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. How much bacterial tissue is produced in a treatment plant for every 1.0 multiplied by 104 kg of wastewater containing 6.0% NH4+ ions by mass?
HELP?!?!
To find the amount of bacterial tissue produced in the treatment plant, we need to determine the number of moles of NH4+ ions in the wastewater and then use the mole ratios from the balanced equation to find the moles of bacterial tissue produced.
Let's break down the steps to solve this problem:
Step 1: Calculate the mass of NH4+ ions in the wastewater.
- We are given that the wastewater contains 6.0% NH4+ ions by mass. This means for every 100 grams of wastewater, we have 6.0 grams of NH4+ ions.
- Since we are given the total mass of wastewater as 1.0 x 10^4 kg, we need to convert it to grams.
1.0 x 10^4 kg x 1000 g/kg = 1.0 x 10^7 g
- Now we can use the mass percent to calculate the mass of NH4+ ions:
Mass of NH4+ ions = (6.0 g / 100 g) x 1.0 x 10^7 g = 6.0 x 10^5 g
Step 2: Convert the mass of NH4+ ions to moles.
- To convert grams to moles, we need the molar mass of NH4+.
- The molar mass of NH4+ = (1 x 14.01 g/mol) + (4 x 1.01 g/mol) = 18.05 g/mol
- Now we can calculate the number of moles of NH4+ ions:
Moles of NH4+ ions = (Mass of NH4+ ions) / (Molar mass of NH4+)
= (6.0 x 10^5 g) / (18.05 g/mol)
≈ 3.32 x 10^4 mol
Step 3: Use the mole ratios from the balanced equation to find the moles of bacterial tissue produced.
- From the balanced equation, the stoichiometric coefficient of NH4+ ions is 55, and the stoichiometric coefficient of bacterial tissue is 54.
- The mole ratio between NH4+ and bacterial tissue is 55:54.
Moles of bacterial tissue produced = (Moles of NH4+ ions) x (54 / 55)
= (3.32 x 10^4 mol) x (54 / 55)
≈ 3.25 x 10^4 mol
Step 4: Convert the moles of bacterial tissue to mass.
- To convert moles to grams, we need the molar mass of bacterial tissue.
- Unfortunately, the empirical formula of bacterial tissue is not given, so we cannot calculate the exact molar mass. However, we can still estimate the molar mass to get an approximate answer. Let's assume a molar mass of approximately 100 g/mol.
- Using the estimated molar mass, we can calculate the mass of bacterial tissue:
Mass of bacterial tissue = (Moles of bacterial tissue produced) x (Estimated molar mass)
= (3.25 x 10^4 mol) x (100 g/mol)
= 3.25 x 10^6 g
Therefore, approximately 3.25 x 10^6 grams (or 3.25 x 10^3 kg) of bacterial tissue is produced in the treatment plant for every 1.0 x 10^4 kg of wastewater containing 6.0% NH4+ ions by mass.