/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 111 Bacterial digestion is an econom... [FREE SOLUTION] | 91影视

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Bacterial digestion is an economical method of sewage treatment. The reaction \(5 \mathrm{CO}_{2}(g)+55 \mathrm{NH}_{4}^{+}(a q)+76 \mathrm{O}_{2}(g) \stackrel{\text { hacteria }}{\longrightarrow}\) \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{O}_{2} \mathrm{~N}(s)+54 \mathrm{NO}_{2}^{-}(a q)+52 \mathrm{H}_{2} \mathrm{O}(t)+109 \mathrm{H}^{+}(a q)\) bacterial tissue 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
First, find the mass of NH鈧勨伜 ions in the wastewater: \( Mass_{NH_4^+} = (3.0 / 100) \times 1.0 \times 10^7 \,g\). Next, calculate the mass of NH鈧勨伜 ions consumed: \(Mass_{NH_4^+ \, consumed} = (95 / 100) \times Mass_{NH_4^+}\). Convert the mass of consumed NH鈧勨伜 ions to moles: \(n_{NH_4^+} = Mass_{NH_4^+ \, consumed} / 18.05\, g/mol\). Use stoichiometry to find moles of bacterial tissue produced: \(n_{C_3H_7O_2N} = (1\,mol\,C_3H_7O_2N / 55\,mol\,NH_4^+) \times n_{NH_4^+}\). Finally, calculate the mass of bacterial tissue produced: \(Mass_{C_3H_7O_2N} = n_{C_3H_7O_2N} \times 60.07\, g/mol\,C_3H_7O_2N\).

Step by step solution

01

Find the mass of NH鈧勨伜 ions in the wastewater.

Since the wastewater contains 3.0% NH鈧勨伜 ions by mass, we can find the mass of ammonium ions as follows: Total mass of wastewater = 1.0 x 10^4 kg = 1.0 x 10^7 g Mass of NH鈧勨伜 ions = (3.0 / 100) 脳 1.0 x 10^7 g
02

Calculate the mass of NH鈧勨伜 ions consumed by the bacteria.

As we know that 95% of the total NH鈧勨伜 ions are consumed by the bacteria, the mass of NH鈧勨伜 ions consumed can be calculated as: Mass of NH鈧勨伜 ions consumed = (95 / 100) 脳 Mass of NH鈧勨伜 ions
03

Determine the number of moles of NH鈧勨伜 ions consumed.

Now, we need to find the number of moles of NH鈧勨伜 ions consumed, using the following formula: Number of moles = mass / molar mass The molar mass of NH鈧勨伜 ions is equal to the sum of the atomic masses of 1 nitrogen (N) and 4 hydrogen (H) atoms: Molar mass of NH鈧勨伜 ions = 14.01 g/mol (N) + 4 脳 1.01 g/mol (H) = 18.05 g/mol. Number of moles of NH鈧勨伜 ions consumed = Mass of NH鈧勨伜 ions consumed / 18.05 g/mol
04

Use stoichiometry to find the number of moles of bacterial tissue produced.

From the balanced equation, we can see that 55 moles of NH鈧勨伜 ions produce 1 mole of bacterial tissue (C鈧僅鈧嘜鈧侼). Using this stoichiometric ratio, we can find the number of moles of bacterial tissue produced: Number of moles of bacterial tissue = (1 mol C鈧僅鈧嘜鈧侼 / 55 mol NH鈧勨伜 ions) 脳 Number of moles of NH鈧勨伜 ions consumed
05

Calculate the mass of bacterial tissue produced using the molar mass of C鈧僅鈧嘜鈧侼.

The molar mass of bacterial tissue (C鈧僅鈧嘜鈧侼) is equal to the sum of atomic masses of 3 carbon (C), 7 hydrogen (H), 2 oxygen (O), and 1 nitrogen (N) atoms: Molar mass of C鈧僅鈧嘜鈧侼 = 3 脳 12.01 g/mol (C) + 7 脳 1.01 g/mol (H) + 2 脳 16.00 g/mol (O) + 14.01 g/mol (N) = 60.07 g/mol. Now, using the number of moles of bacterial tissue and molar mass, we can find the mass of bacterial tissue produced: Mass of bacterial tissue = Number of moles of bacterial tissue 脳 60.07 g/mol C鈧僅鈧嘜鈧侼 By following these steps, we can find the mass of bacterial tissue produced in a treatment plant for every 1.0 x 10^4 kg of wastewater containing 3.0% NH鈧勨伜 ions by mass, provided that 95% of the ammonium ions are consumed by the bacteria.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Stoichiometric Calculations
Stoichiometry is the heart of chemical reactions, essentially serving as a recipe that allows chemists鈥攁nd environmental engineers working with sewage treatment鈥攖o predict the products and byproducts of a chemical reaction. In the case of bacterial digestion, we deduce how much bacterial biomass, or tissue, can be generated from a given amount of ammonium ions in wastewater.

