 × 100% = 8.33% O (oxygen) | 8 | 8/12 × 100% = 66.7% S (sulfur) | 2 | 2/12 × 100% = 16.7% 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 Cr (chromium) | 1 | 8.33% | 51.9961 K (potassium) | 1 | 8.33% | 39.0983 O (oxygen) | 8 | 66.7% | 15.999 S (sulfur) | 2 | 16.7% | 32.06 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 Cr (chromium) | 1 | 8.33% | 51.9961 | 1 × 51.9961 = 51.9961 K (potassium) | 1 | 8.33% | 39.0983 | 1 × 39.0983 = 39.0983 O (oxygen) | 8 | 66.7% | 15.999 | 8 × 15.999 = 127.992 S (sulfur) | 2 | 16.7% | 32.06 | 2 × 32.06 = 64.12 m = 51.9961 u + 39.0983 u + 127.992 u + 64.12 u = 283.2064 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 Cr (chromium) | 1 | 8.33% | 51.9961/283.2064 K (potassium) | 1 | 8.33% | 39.0983/283.2064 O (oxygen) | 8 | 66.7% | 127.992/283.2064 S (sulfur) | 2 | 16.7% | 64.12/283.2064 Check: 51.9961/283.2064 + 39.0983/283.2064 + 127.992/283.2064 + 64.12/283.2064 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Cr (chromium) | 1 | 8.33% | 51.9961/283.2064 × 100% = 18.36% K (potassium) | 1 | 8.33% | 39.0983/283.2064 × 100% = 13.81% O (oxygen) | 8 | 66.7% | 127.992/283.2064 × 100% = 45.19% S (sulfur) | 2 | 16.7% | 64.12/283.2064 × 100% = 22.64%

Mass fraction pie chart