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A first order reaction with rate constant 0.5 per minute is run in two equal CSTRs in series, each of space time 2 minutes. What overall conversion results?

  • A.67 per cent
  • B.100 per cent
  • C.75 per cent
  • D.50 per cent

Answer: C

Correct answer: 75 per cent

For a first order reaction each equal tank multiplies the concentration by \( 1/(1+k\tau) \), and here \( k\tau = 0.5\times2 = 1 \): \[ \frac{C_2}{C_0} = \left(\frac{1}{1+1}\right)^{2} = \frac{1}{4}, \qquad X = 1-\tfrac14 = 75\%. \] A single tank of the same total space time, \( \tau=4 \), would give \( 1-1/3 = 67 \) per cent - which is the distractor offered, and the measure of what the split is worth.

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