mass fractions of magnesium hydroxide

magnesium hydroxide | elemental composition

Find the elemental composition for magnesium hydroxide 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: Mg(OH)_2 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) | 2 Mg (magnesium) | 1 O (oxygen) | 2 N_atoms = 2 + 1 + 2 = 5 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) | 2 | 2/5 Mg (magnesium) | 1 | 1/5 O (oxygen) | 2 | 2/5 Check: 2/5 + 1/5 + 2/5 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 2 | 2/5 × 100% = 40.0% Mg (magnesium) | 1 | 1/5 × 100% = 20.0% O (oxygen) | 2 | 2/5 × 100% = 40.0% 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 H (hydrogen) | 2 | 40.0% | 1.008 Mg (magnesium) | 1 | 20.0% | 24.305 O (oxygen) | 2 | 40.0% | 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 H (hydrogen) | 2 | 40.0% | 1.008 | 2 × 1.008 = 2.016 Mg (magnesium) | 1 | 20.0% | 24.305 | 1 × 24.305 = 24.305 O (oxygen) | 2 | 40.0% | 15.999 | 2 × 15.999 = 31.998 m = 2.016 u + 24.305 u + 31.998 u = 58.319 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) | 2 | 40.0% | 2.016/58.319 Mg (magnesium) | 1 | 20.0% | 24.305/58.319 O (oxygen) | 2 | 40.0% | 31.998/58.319 Check: 2.016/58.319 + 24.305/58.319 + 31.998/58.319 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 2 | 40.0% | 2.016/58.319 × 100% = 3.457% Mg (magnesium) | 1 | 20.0% | 24.305/58.319 × 100% = 41.68% O (oxygen) | 2 | 40.0% | 31.998/58.319 × 100% = 54.87%

Mass fraction pie chart