Question

Cyclohexane (C₆H₁₂) is produced from benzene (C₆H₆) and hydrogen (H₂) according to the following reaction.
\[ C_6H_6 + 3H_2 \rightarrow C_6H_{12} \]
Consider the process flow diagram shown in the figure.

In this process, the overall and single-pass conversions are 90% and 25%, respectively. The recycle stream contains 25 mol% C₆H₆ and 75 mol% H₂. If the fresh feed contains 25% excess H₂, at steady state, the ratio of the molar flow rate of the recycle stream to that of the fresh feed is ______ (rounded off to one decimal place).

Hint:

Since benzene leaves the process only through reaction, reacted per pass must equal total reacted overall; use this to relate recycle flow to fresh feed.

Answer 1

Correct Answer: 2.2

Let $r = 0.25R/F$ (recycle-to-fresh benzene ratio). C6H6 to reactor = $F(1+r)$. Single pass: reacted $=0.25F(1+r) = 0.90F \Rightarrow 1+r=3.6 \Rightarrow r=2.6$. So $R=10.4F$. Fresh feed $=4.75F$. Ratio $=10.4/4.75\approx2.2$.

\[ \boxed{\dfrac{R}{F_{fresh}} \approx 2.2} \]