mass fractions of cadmium sulfate monohydrate

cadmium sulfate monohydrate | elemental composition

Find the elemental composition for cadmium sulfate monohydrate 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: CdSO_4·H_2O Use the chemical formula, CdSO_4·H_2O, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms Cd (cadmium) | 1 H (hydrogen) | 2 O (oxygen) | 5 S (sulfur) | 1 N_atoms = 1 + 2 + 5 + 1 = 9 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 Cd (cadmium) | 1 | 1/9 H (hydrogen) | 2 | 2/9 O (oxygen) | 5 | 5/9 S (sulfur) | 1 | 1/9 Check: 1/9 + 2/9 + 5/9 + 1/9 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Cd (cadmium) | 1 | 1/9 × 100% = 11.1% H (hydrogen) | 2 | 2/9 × 100% = 22.2% O (oxygen) | 5 | 5/9 × 100% = 55.6% S (sulfur) | 1 | 1/9 × 100% = 11.1% 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 Cd (cadmium) | 1 | 11.1% | 112.414 H (hydrogen) | 2 | 22.2% | 1.008 O (oxygen) | 5 | 55.6% | 15.999 S (sulfur) | 1 | 11.1% | 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 Cd (cadmium) | 1 | 11.1% | 112.414 | 1 × 112.414 = 112.414 H (hydrogen) | 2 | 22.2% | 1.008 | 2 × 1.008 = 2.016 O (oxygen) | 5 | 55.6% | 15.999 | 5 × 15.999 = 79.995 S (sulfur) | 1 | 11.1% | 32.06 | 1 × 32.06 = 32.06 m = 112.414 u + 2.016 u + 79.995 u + 32.06 u = 226.485 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 Cd (cadmium) | 1 | 11.1% | 112.414/226.485 H (hydrogen) | 2 | 22.2% | 2.016/226.485 O (oxygen) | 5 | 55.6% | 79.995/226.485 S (sulfur) | 1 | 11.1% | 32.06/226.485 Check: 112.414/226.485 + 2.016/226.485 + 79.995/226.485 + 32.06/226.485 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Cd (cadmium) | 1 | 11.1% | 112.414/226.485 × 100% = 49.63% H (hydrogen) | 2 | 22.2% | 2.016/226.485 × 100% = 0.8901% O (oxygen) | 5 | 55.6% | 79.995/226.485 × 100% = 35.32% S (sulfur) | 1 | 11.1% | 32.06/226.485 × 100% = 14.16%

Mass fraction pie chart