Question

A reaction \( A \to B \) is to be conducted in two CSTRs in series. The steady-state conversion desired is \( X_f \). The reaction rate as a function of conversion is given by \( r = -\frac{1}{1 + X} \). If the feed contains no B, then the conversion in the first reactor that minimizes the total volume of the two reactors is

• A. \( 1 - X_f \)
• B. \( 0.2 X_f \)
• C. \( 0.5 X_f \)
• D. \( 0.5 (1 - X_f) \)

Hint:

In reactor design, when dealing with multiple reactors in series, converting part of the reactant in the first reactor reduces the overall volume needed to achieve the desired conversion.

Answer 1

The Correct Option is D

- To minimize the total volume of the two CSTRs, the conversion in the first reactor should be half of the desired final conversion. 
- This is based on the optimal conversion distribution for reactors in series, where the first reactor operates at \( 0.5(1 - X_f) \). 
Conclusion: The conversion in the first reactor that minimizes the total volume is \( 0.5(1 - X_f) \), as given by option (D).