Question

Bacterial digestion is an economical method of sewage treatment. The reaction

$$\begin{gathered} {\text{5CO}}_{\text{2}}\text{(g) + 55N}{{\text{H}}_{\text{4}}}^{\text{+}}{\text{(aq) + 76O}}_{\text{2}}\text{(g)}\stackrel{Bacteria}{\to }{\text{C}}_5{\text{H}}_7{\text{O}}_2{{\text{N(s) + 54NO}}_2}^{\text{-}}{\text{(aq)52H}}_2{\text{O(I)+109H}}^{+}\text{(aq)} \\ BacterialTissue \end{gathered}$$

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${\text{1.0×10}}^4\text{kg}$of wastewater containing${\text{3.0\% NH}}_{\text{4}}^{\text{+}}$ions by mass? Assume that 95% of the ammonium ions are consumed by the bacteria.

Short answer

Therefore, $\text{32.53kg}$ is the mass of bacterial tissue produced.

Step-by-step solution

Definition of mass

Mass is expressed in grams (g) and kilograms (kg). Mass can also be thought of as a feature of stuff that causes it to resist acceleration. The greater an object's mass, the more difficult it is to accelerate it.

Write the formula of mass of substance

The mass of a substance can be estimated using the number of moles present and the molar mass of the substance.

$Massofsubs\tan ce=(numberofmoles)\times (molarmassofthesubs\tan ce)$

Calculate  MolesNH4 + 

The mass of the wastewater is equal to ${\text{1.0×10}}^4\text{kg}$.

In water, the mass proportion of ${\text{NH}}_{\text{4}}^{\text{+}}$$\text{3.0 \%}$ .

The mass percentage is calculated by dividing the mass of a component by the total mass of the combination and multiplying the result by $100\%$.

Mass $\%\left({\text{NH}}_4^{+}\right)=\frac{\text{Mass}\left({\text{NH}}_4^{+}\right)}{\text{Massofwastewater}}\text{×100}$

As a result, the mass of ${\text{NH}}_{\text{4}}^{\text{+}}$ions is:

Mass $\left({\text{NH}}_4^{+}\right){\text{=1.0×10}}^4\text{kg×}\frac{\text{3.0}}{\text{100}}$

$\text{Mass}\left({\text{NH}}_4^{+}\right){\text{=300kg=3×10}}^5\text{g}$

The mass of${\text{NH}}_4^{+}$and the molar mass of${\text{NH}}_4^{+}$can be used to compute the moles of the${\text{NH}}_4^{+}$.

$$\begin{gathered} \text{Moles}\left({\text{NH}}_4^{+}\right)=\frac{{\text{massofNH}}_4^{+}}{{\text{molarmassofNH}}_4^{+}} \\ \text{Moles}\left({\text{NH}}_4^{+}\right)=\frac{{\text{3×10}}^{5}g}{\text{18g/mol}} \\ \text{Moles}\left({\text{NH}}_4^{+}\right){\text{=1.67×10}}^4\text{mol} \end{gathered}$$

Write reaction of bacterial digestion

According to the textbook's data, the bacteria use${\text{95\% NH}}_{\text{4}}^{\text{+}}$.

The amount of moles of${\text{NH}}_4^{+}$consumed by bacteria is equivalent todata-custom-editor="chemistry" ${\text{0.95×1.67×10}}^4\text{mol}$, or${\text{1.58×10}}^4\text{mol}$. The bacterial digestive reaction is given below.

${\text{5CO}}_2\left(g\right){\text{+55NH}}_4^{+}\left(\text{aq}\right){\text{+76O}}_2\left(g\right)\to C_5{H}_7\text{N}\left(s\right){\text{+54NO}}_2^{-}\left(\text{aq}\right){\text{+52H}}_{2}O\left(l\right){\text{+109H}}^{+}\left(\text{aq}\right)$

Calculate moles of bacterial tissue

According to the given reaction, 55 moles of ${\text{NH}}_4^{+}$ions create one mole of bacterial tissue $\left(C_5{H}_7\text{N}\right)$.

$\frac{{\text{moles of NH}}_{\text{4}}^{\text{+}}}{\text{moles of bacterial tissue}}\text{=}\frac{\text{55}}{\text{1}}$

Bacterial tissue moles $\text{=}\frac{{\text{moles of NH}}_{\text{4}}^{\text{+}}}{\text{55}}$

Bacterial tissue moles $=\frac{{\text{1.58×10}}^4\text{mol}}{\text{55}}$

Bacterial tissue moles $\text{=287.9mol}$

Calculate mass of bacterial tissue

The moles of bacterial tissue are used to calculate the mass of bacterial tissue.

Bacterial tissue mass ${\text{=molesofbacterialtissue×molarmassofC}}_5{H}_7\text{N}$

Bacterial tissue mass$\text{=287.9mol×113g/mol}$

Bacterial tissue mass $=32.53kg$

$=32.53kg$ is the mass of bacterial tissue produced.