Question

The overall stoichiometry for an aerobic cell growth is \( 3C_6H_{12}O_6 + 2.5 NH_3 + O_2 \rightarrow 1.5 C_a H_b O_c N_d + 3 CO_2 + 5 H_2O \).
What is the elemental composition formula of the biomass?

• A. \( C_9 H_{18.2} O_5 N_{1.667} \)
• B. \( C_9 H_{22.33} O_6 N_{1.667} \)
• C. \( C_{10} H_{18.2} O_5 N_{1.667} \)
• D. \( C_{10} H_{22.33} O_6 N_{1.667} \)

Hint:

In stoichiometry for biochemical reactions, balance the elements (C, H, O, N) carefully using the given reaction to determine the composition of the product (biomass).

Answer 1

The Correct Option is D

To find the elemental composition of the biomass, we need to analyze the stoichiometry of the reaction and calculate the proportions of carbon, hydrogen, oxygen, and nitrogen in the biomass (represented by \( C_a H_b O_c N_d \)). 1. Carbon (C): - The glucose (\( C_6H_{12}O_6 \)) contributes 3 moles of carbon atoms per mole of biomass, with 3 moles of glucose involved in the reaction. - The carbon from \( CO_2 \) is released as a byproduct and does not contribute to the biomass. 2. Hydrogen (H): - The hydrogen atoms come from glucose (\( 12 \, \text{H} \) per glucose) and ammonia (\( NH_3 \)), with 2.5 moles of \( NH_3 \). 3. Oxygen (O): - Oxygen atoms come from glucose, oxygen molecules, and the \( CO_2 \) byproduct. 4. Nitrogen (N): - Nitrogen comes from ammonia (\( NH_3 \)) in the reaction, contributing nitrogen to the biomass. By balancing the reaction and applying the stoichiometry, we calculate the elemental composition of the biomass: - \( C_{10} H_{22.33} O_6 N_{1.667} \) Thus, the correct elemental composition formula of the biomass is (D).