mass fractions of rhodamine B

rhodamine B | elemental composition

Find the elemental composition for rhodamine B 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: C_28H_31N_2O_3Cl 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) | 28 Cl (chlorine) | 1 H (hydrogen) | 31 N (nitrogen) | 2 O (oxygen) | 3 N_atoms = 28 + 1 + 31 + 2 + 3 = 65 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) | 28 | 28/65 Cl (chlorine) | 1 | 1/65 H (hydrogen) | 31 | 31/65 N (nitrogen) | 2 | 2/65 O (oxygen) | 3 | 3/65 Check: 28/65 + 1/65 + 31/65 + 2/65 + 3/65 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 28 | 28/65 × 100% = 43.1% Cl (chlorine) | 1 | 1/65 × 100% = 1.54% H (hydrogen) | 31 | 31/65 × 100% = 47.7% N (nitrogen) | 2 | 2/65 × 100% = 3.08% O (oxygen) | 3 | 3/65 × 100% = 4.62% 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) | 28 | 43.1% | 12.011 Cl (chlorine) | 1 | 1.54% | 35.45 H (hydrogen) | 31 | 47.7% | 1.008 N (nitrogen) | 2 | 3.08% | 14.007 O (oxygen) | 3 | 4.62% | 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) | 28 | 43.1% | 12.011 | 28 × 12.011 = 336.308 Cl (chlorine) | 1 | 1.54% | 35.45 | 1 × 35.45 = 35.45 H (hydrogen) | 31 | 47.7% | 1.008 | 31 × 1.008 = 31.248 N (nitrogen) | 2 | 3.08% | 14.007 | 2 × 14.007 = 28.014 O (oxygen) | 3 | 4.62% | 15.999 | 3 × 15.999 = 47.997 m = 336.308 u + 35.45 u + 31.248 u + 28.014 u + 47.997 u = 479.017 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) | 28 | 43.1% | 336.308/479.017 Cl (chlorine) | 1 | 1.54% | 35.45/479.017 H (hydrogen) | 31 | 47.7% | 31.248/479.017 N (nitrogen) | 2 | 3.08% | 28.014/479.017 O (oxygen) | 3 | 4.62% | 47.997/479.017 Check: 336.308/479.017 + 35.45/479.017 + 31.248/479.017 + 28.014/479.017 + 47.997/479.017 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 28 | 43.1% | 336.308/479.017 × 100% = 70.21% Cl (chlorine) | 1 | 1.54% | 35.45/479.017 × 100% = 7.401% H (hydrogen) | 31 | 47.7% | 31.248/479.017 × 100% = 6.523% N (nitrogen) | 2 | 3.08% | 28.014/479.017 × 100% = 5.848% O (oxygen) | 3 | 4.62% | 47.997/479.017 × 100% = 10.02%

Mass fraction pie chart