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).
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).
\[ C_6H_6 + 3H_2 \rightarrow C_6H_{12} \]
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).
Show 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.
Updated On: Jul 17, 2026
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Verified By Collegedunia
Correct Answer: 2.2
Solution and Explanation
Step 1: Basis F mol fresh benzene.
Fresh H2 = 1.25 x 3F = 3.75F. Total fresh feed = F + 3.75F = 4.75F.
Fresh H2 = 1.25 x 3F = 3.75F. Total fresh feed = F + 3.75F = 4.75F.
Step 2: Recycle R with 25% benzene, 75% H2.
C6H6 to reactor = F + 0.25R.
C6H6 to reactor = F + 0.25R.
Step 3: Single-pass conversion 25%.
Reacted per pass = 0.25(F+0.25R). This equals overall reacted = 0.90F (benzene leaves only via reaction).
Reacted per pass = 0.25(F+0.25R). This equals overall reacted = 0.90F (benzene leaves only via reaction).
Step 4: Solve.
\[ 0.25(F+0.25R) = 0.90F \implies F+0.25R=3.6F \implies 0.25R=2.6F \implies R=10.4F \]
\[ 0.25(F+0.25R) = 0.90F \implies F+0.25R=3.6F \implies 0.25R=2.6F \implies R=10.4F \]
Step 5: Ratio.
\[ \frac{R}{F_{fresh}} = \frac{10.4F}{4.75F} = 2.189 \approx 2.2 \]
\[ \frac{R}{F_{fresh}} = \frac{10.4F}{4.75F} = 2.189 \approx 2.2 \]
\[ \boxed{\frac{R}{F_{fresh}} \approx 2.2} \]
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