GATE 2020 BT Q.19: solution and answer

GATE 2020 · BTQ.19 · 1 mark · NAT

The elemental composition of dry biomass of a yeast species is $CH_{1.6} O_{0.4} N_{0.2} S_{0.0024} P_{0.017}$ . The contribution of carbon to the dry biomass is ________ % (round off to 2 decimal places).

[Given: atomic weights of H, C, N, O, P and S are 1, 12, 14, 16, 31 and 32, respectively]

See the question in the paper

Tap to open full size

Answer and solution

ANSWER

Carbon makes up 51.27 % of the dry biomass by mass (12 g of carbon in a C-mole weight of 23.4038 g).

Official answer: 51.01 to 52.99Source: Official answer key, GATE 2020 BT (IIT Delhi)

The formula is written per C-mole: it contains exactly one carbon atom, so one C-mole of biomass contains $1 \times 12 = 12 g$ of carbon.
Mass of every other element in one C-mole (subscript $\times$ atomic weight): $H : 1.6 \times 1 = 1.6$ , $O : 0.4 \times 16 = 6.4$ , $N : 0.2 \times 14 = 2.8$ , $S : 0.0024 \times 32 = 0.0768$ , $P : 0.017 \times 31 = 0.527$ (all in g).
C-mole weight of the biomass (the mass of biomass that contains one mole of carbon): $M_{C-mol} = 12 + 1.6 + 6.4 + 2.8 + 0.0768 + 0.527 = 23.4038 g (C-mol)^{- 1}$
Mass percentage of carbon in the dry biomass: $w_{C} = \frac{12}{23.4038} \times 100 = 51.274 % \approx 51.27 %$
No ash content is given, so the dry biomass is taken to be exactly the stated formula and nothing is added to the denominator.

KEY IDEA

A biomass formula normalised to one carbon atom gives the C-mole weight when each subscript is multiplied by its atomic weight and the results are added. The carbon mass fraction is then 12 divided by that C-mole weight.

WATCH OUT FOR

Dropping the small S and P terms, or leaving out carbon's own 12 g from the denominator. Dropping S and P gives 12/22.8 = 52.63 %, which still falls inside the key range but does not answer the question as it was asked. Another mistake is to use atom counts in place of masses, which gives 1/3.2194 = 31.06 %.

From the GATE 2020 BT paper. Every question of this paper · Download the full paper · All 24 Growth kinetics questions, with notes

GATE 2020 BT Q.19: solution and answer

Answer and solution

More Growth kinetics questions