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GATE 2024 CE (CE1) – Question 60

Water and Waste Water Quality and Treatment · Unit processes and operations · 2 marks · Numerical answer

Activated carbon is used to remove a pollutant from wastewater in a mixed batch reactor, which follows first-order reaction kinetics.
At a reaction rate of 0.38 /day, the time (in days) required to remove the pollutant by 95% is ______________ (rounded off to 1 decimal place).

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Correct answer: 7.86 to 7.94

Explanation

For first-order kinetics in a batch reactor, $\frac{C}{C_0} = e^{-kt}$. Removing 95% leaves $0.05$, so $t = \frac{\ln(1/0.05)}{k} = \frac{2.996}{0.38} = 7.9$ days.