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GATE 2017 CE (CE2) – Question 61

Water and Waste Water Quality and Treatment · Primary, secondary and tertiary treatment, effluent standards · 2 marks · Numerical answer

The ratio of five-day BOD at 20°C to ultimate BOD is 0.68. The first-order BOD rate constant (base e), to two decimals, is ______ day⁻¹.

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Correct answer: 0.22 to 0.24

Explanation

First-order exerted fraction is $1-e^{-kt}$. Thus $0.68=1-e^{-5k}$, giving $k=-\ln(0.32)/5=0.227887$ day⁻¹, or 0.23 day⁻¹. The natural logarithm is required for the stated base-e constant.