GATE 2022 BT – Question 62
Aerobic yeast has growth rate $0.5\ \mathrm{h^{-1}}$ and stoichiometry $2C_6H_{12}O_6+0.2NH_3+10.35O_2\to CH_{1.8}O_{0.5}N_{0.2}+0.2C_2H_6O+10.6CO_2+10.8H_2O$. Combustion heats (kJ/mol) are glucose 2802, ammonia 383, biomass 560 and ethanol 1366, relative to $CO_2,H_2O,O_2,N_2$. Specific heat production (kJ/(mol h), nearest integer) is ___________.
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Correct answer: 2424
Explanation
The heat released by the culture is the difference between the heat of combustion of the reactants and that of the products (all relative to $CO_2$, $H_2O$, $O_2$ and $N_2$).
**Step 1: heat per mole of biomass formed.** The stoichiometry produces one mole of biomass $CH_{1.8}O_{0.5}N_{0.2}$ from 2 mol of glucose and 0.2 mol of ammonia, and also 0.2 mol of ethanol:
$$Q=\left(2\times2802+0.2\times383\right)-\left(560+0.2\times1366\right)$$
$$Q=5604+76.6-560-273.2=4847.4\text{ kJ per mol biomass}.$$
**Step 2: specific heat production rate.** Multiply by the specific growth rate $\mu=0.5\ \text{h}^{-1}$:
$$q=\mu\,Q=0.5\times4847.4=2423.7\approx\mathbf{2424\ kJ\,mol^{-1}h^{-1}}.$$