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GATE 2026 BT – Question 40

Fundamentals of Biological Engineering · Bioreaction Engineering: Kinetics of cell growth, substrate utilization and product formation, structured and unstructured models · 2 marks · Multiple choice

By elemental analysis of a biomass sample, it was found that the cells in the given sample are composed of (by weight) C=50%, H=8%, O=20%, N=10% and ash content=12%. Which of the following is the correct empirical formula of the ash-free cells, normalized with respect to Nitrogen?

  1. $C_{5.8}H_{11.2}O_{1.7}N$
  2. $C_{5.0}H_{10.2}O_{1.1}N$
  3. $C_{6.8}H_{12.2}O_{2.1}N$
  4. $C_{4.8}H_{9.2}O_{3.1}N$

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Correct answer: (A) $C_{5.8}H_{11.2}O_{1.7}N$

Explanation

The moles per 100 g are $C = \frac{50}{12} = 4.17$, $H = \frac{8}{1} = 8$, $O = \frac{20}{16} = 1.25$ and $N = \frac{10}{14} = 0.714$. Dividing by the nitrogen gives $C = 5.83$, $H = 11.2$, $O = 1.75$, so the formula is about $C_{5.8}H_{11.2}O_{1.7}N$. The ash is left out.