Bacterial digestion is an economical method of sewage treatment. 5CO2(g) + 55NH4+(aq) + 76O2(g) right arrow Bacteria C5H7O2N(s) + 54NO2-(aq) + 52H2O(l) + 109H+(aq) bacterial tissue The above reaction is an intermediate step in the conversion of the nitrogen in organic compounds into nitrate ions. a. How much bacterial tissue is produced in a treatment plant for every 1.0 x 10^4 of wastewater containing 3.0% NH4+ ions by mass? b. Assume that 95% of the ammonium ions are consumed by the bacteria.
sorry, there were some typos in this one..
To determine the amount of bacterial tissue produced in a treatment plant, we need to calculate the moles of bacterial tissue formed and then convert it to grams using the molar mass of bacterial tissue.
a. To find the amount of bacterial tissue produced, we first need to determine the moles of NH4+ ions present in the wastewater.
1. Calculate the mass of NH4+ ions in 1.0 x 10^4 grams of wastewater:
Mass of NH4+ ions = Mass of wastewater x Percentage of NH4+ ions
Mass of NH4+ ions = 1.0 x 10^4 g x 0.03 = 300 g
2. Convert the mass of NH4+ ions to moles:
Moles of NH4+ ions = Mass of NH4+ ions / molar mass of NH4+
The molar mass of NH4+ is:
Molar mass of NH4+ = 1(atomic mass of N) + 4(atomic mass of H)
= 1(14.01 g/mol) + 4(1.01 g/mol)
= 14.01 g/mol + 4.04 g/mol
= 18.05 g/mol
Moles of NH4+ ions = 300 g / 18.05 g/mol
≈ 16.63 mol
3. Use the stoichiometry of the reaction to find the moles of bacterial tissue produced:
From the balanced equation, we can see that 55 NH4+ ions react to form 1 mol of bacterial tissue.
Moles of bacterial tissue = Moles of NH4+ ions / 55
≈ 16.63 mol / 55
≈ 0.30 mol
b. To account for the fact that 95% of the ammonium ions are consumed by the bacteria, we can adjust the calculated moles of bacterial tissue.
Adjusted moles of bacterial tissue = Moles of bacterial tissue x Percentage of NH4+ ions consumed
= 0.30 mol x 0.95
≈ 0.285 mol
Finally, to convert the moles of bacterial tissue to grams, we multiply by the molar mass of bacterial tissue.
Molar mass of bacterial tissue must be given in the question or through further information for us to complete this calculation.