A batch test reduces a first-order toxic compound from $2\times10^{-3}$ M to $2\times10^{-4}$ M in 10 min. At the same temperature, a field plug-flow reactor treats1 m³/hour from $.5$ M to $10^{-4}$ M. Find required volume in m³,to two decimals.
The batch test gives $k=\ln(10)/10=.2302585$ min⁻¹. First-order plug-flow residence time is $\tau=\ln(C_0/C)/k=\ln(5000)/.2302585=36.9897$ min=.616495 hour. At1 m³/hour,$V=Q\tau=.616495$ m³,rounded **0.62 m³**. Equal temperature permits using the measured rate constant.
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