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GATE 2022 BT – Question 16

Fundamentals of Biological Engineering · Bioreaction Engineering: Kinetics of cell growth, substrate utilization and product formation, structured and unstructured models · 1 mark · Multiple choice

The overall stoichiometry is $3C_6H_{12}O_6+2.5NH_3+O_2\to1.5C_aH_bO_cN_d+3CO_2+5H_2O$. What is the biomass elemental formula?

  1. $C_9H_{18.2}O_5N_{1.667}$
  2. $C_9H_{22.33}O_6N_{1.667}$
  3. $C_{10}H_{18.2}O_5N_{1.667}$
  4. $C_{10}H_{22.33}O_6N_{1.667}$

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Correct answer: (D) $C_{10}H_{22.33}O_6N_{1.667}$

Explanation

Balance each element on both sides of
$$3C_6H_{12}O_6+2.5NH_3+O_2\to1.5\,C_aH_bO_cN_d+3CO_2+5H_2O .$$

**Carbon:** left $3\times6=18$; right $1.5a+3$.
$$1.5a=15\;\Rightarrow\;a=10 .$$

**Hydrogen:** left $3\times12+2.5\times3=36+7.5=43.5$; right $1.5b+5\times2=1.5b+10$.
$$1.5b=33.5\;\Rightarrow\;b=22.33 .$$

**Oxygen:** left $3\times6+2=20$; right $1.5c+3\times2+5=1.5c+11$.
$$1.5c=9\;\Rightarrow\;c=6 .$$

**Nitrogen:** left $2.5$; right $1.5d$.
$$d=\frac{2.5}{1.5}=1.667 .$$

Biomass formula: $C_{10}H_{22.33}O_6N_{1.667}$ (option **D**).