mass fractions of titanium(IV) phthalocyanine dichloride

titanium(IV) phthalocyanine dichloride | elemental composition

Find the elemental composition for titanium(IV) phthalocyanine dichloride 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_32H_16Cl_2N_8Ti 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) | 32 Cl (chlorine) | 2 H (hydrogen) | 16 N (nitrogen) | 8 Ti (titanium) | 1 N_atoms = 32 + 2 + 16 + 8 + 1 = 59 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) | 32 | 32/59 Cl (chlorine) | 2 | 2/59 H (hydrogen) | 16 | 16/59 N (nitrogen) | 8 | 8/59 Ti (titanium) | 1 | 1/59 Check: 32/59 + 2/59 + 16/59 + 8/59 + 1/59 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 32 | 32/59 × 100% = 54.2% Cl (chlorine) | 2 | 2/59 × 100% = 3.39% H (hydrogen) | 16 | 16/59 × 100% = 27.1% N (nitrogen) | 8 | 8/59 × 100% = 13.6% Ti (titanium) | 1 | 1/59 × 100% = 1.69% 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) | 32 | 54.2% | 12.011 Cl (chlorine) | 2 | 3.39% | 35.45 H (hydrogen) | 16 | 27.1% | 1.008 N (nitrogen) | 8 | 13.6% | 14.007 Ti (titanium) | 1 | 1.69% | 47.867 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) | 32 | 54.2% | 12.011 | 32 × 12.011 = 384.352 Cl (chlorine) | 2 | 3.39% | 35.45 | 2 × 35.45 = 70.90 H (hydrogen) | 16 | 27.1% | 1.008 | 16 × 1.008 = 16.128 N (nitrogen) | 8 | 13.6% | 14.007 | 8 × 14.007 = 112.056 Ti (titanium) | 1 | 1.69% | 47.867 | 1 × 47.867 = 47.867 m = 384.352 u + 70.90 u + 16.128 u + 112.056 u + 47.867 u = 631.303 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) | 32 | 54.2% | 384.352/631.303 Cl (chlorine) | 2 | 3.39% | 70.90/631.303 H (hydrogen) | 16 | 27.1% | 16.128/631.303 N (nitrogen) | 8 | 13.6% | 112.056/631.303 Ti (titanium) | 1 | 1.69% | 47.867/631.303 Check: 384.352/631.303 + 70.90/631.303 + 16.128/631.303 + 112.056/631.303 + 47.867/631.303 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 32 | 54.2% | 384.352/631.303 × 100% = 60.88% Cl (chlorine) | 2 | 3.39% | 70.90/631.303 × 100% = 11.23% H (hydrogen) | 16 | 27.1% | 16.128/631.303 × 100% = 2.555% N (nitrogen) | 8 | 13.6% | 112.056/631.303 × 100% = 17.75% Ti (titanium) | 1 | 1.69% | 47.867/631.303 × 100% = 7.582%

Mass fraction pie chart