In our example, the stoichiometric calculation leans on a balanced chemical equation where the coefficients indicate the proportional relationship between reactants and products. This relationship helps us determine how moles of one substance (ammonium ions) convert to moles of another (bacterial tissue). With sewage treatment, such precision ensures that the treatment plant operates efficiently, managing resources and predicting the extent of waste treatment.
Molar Mass
Understanding molar mass is crucial in stoichiometric calculations. It is the weight of one mole of a substance, typically measured in grams per mole (g/mol), and can be calculated by summing the atomic masses of all the atoms in a molecule. For instance, the molar mass of the ammonium ion, NH鈧勨伜, is tallied by adding the atomic mass of nitrogen (14.01 g/mol) with four times the atomic mass of hydrogen (4 x 1.01 g/mol), which totals 18.05 g/mol.

Knowing this value is instrumental in converting between mass and moles, a frequent task in stoichiometry, allowing us to pivot from the physical weight of a sampled wastewater to the more abstract but chemically relevant quantity of moles. This step is essential for stoichiometric calculations that lead to figuring out how much bacterial tissue can be produced from ammonium ions.
Bacterial Digestion
Bacterial digestion is a biotechnological marvel wherein bacteria metabolize waste, such as ammonium ions in sewage, transforming pollutants into harmless or even useful substances. These microorganisms act as natural recyclers, turning potential environmental hazards into stable compounds that can be safely reintroduced into the ecosystem.

In sewage treatment, the bacteria's role is pivotal, as they enable the biochemical conversion of wastewater contaminants through metabolic processes into less harmful substances like nitrates, which can then be dealt with safely. This not only purifies the water but also results in the formation of bacterial biomass, which can be studied quantitatively through stoichiometric calculations.
Ammonium Ion Consumption
In wastewater treatment, monitoring the consumption of ammonium ions by bacteria is key to assessing the efficiency of the treatment process. In our scenario, it is estimated that 95% of the ammonium ions in the wastewater are consumed by bacteria, which reflects the efficacy of the bacterial digestion in transforming these ions.

The consumption rate is critical because it directly influences the amount of bacterial tissue produced. With high consumption rates, we can anticipate more biomass generation鈥攁 variable that can be precisely measured using stoichiometry. Therefore, understanding the nuances of ammonium ion consumption can inform the operational parameters of wastewater treatment facilities, leading to optimized processes that better support the environment and public health.

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Most popular questions from this chapter

ABS plastic is a tough, hard plastic used in applications requiring shock resistance. The polymer consists of three monomer units: acrylonitrile \(\left(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{~N}\right)\), butadiene \(\left(\mathrm{C}_{4} \mathrm{H}_{6}\right)\), and styrene \(\left(\mathrm{C}_{8} \mathrm{H}_{8}\right)\). a. A sample of ABS plastic contains \(8.80 \% \mathrm{~N}\) by mass. It took \(0.605 \mathrm{~g}\) of \(\mathrm{Br}_{2}\) to react completely with a \(1.20-\mathrm{g}\) sample of ABS plastic. Bromine reacts \(1: 1\) (by moles) with the butadiene molecules in the polymer and nothing else. What is the percent by mass of acrylonitrile and butadiene in this polymer? b. What are the relative numbers of each of the monomer units in this polymer?

Aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) is synthesized by reacting salicylic acid \(\left(\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}\right)\) with acetic anhydride \(\left(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3}\right)\). The balanced equa- tion is $$ \mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{3}+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3} \longrightarrow \mathrm{C}_{9} \mathrm{H}_{3} \mathrm{O}_{4}+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2} $$ a. What mass of acetic anhydride is needed to completely consume \(1.00 \times 10^{2} \mathrm{~g}\) salicylic acid? b. What is the maximum mass of aspirin (the theoretical yield) that could be produced in this reaction?

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What amount (moles) is represented by each of these samples? a. \(20.0 \mathrm{mg}\) caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2}\) b. \(2.72 \times 10^{21}\) molecules of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) c. \(1.50 \mathrm{~g}\) of dry ice, \(\mathrm{CO}_{2}\)

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