Question 24.2: A wastewater stream is contaminated with 200 mg/L of dissolv......
A wastewater stream is contaminated with 200 mg/L of dissolved trichloroethylene (TCE) at 20 C, which is below its solubility limit in water. What are the molar concentration (in SI units) and the mole fraction of TCE in the wastewater, assuming a dilute solution? At 20 C, the mass transfer of liquid water is 998.2 kg/m³ (Appendix I). The molecular weight of the TCE is 131.4 g/gmole, and the molecular weight of water is 18 g/gmole (18 kg/kgmole).
Let species A represent TCE (solute) and species B represent water (solvent). The molar concentration of TCE in the wastewater (c_{A}) is determined from the mass concentration (\rho_{A}):
c_{A}=\frac{\rho_{A}}{M_{A}}=\frac{200\;\mathrm{mg}\;\mathrm{A}/\mathrm{L}}{131.4\;\mathrm{g/gmole}} \frac{1\ g}{1000\ mg} \frac{1\,\mathrm{kgmole}}{1000\,\mathrm{gmole}}\frac{1000\,\mathrm{L}}{1\,\mathrm{m^{3}}}=1.52\times10^{-3}\frac{\mathrm{kgmole}}{\mathrm{m^{3}}}
For a dilute solution of TCE (solute A) in water (solvent B), the total molar concentration approximates the molar concentration of the solvent:
c\cong c_{B}={\frac{\rho_{B}}{M_{B}}}={\frac{998.3\,{\mathrm{kg/m}}^{3}}{18\,{\mathrm{kg/kgmole}}}}=55.5{\frac{{\mathrm{kgmole}}}{{\mathrm{m}}^{3}}}
and so the mole fraction (x_{A}) is
x_{A}={\frac{c_{A}}{c}}={\frac{1.52\times10^{-3}\,\,{\mathrm{kgmole/m}}^{3}}{55.5\,{\mathrm{kgmole}}/{\mathrm{m}}^{3}}}=2.74\times10^{-5}