Bacterial digestion is an economical method of sewage treatment.
5CO2(g) + 55NH4+(aq) + 76O2(g) -> 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.
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To solve this problem, we need to use stoichiometry to find the amount of bacterial tissue produced. Let's break down the information given in the question:
Equation: 5CO2(g) + 55NH4+(aq) + 76O2(g) -> C5H7O2N(s) + 54NO2-(aq) + 52H2O(l) + 109H+(aq)
a. The question asks for the amount of bacterial tissue produced in a treatment plant for every 1.0 x 10^4 g of wastewater containing 3.0% NH4+ ions by mass.
Step 1: Calculate the mass of NH4+ ions in the wastewater.
Wastewater mass = 1.0 x 10^4 g
% NH4+ ions = 3.0%
Mass of NH4+ ions = (3.0/100) * 1.0 x 10^4 g
Step 2: Calculate the moles of NH4+ ions.
Molar mass of NH4+ = 14.01 g/mol
Moles of NH4+ ions = Mass of NH4+ ions / Molar mass of NH4+
Step 3: Use stoichiometry to calculate the moles of bacterial tissue produced.
From the balanced equation, we can see that the ratio between NH4+ ions and bacterial tissue is 55:1.
Moles of bacterial tissue = Moles of NH4+ ions / 55
Step 4: Convert moles of bacterial tissue to mass of bacterial tissue.
Molar mass of bacterial tissue = C5H7O2N = 113.12 g/mol
Mass of bacterial tissue = Moles of bacterial tissue * Molar mass of bacterial tissue
b. The question states that 95% of the ammonium ions are consumed by the bacteria.
To calculate this, we will consider the moles of NH4+ ions consumed and multiply it by the molar mass of NH4+ to get the mass:
Step 5: Calculate the moles of NH4+ ions consumed.
Moles of NH4+ ions consumed = 0.95 * Moles of NH4+ ions
Step 6: Convert moles of NH4+ ions consumed to mass.
Mass of NH4+ ions consumed = Moles of NH4+ ions consumed * Molar mass of NH4+
Now, you can apply these steps to solve the problem using the given values.