mass fractions of uranium peroxide dihydrate

uranium peroxide dihydrate | elemental composition

Find the elemental composition for uranium peroxide dihydrate 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: UO_4·2H_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 H (hydrogen) | 4 O (oxygen) | 6 U (uranium) | 1 N_atoms = 4 + 6 + 1 = 11 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 H (hydrogen) | 4 | 4/11 O (oxygen) | 6 | 6/11 U (uranium) | 1 | 1/11 Check: 4/11 + 6/11 + 1/11 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 4 | 4/11 × 100% = 36.4% O (oxygen) | 6 | 6/11 × 100% = 54.5% U (uranium) | 1 | 1/11 × 100% = 9.09% 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 H (hydrogen) | 4 | 36.4% | 1.008 O (oxygen) | 6 | 54.5% | 15.999 U (uranium) | 1 | 9.09% | 238.02891 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 H (hydrogen) | 4 | 36.4% | 1.008 | 4 × 1.008 = 4.032 O (oxygen) | 6 | 54.5% | 15.999 | 6 × 15.999 = 95.994 U (uranium) | 1 | 9.09% | 238.02891 | 1 × 238.02891 = 238.02891 m = 4.032 u + 95.994 u + 238.02891 u = 338.05491 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 H (hydrogen) | 4 | 36.4% | 4.032/338.05491 O (oxygen) | 6 | 54.5% | 95.994/338.05491 U (uranium) | 1 | 9.09% | 238.02891/338.05491 Check: 4.032/338.05491 + 95.994/338.05491 + 238.02891/338.05491 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 4 | 36.4% | 4.032/338.05491 × 100% = 1.193% O (oxygen) | 6 | 54.5% | 95.994/338.05491 × 100% = 28.40% U (uranium) | 1 | 9.09% | 238.02891/338.05491 × 100% = 70.41%

Mass fraction pie chart