Anerobic digestion is a process in which organic wastewater solids are converted
ID: 951896 • Letter: A
Question
Anerobic digestion is a process in which organic wastewater solids are converted to gases, primarily methane and carbon dioxide (CO2(g)). The CO2 concentration in the gas phase of an anaerobic digester is measured to be .28 atm. Assume the following equilibrium holds between dissolved CO2 (as H2CO3*) and CO2 in the gas phase (as described in the reaction below).
a. If the total pressure in the digester is 1 atm, what is the CO2 concentration in the gas in ppm?
b. What is the CO2 concentration in the gas in mg/m3? Assume the temperature is 25 oC.
c. If the gas in the digester is in equilibrium with the digester water, what is the concentration of H2CO3* (formula weight = 62 g/mol) in the digester water in M and in mg/L.
Explanation / Answer
(a): Partial pressure of CO2 = 0.28
=> mole fraction of CO2 = 0.28
Hence concentration of CO2 in ppm(molecules of CO2 per million molecules of the gas)
= 0.28 x 106 ppm = 280000 ppm (answer)
(b): moles of gas equivalent to 1 million(10^6) molecules = 106 / 6.023x1023 = 1.66x10-18 mol
Hence volume of gas occupied by 1 million(10^6) molecules
= nRT/P = 1.66x10-18 mol x 0.0821 L.atmmol-1K-1x298K / 1 atm = 4.06x10-17 L = 4.06x10-20 m3
Moles of CO2 in 4.06x10-20 m3 of gas = 280000 CO2 molecule / 6.023x1023 = 4.65x10-19 mol
Hence concentration of CO2 in mol/m3 = 4.65x10-19 mol / 4.06x10-20 m3 = 11.45 mol/m3
Hence concentration of CO2 in g/m3 = 11.45 mol x 44 g/mol/m3 = 504 g/m3
Hence concentration of CO2 in mg/m3 = 504 g x (1000 mg/g)/m3 = 504000 mg/m3 (answer)
(c): Applying Henry's law
KH(CO2) = P(CO2) / Caq
=> Caq = P(CO2) / KH(CO2) = 0.28 atm / 31.6 atm-L/mol = 0.008861 mol/L = 0.00886 M (answer)
molecular mass of H2CO3 = 62 g/mol
=> concentration in terms of mg/L = 0.00886 mol x 62 g/mol/L = 0.549 mg/L (amswer)