mass fractions of manganese(II) perchlorate hexahydrate

manganese(II) perchlorate hexahydrate | elemental composition

Find the elemental composition for manganese(II) perchlorate hexahydrate 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: Cl_2H_12MnO_14 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 Cl (chlorine) | 2 H (hydrogen) | 12 Mn (manganese) | 1 O (oxygen) | 14 N_atoms = 2 + 12 + 1 + 14 = 29 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 Cl (chlorine) | 2 | 2/29 H (hydrogen) | 12 | 12/29 Mn (manganese) | 1 | 1/29 O (oxygen) | 14 | 14/29 Check: 2/29 + 12/29 + 1/29 + 14/29 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Cl (chlorine) | 2 | 2/29 × 100% = 6.90% H (hydrogen) | 12 | 12/29 × 100% = 41.4% Mn (manganese) | 1 | 1/29 × 100% = 3.45% O (oxygen) | 14 | 14/29 × 100% = 48.3% 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 Cl (chlorine) | 2 | 6.90% | 35.45 H (hydrogen) | 12 | 41.4% | 1.008 Mn (manganese) | 1 | 3.45% | 54.938044 O (oxygen) | 14 | 48.3% | 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 Cl (chlorine) | 2 | 6.90% | 35.45 | 2 × 35.45 = 70.90 H (hydrogen) | 12 | 41.4% | 1.008 | 12 × 1.008 = 12.096 Mn (manganese) | 1 | 3.45% | 54.938044 | 1 × 54.938044 = 54.938044 O (oxygen) | 14 | 48.3% | 15.999 | 14 × 15.999 = 223.986 m = 70.90 u + 12.096 u + 54.938044 u + 223.986 u = 361.920044 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 Cl (chlorine) | 2 | 6.90% | 70.90/361.920044 H (hydrogen) | 12 | 41.4% | 12.096/361.920044 Mn (manganese) | 1 | 3.45% | 54.938044/361.920044 O (oxygen) | 14 | 48.3% | 223.986/361.920044 Check: 70.90/361.920044 + 12.096/361.920044 + 54.938044/361.920044 + 223.986/361.920044 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Cl (chlorine) | 2 | 6.90% | 70.90/361.920044 × 100% = 19.59% H (hydrogen) | 12 | 41.4% | 12.096/361.920044 × 100% = 3.342% Mn (manganese) | 1 | 3.45% | 54.938044/361.920044 × 100% = 15.18% O (oxygen) | 14 | 48.3% | 223.986/361.920044 × 100% = 61.89%

Mass fraction pie chart