mass fractions of lithium cobalt(III) oxide

lithium cobalt(III) oxide | elemental composition

Find the elemental composition for lithium cobalt(III) oxide 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: CoLiO_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 Co (cobalt) | 1 Li (lithium) | 1 O (oxygen) | 2 N_atoms = 1 + 1 + 2 = 4 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 Co (cobalt) | 1 | 1/4 Li (lithium) | 1 | 1/4 O (oxygen) | 2 | 2/4 Check: 1/4 + 1/4 + 2/4 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Co (cobalt) | 1 | 1/4 × 100% = 25.0% Li (lithium) | 1 | 1/4 × 100% = 25.0% O (oxygen) | 2 | 2/4 × 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 Co (cobalt) | 1 | 25.0% | 58.933194 Li (lithium) | 1 | 25.0% | 6.94 O (oxygen) | 2 | 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 Co (cobalt) | 1 | 25.0% | 58.933194 | 1 × 58.933194 = 58.933194 Li (lithium) | 1 | 25.0% | 6.94 | 1 × 6.94 = 6.94 O (oxygen) | 2 | 50.0% | 15.999 | 2 × 15.999 = 31.998 m = 58.933194 u + 6.94 u + 31.998 u = 97.871194 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 Co (cobalt) | 1 | 25.0% | 58.933194/97.871194 Li (lithium) | 1 | 25.0% | 6.94/97.871194 O (oxygen) | 2 | 50.0% | 31.998/97.871194 Check: 58.933194/97.871194 + 6.94/97.871194 + 31.998/97.871194 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Co (cobalt) | 1 | 25.0% | 58.933194/97.871194 × 100% = 60.22% Li (lithium) | 1 | 25.0% | 6.94/97.871194 × 100% = 7.09% O (oxygen) | 2 | 50.0% | 31.998/97.871194 × 100% = 32.69%

Mass fraction pie chart