mass fractions of cobalt(II) carbonate hydrate

cobalt(II) carbonate hydrate | elemental composition

Find the elemental composition for cobalt(II) carbonate hydrate 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: CoCO_3·xH_2O 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) | 1 Co (cobalt) | 1 H (hydrogen) | 2 O (oxygen) | 4 N_atoms = 1 + 1 + 2 + 4 = 8 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) | 1 | 1/8 Co (cobalt) | 1 | 1/8 H (hydrogen) | 2 | 2/8 O (oxygen) | 4 | 4/8 Check: 1/8 + 1/8 + 2/8 + 4/8 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 1 | 1/8 × 100% = 12.5% Co (cobalt) | 1 | 1/8 × 100% = 12.5% H (hydrogen) | 2 | 2/8 × 100% = 25.0% O (oxygen) | 4 | 4/8 × 100% = 50.0% 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) | 1 | 12.5% | 12.011 Co (cobalt) | 1 | 12.5% | 58.933194 H (hydrogen) | 2 | 25.0% | 1.008 O (oxygen) | 4 | 50.0% | 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) | 1 | 12.5% | 12.011 | 1 × 12.011 = 12.011 Co (cobalt) | 1 | 12.5% | 58.933194 | 1 × 58.933194 = 58.933194 H (hydrogen) | 2 | 25.0% | 1.008 | 2 × 1.008 = 2.016 O (oxygen) | 4 | 50.0% | 15.999 | 4 × 15.999 = 63.996 m = 12.011 u + 58.933194 u + 2.016 u + 63.996 u = 136.956194 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) | 1 | 12.5% | 12.011/136.956194 Co (cobalt) | 1 | 12.5% | 58.933194/136.956194 H (hydrogen) | 2 | 25.0% | 2.016/136.956194 O (oxygen) | 4 | 50.0% | 63.996/136.956194 Check: 12.011/136.956194 + 58.933194/136.956194 + 2.016/136.956194 + 63.996/136.956194 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 1 | 12.5% | 12.011/136.956194 × 100% = 8.770% Co (cobalt) | 1 | 12.5% | 58.933194/136.956194 × 100% = 43.03% H (hydrogen) | 2 | 25.0% | 2.016/136.956194 × 100% = 1.472% O (oxygen) | 4 | 50.0% | 63.996/136.956194 × 100% = 46.73%

Mass fraction pie chart