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Chapter 5: Problem 111

is an intermediate step in the conversion of the nitrogen in organic compounds into nitrate ions. What mass of bacterial tissue is produced in a treatment plant for every \(1.0 \times 10^{4} \mathrm{kg}\) of wastewater containing \(3.0 \% \mathrm{NH}_{4}^{+}\) ions by mass? Assume that \(95 \%\) of the ammonium ions are consumed by the bacteria.

Short Answer

Expert verified
The mass of bacterial tissue produced in the treatment plant for every \(1.0 \times 10^{4} kg\) of wastewater containing 3% ammonium ions by mass is \(2.85 \times 10^{2} kg\).

Step by step solution

01

Calculate the mass of ammonium ions in the wastewater

Given, the total mass of wastewater is \(1.0 \times 10^{4} kg\) and it contains 3% of ammonium ions by mass. Let's calculate the mass of ammonium ions in the wastewater. Mass of ammonium ions = (\(\frac{3}{100}\)) x (Total mass of wastewater) Mass of ammonium ions = (\(\frac{3}{100}\)) x (\(1.0 \times 10^{4}\) kg)
02

Calculate the amount of ammonium ions consumed by the bacteria

Now, given that 95% of ammonium ions are consumed by the bacteria. Let's calculate the mass of ammonium ions consumed by the bacteria. Mass of ammonium ions consumed = (\(\frac{95}{100}\)) × (Mass of ammonium ions) Mass of ammonium ions consumed = (\(\frac{95}{100}\)) × (\(\frac{3}{100}\)) x (\(1.0 \times 10^{4}\) kg)
03

Calculate the mass of bacterial tissue produced

The mass of bacterial tissue produced will be equal to the mass of ammonium ions consumed by the bacteria. Therefore, the mass of bacterial tissue is: Mass of bacterial tissue = Mass of ammonium ions consumed Mass of bacterial tissue = (\(\frac{95}{100}\)) × (\(\frac{3}{100}\)) x (\(1.0 \times 10^{4}\) kg) Now, we can simplify this expression: Mass of bacterial tissue = \(0.95 \cdot 0.03 \cdot 1.0 \times 10^{4}\) kg Mass of bacterial tissue = \(2.85 \times 10^{2}\) kg The mass of bacterial tissue produced in the treatment plant for every \(1.0 \times 10^{4} kg\) of wastewater containing 3% ammonium ions by mass is \(2.85 \times 10^{2} kg\).

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