Microbes in Human Welfare Set-6

Q1. Complete anaerobic fermentation of glucose by Saccharomyces follows $C_6H_{12}O_6 \rightarrow 2\,C_2H_5OH + 2\,CO_2$. If $180\ \text{g}$ of glucose is fermented completely, what volume of $CO_2$ (at STP, $1\ \text{mol gas}=22.4\ \text{L}$) will be produced?

Q2. An industrial fermenter of volume $2000\ \text{L}$ initially contains $500\ \text{kg}$ of glucose. After fermentation the ethanol concentration is $12\%$ v/v. Density of ethanol $=0.789\ \text{g mL}^{-1}$. Theoretical yield of ethanol from glucose is $0.51\ \text{g ethanol per g glucose}$. Approximately how much unfermented glucose (in kg) remains at the end?

Q3. A household requires $30\ \text{MJ/day}$ for cooking. A biogas plant produces $1.20\ \text{m}^3$ biogas per day with methane content $60\%$. Calorific value of methane is $35.8\ \text{MJ m}^{-3}$. How much additional biogas (in $\text{m}^3$/day) is required to meet the $30\ \text{MJ}$ demand? (Assume only methane contributes to usable energy.)

Q4. Assertion (A): Application of Azotobacter as a biofertilizer in legume fields increases soil nitrogen more effectively than inoculation with Rhizobium.
Reason (R): Azotobacter fixes atmospheric nitrogen as free-living aerobes, whereas Rhizobium requires root nodule symbiosis; therefore Azotobacter supplies larger net N per hectare.

Q5. A wastewater contains BOD = $1000\ \text{mg L}^{-1}$ and $NH_4^+$–N = $50\ \text{mg L}^{-1}$. For aerobic treatment, nitrification consumes $4.57\ \text{g O}_2$ per g $NH_4^+$–N oxidized, and heterotrophic BOD removal needs $1.5\ \text{g O}_2$ per g BOD removed. If aeration supplies $400\ \text{mg L}^{-1}$ dissolved O$_2$ and complete nitrification is required, what percentage of the initial BOD can be oxidized?

Q6. Complete fermentation of glucose by yeast is represented by $C_6H_{12}O_6 \rightarrow 2C_2H_5OH + 2CO_2$. If $180\ \text{g}$ of glucose is fermented and the process has a mass-yield efficiency of $90\%$, how many grams of ethanol are produced? (Atomic masses: $C=12,\ H=1,\ O=16$)

Q7. A sewage influent has biochemical oxygen demand (BOD) $=400\ \text{mg/L}$. Primary sedimentation reduces BOD by $30\%$. The secondary (activated sludge) unit removes $85\%$ of the BOD entering it. What is the final BOD after secondary treatment, and is tertiary treatment needed if the regulatory discharge limit is $30\ \text{mg/L}$?

Q8. For a disease with basic reproduction number $R_0=5$ and a vaccine efficacy of $80\%$ (i.e., vaccine reduces susceptibility by factor $0.8$), the critical vaccination coverage required to interrupt transmission can be estimated by $p_c=\dfrac{1-1/R_0}{\text{vaccine efficacy}}$. What minimum fraction of the population must be vaccinated?

Q9. A homofermentative Lactobacillus strain (producing mainly lactic acid from hexoses) is switched from glucose feed to an equimolar sucrose feed (sucrose = glucose + fructose) without changing strain or process parameters. Observed outcomes: total lactic acid yield falls, ethanol and $CO_2$ by-products increase, and optical purity of lactic acid decreases. Which explanation best accounts for these observations?

Q10. In a recombinant E. coli culture antibiotic selection is removed. Plasmid segregational loss rate is $s=0.01$ per cell division (each dividing plasmid-bearing cell produces on average $2s$ plasmid-free daughters per division) and plasmid-free cells have a $1\%$ growth advantage (their per-generation multiplication factor is $2\times1.01$ while plasmid-bearing cells multiply by $2\times(1-s)$). If the culture starts with all cells plasmid-bearing, approximately what fraction of the population will retain the plasmid after $10$ generations? (Assume discrete synchronous generations and no back-mutation.)

Q11. A household biogas plant produces $0.5\ \text{m}^3$ of biogas per day composed of $60\%$ CH$_4$ and $40\%$ CO$_2$. Given the calorific value of methane is $35.8\ \text{MJ m}^{-3}$ and CO$_2$ contributes negligible calorific value, estimate the daily usable energy output (MJ/day). Use $E = V_{\text{total}}\times f_{\text{CH}_4}\times CV_{\text{CH}_4}$.

Q12. A bacterial population of $10^{9}$ cells contains resistant mutants at a frequency of $1$ in $10^{6}$. An antibiotic kills $99.9\%$ of susceptible cells each hour (only $0.1\%$ of susceptibles survive per hour); resistant cells are unaffected and double every hour. Approximately what fraction of the population will be resistant after $2$ hours?

Q13. A sewage influent has biochemical oxygen demand (BOD) $=300\ \text{mg L}^{-1}$ and ammonia $=50\ \text{mg L}^{-1}$. Primary treatment removes $30\%$ of BOD and $10\%$ of ammonia. Secondary (activated sludge) treatment subsequently removes $80\%$ of the remaining BOD and $50\%$ of the remaining ammonia. What are the approximate final BOD and ammonia concentrations (in $\text{mg L}^{-1}$) after both stages?

Q14. Assertion (A): In submerged fermentation by Aspergillus niger for industrial citric acid production, maintaining a very low manganese concentration (e.g. $<10^{-6}\ \text{M}$) together with high sugar concentration maximizes citric acid yield.
Reason (R): Low manganese inhibits enzymes such as aconitase in the TCA cycle, reducing conversion of citrate to isocitrate, while excess sugar increases glycolytic flux supplying abundant acetyl-CoA and oxaloacetate so that citrate accumulates and is secreted.

Q15. Consider a bacterial population of size $N=10^{12}$. The spontaneous mutation rates per generation to resistance against antibiotic A and antibiotic B are $\mu_A=10^{-8}$ and $\mu_B=10^{-9}$ respectively. If resistance to both antibiotics requires two independent point mutations occurring in the same lineage, estimate the expected number of bacteria resistant to both antibiotics present before treatment.