element mass fraction of magnesium phosphate

magnesium phosphate | elemental composition

Find the elemental composition for magnesium phosphate 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: MgHPO_4·3H_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) | 1 Mg (magnesium) | 1 O (oxygen) | 4 P (phosphorus) | 1 N_atoms = 1 + 1 + 4 + 1 = 7 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) | 1 | 1/7 Mg (magnesium) | 1 | 1/7 O (oxygen) | 4 | 4/7 P (phosphorus) | 1 | 1/7 Check: 1/7 + 1/7 + 4/7 + 1/7 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent H (hydrogen) | 1 | 1/7 × 100% = 14.3% Mg (magnesium) | 1 | 1/7 × 100% = 14.3% O (oxygen) | 4 | 4/7 × 100% = 57.1% P (phosphorus) | 1 | 1/7 × 100% = 14.3% 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) | 1 | 14.3% | 1.008 Mg (magnesium) | 1 | 14.3% | 24.305 O (oxygen) | 4 | 57.1% | 15.999 P (phosphorus) | 1 | 14.3% | 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) | 1 | 14.3% | 1.008 | 1 × 1.008 = 1.008 Mg (magnesium) | 1 | 14.3% | 24.305 | 1 × 24.305 = 24.305 O (oxygen) | 4 | 57.1% | 15.999 | 4 × 15.999 = 63.996 P (phosphorus) | 1 | 14.3% | 30.973761998 | 1 × 30.973761998 = 30.973761998 m = 1.008 u + 24.305 u + 63.996 u + 30.973761998 u = 120.282761998 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) | 1 | 14.3% | 1.008/120.282761998 Mg (magnesium) | 1 | 14.3% | 24.305/120.282761998 O (oxygen) | 4 | 57.1% | 63.996/120.282761998 P (phosphorus) | 1 | 14.3% | 30.973761998/120.282761998 Check: 1.008/120.282761998 + 24.305/120.282761998 + 63.996/120.282761998 + 30.973761998/120.282761998 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent H (hydrogen) | 1 | 14.3% | 1.008/120.282761998 × 100% = 0.8380% Mg (magnesium) | 1 | 14.3% | 24.305/120.282761998 × 100% = 20.21% O (oxygen) | 4 | 57.1% | 63.996/120.282761998 × 100% = 53.20% P (phosphorus) | 1 | 14.3% | 30.973761998/120.282761998 × 100% = 25.75%

Mass fraction pie chart