GATE 2022 BT Q.28: solution and answer

GATE 2022 · BTQ.28 · 1 mark · NAT

A microorganism is grown in a batch culture using glucose as a carbon source. The apparent growth yield is $0.5 \frac{g biomass}{g substrate}$ . The initial concentrations of biomass and substrate are $2 g L^{- 1}$ and $200 g L^{- 1}$ , respectively. Assuming that there is no endogenous metabolism, the maximum biomass concentration that can be achieved is ________ $g L^{- 1}$ .

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Answer and solution

ANSWER

The maximum biomass concentration is $102 g L^{- 1}$ .

Official answer: 102Source: Official answer key, GATE 2022 BT (IIT Kharagpur)

Let $X$ be the biomass concentration and $S$ the substrate (glucose) concentration, both in $g L^{- 1}$ , with initial values $X_{0} = 2 g L^{- 1}$ and $S_{0} = 200 g L^{- 1}$ . The apparent growth yield $Y_{X / S}$ is biomass formed per unit substrate consumed: $Y_{X / S} = \frac{X - X _{0}}{S _{0} - S} = 0.5 \frac{g biomass}{g substrate}$
With no endogenous metabolism, no substrate is diverted to maintenance, so this yield holds unchanged until the end of the batch. Every gram of glucose consumed gives $0.5 g$ of new biomass.
Biomass is therefore highest when all the substrate has been used up ( $S = 0$ ): $X_{ma x} = X_{0} + Y_{X / S} (S_{0} - 0)$
$X_{ma x} = 2 + 0.5 \times 200 = 2 + 100 = 102 g L^{- 1}$

KEY IDEA

The yield $Y_{X / S}$ links the biomass formed to the substrate consumed. With no endogenous (maintenance) metabolism it stays constant, so the most biomass you can get is the inoculum plus the yield times all of the substrate: $X_{ma x} = X_{0} + Y_{X / S} S_{0}$ .

WATCH OUT FOR

Answering $100 g L^{- 1}$ ( $0.5 \times 200$ ) and leaving out the initial biomass $X_{0} = 2 g L^{- 1}$ . The yield gives only the biomass newly formed, not the total. A second slip is using $Y_{X / S}$ as substrate per biomass and getting $400$ .

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GATE 2022 BT Q.28: solution and answer

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