mass fractions of cyanamide

cyanamide | elemental composition

Find the elemental composition for cyanamide 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: NCNH_2 Use the chemical formula, NCNH_2, to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms: | number of atoms C (carbon) | 1 H (hydrogen) | 2 N (nitrogen) | 2 N_atoms = 1 + 2 + 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 C (carbon) | 1 | 1/5 H (hydrogen) | 2 | 2/5 N (nitrogen) | 2 | 2/5 Check: 1/5 + 2/5 + 2/5 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 1 | 1/5 × 100% = 20.0% H (hydrogen) | 2 | 2/5 × 100% = 40.0% N (nitrogen) | 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 C (carbon) | 1 | 20.0% | 12.011 H (hydrogen) | 2 | 40.0% | 1.008 N (nitrogen) | 2 | 40.0% | 14.007 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 | 20.0% | 12.011 | 1 × 12.011 = 12.011 H (hydrogen) | 2 | 40.0% | 1.008 | 2 × 1.008 = 2.016 N (nitrogen) | 2 | 40.0% | 14.007 | 2 × 14.007 = 28.014 m = 12.011 u + 2.016 u + 28.014 u = 42.041 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 | 20.0% | 12.011/42.041 H (hydrogen) | 2 | 40.0% | 2.016/42.041 N (nitrogen) | 2 | 40.0% | 28.014/42.041 Check: 12.011/42.041 + 2.016/42.041 + 28.014/42.041 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 1 | 20.0% | 12.011/42.041 × 100% = 28.57% H (hydrogen) | 2 | 40.0% | 2.016/42.041 × 100% = 4.795% N (nitrogen) | 2 | 40.0% | 28.014/42.041 × 100% = 66.63%

Mass fraction pie chart