Chapter 3.9, Problem 10P

(A)

Interpretation Introduction

Interpretation:

The mass of ammonia required to produce the biomass.

Concept Introduction:

The molecular weight of biomass mixture:

$\text{MW}=\text{4C+7H+2O+N}$

Here, carbon is $\text{C}$, hydrogen is $\text{H}$, oxygen is $\text{O}$, and nitrogen is $\text{N}$.

The amount of nitrogen present in $5000\text{ L}$ of broth:

${\text{N}}_{\text{T}}=\frac{V_B\times {\text{M}}_{\text{B}}}{{\text{MW}}_{\text{B}}}$

Here, mass of biomass is ${\text{M}}_{\text{B}}$ and total volume of broth is $V_B$.

The expression for the mass of ammonia required to produce the biomass.

${\text{M}}_{\text{N}}=\left({\text{N}}_{\text{T}}\right)\left({\text{MW}}_{{\text{NH}}_{\text{3}}}\right)$

Here, molecular weight of ammonia is ${\text{MW}}_{{\text{NH}}_{\text{3}}}$.

(B)

Interpretation Introduction

Interpretation:

Determine the mass of the glucose was required to produce biomass.

Concept Introduction:

The mass of glucose required to produce the biomass:

${\text{M}}_{\text{G}}\text{=}\left({\text{MW}}_{\text{G}}\right)\left({\text{N}}_{\text{G}}\right)$

Here, molecular weight of glucose is ${\text{MW}}_{\text{G}}$.

The expression to obtain the total number of moles of glucose required.

${\text{N}}_{\text{G}}={\text{N}}_{\text{T}}\left(\frac{4\text{mol}\text{C}}{1\text{mol}\text{biomass}}\right)\left(\frac{1\text{mol}\text{biomass}}{6\text{mol}\text{C}}\right)$

(C)

Interpretation Introduction

Interpretation:

Determine the mass of the byproduct and propose the balanced chemical reaction.

Concept Introduction:

The expression for total mass of the reaction system:

$\begin{array}{l}{M}_{initial}=M_{final}\\ M_{ammonia}+M_{glu\cos e}=M_{biomass}+M_{byproduct}\end{array}$

Here, mass of byproduct is $M_{byproduct}$.