mass fractions of phosphoric acid

phosphoric acid | elemental composition

Find the elemental composition for phosphoric 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: H_3PO_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 H (hydrogen) | 3 O (oxygen) | 4 P (phosphorus) | 1 N_atoms = 3 + 4 + 1 = 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 H (hydrogen) | 3 | 3/8 O (oxygen) | 4 | 4/8 P (phosphorus) | 1 | 1/8 Check: 3/8 + 4/8 + 1/8 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 3 | 3/8 × 100% = 37.5% O (oxygen) | 4 | 4/8 × 100% = 50.0% P (phosphorus) | 1 | 1/8 × 100% = 12.5% 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) | 3 | 37.5% | 1.008 O (oxygen) | 4 | 50.0% | 15.999 P (phosphorus) | 1 | 12.5% | 30.973761998 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) | 3 | 37.5% | 1.008 | 3 × 1.008 = 3.024 O (oxygen) | 4 | 50.0% | 15.999 | 4 × 15.999 = 63.996 P (phosphorus) | 1 | 12.5% | 30.973761998 | 1 × 30.973761998 = 30.973761998 m = 3.024 u + 63.996 u + 30.973761998 u = 97.993761998 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) | 3 | 37.5% | 3.024/97.993761998 O (oxygen) | 4 | 50.0% | 63.996/97.993761998 P (phosphorus) | 1 | 12.5% | 30.973761998/97.993761998 Check: 3.024/97.993761998 + 63.996/97.993761998 + 30.973761998/97.993761998 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 3 | 37.5% | 3.024/97.993761998 × 100% = 3.086% O (oxygen) | 4 | 50.0% | 63.996/97.993761998 × 100% = 65.31% P (phosphorus) | 1 | 12.5% | 30.973761998/97.993761998 × 100% = 31.61%

Mass fraction pie chart