mass fractions of perchloric acid

perchloric acid | elemental composition

Find the elemental composition for perchloric acid 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: HClO_4 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) | 1 H (hydrogen) | 1 O (oxygen) | 4 N_atoms = 1 + 1 + 4 = 6 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) | 1 | 1/6 H (hydrogen) | 1 | 1/6 O (oxygen) | 4 | 4/6 Check: 1/6 + 1/6 + 4/6 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent Cl (chlorine) | 1 | 1/6 × 100% = 16.7% H (hydrogen) | 1 | 1/6 × 100% = 16.7% O (oxygen) | 4 | 4/6 × 100% = 66.7% 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 Cl (chlorine) | 1 | 16.7% | 35.45 H (hydrogen) | 1 | 16.7% | 1.008 O (oxygen) | 4 | 66.7% | 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) | 1 | 16.7% | 35.45 | 1 × 35.45 = 35.45 H (hydrogen) | 1 | 16.7% | 1.008 | 1 × 1.008 = 1.008 O (oxygen) | 4 | 66.7% | 15.999 | 4 × 15.999 = 63.996 m = 35.45 u + 1.008 u + 63.996 u = 100.454 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) | 1 | 16.7% | 35.45/100.454 H (hydrogen) | 1 | 16.7% | 1.008/100.454 O (oxygen) | 4 | 66.7% | 63.996/100.454 Check: 35.45/100.454 + 1.008/100.454 + 63.996/100.454 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent Cl (chlorine) | 1 | 16.7% | 35.45/100.454 × 100% = 35.29% H (hydrogen) | 1 | 16.7% | 1.008/100.454 × 100% = 1.003% O (oxygen) | 4 | 66.7% | 63.996/100.454 × 100% = 63.71%

Mass fraction pie chart