mass fractions of nitromethane

nitromethane | elemental composition

Find the elemental composition for nitromethane 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: CH_3NO_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 C (carbon) | 1 H (hydrogen) | 3 N (nitrogen) | 1 O (oxygen) | 2 N_atoms = 1 + 3 + 1 + 2 = 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 C (carbon) | 1 | 1/7 H (hydrogen) | 3 | 3/7 N (nitrogen) | 1 | 1/7 O (oxygen) | 2 | 2/7 Check: 1/7 + 3/7 + 1/7 + 2/7 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 1 | 1/7 × 100% = 14.3% H (hydrogen) | 3 | 3/7 × 100% = 42.9% N (nitrogen) | 1 | 1/7 × 100% = 14.3% O (oxygen) | 2 | 2/7 × 100% = 28.6% 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 | 14.3% | 12.011 H (hydrogen) | 3 | 42.9% | 1.008 N (nitrogen) | 1 | 14.3% | 14.007 O (oxygen) | 2 | 28.6% | 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 | 14.3% | 12.011 | 1 × 12.011 = 12.011 H (hydrogen) | 3 | 42.9% | 1.008 | 3 × 1.008 = 3.024 N (nitrogen) | 1 | 14.3% | 14.007 | 1 × 14.007 = 14.007 O (oxygen) | 2 | 28.6% | 15.999 | 2 × 15.999 = 31.998 m = 12.011 u + 3.024 u + 14.007 u + 31.998 u = 61.040 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 | 14.3% | 12.011/61.040 H (hydrogen) | 3 | 42.9% | 3.024/61.040 N (nitrogen) | 1 | 14.3% | 14.007/61.040 O (oxygen) | 2 | 28.6% | 31.998/61.040 Check: 12.011/61.040 + 3.024/61.040 + 14.007/61.040 + 31.998/61.040 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 1 | 14.3% | 12.011/61.040 × 100% = 19.68% H (hydrogen) | 3 | 42.9% | 3.024/61.040 × 100% = 4.954% N (nitrogen) | 1 | 14.3% | 14.007/61.040 × 100% = 22.95% O (oxygen) | 2 | 28.6% | 31.998/61.040 × 100% = 52.42%

Mass fraction pie chart