mass fractions of sodium bicarbonate

sodium bicarbonate | elemental composition

Find the elemental composition for sodium bicarbonate 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: NaHCO_3 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 C (carbon) | 1 H (hydrogen) | 1 Na (sodium) | 1 O (oxygen) | 3 N_atoms = 1 + 1 + 1 + 3 = 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 C (carbon) | 1 | 1/6 H (hydrogen) | 1 | 1/6 Na (sodium) | 1 | 1/6 O (oxygen) | 3 | 3/6 Check: 1/6 + 1/6 + 1/6 + 3/6 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 1 | 1/6 × 100% = 16.7% H (hydrogen) | 1 | 1/6 × 100% = 16.7% Na (sodium) | 1 | 1/6 × 100% = 16.7% O (oxygen) | 3 | 3/6 × 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 C (carbon) | 1 | 16.7% | 12.011 H (hydrogen) | 1 | 16.7% | 1.008 Na (sodium) | 1 | 16.7% | 22.98976928 O (oxygen) | 3 | 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 C (carbon) | 1 | 16.7% | 12.011 | 1 × 12.011 = 12.011 H (hydrogen) | 1 | 16.7% | 1.008 | 1 × 1.008 = 1.008 Na (sodium) | 1 | 16.7% | 22.98976928 | 1 × 22.98976928 = 22.98976928 O (oxygen) | 3 | 50.0% | 15.999 | 3 × 15.999 = 47.997 m = 12.011 u + 1.008 u + 22.98976928 u + 47.997 u = 84.00576928 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 C (carbon) | 1 | 16.7% | 12.011/84.00576928 H (hydrogen) | 1 | 16.7% | 1.008/84.00576928 Na (sodium) | 1 | 16.7% | 22.98976928/84.00576928 O (oxygen) | 3 | 50.0% | 47.997/84.00576928 Check: 12.011/84.00576928 + 1.008/84.00576928 + 22.98976928/84.00576928 + 47.997/84.00576928 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 1 | 16.7% | 12.011/84.00576928 × 100% = 14.30% H (hydrogen) | 1 | 16.7% | 1.008/84.00576928 × 100% = 1.200% Na (sodium) | 1 | 16.7% | 22.98976928/84.00576928 × 100% = 27.37% O (oxygen) | 3 | 50.0% | 47.997/84.00576928 × 100% = 57.14%

Mass fraction pie chart