Discussion
A first order reaction with rate constant 0.2 per minute is run in a CSTR at 90 per cent conversion. What space time is needed?
Answer: B
Correct answer: 45 minutes
For a first order reaction in a CSTR, \[ \tau = \frac{X}{k(1-X)} = \frac{0.9}{0.2\times0.1} = \frac{0.9}{0.02} = 45\ \mathrm{min}. \] The 11.5 minutes offered is the PFR answer, \( -\ln(0.1)/0.2 \) - and the comparison is worth noting: at 90 per cent conversion the CSTR needs almost four times the volume, exactly the penalty described in the first item of this topic.
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