PFR Reaction Rate: Understanding CSTR vs. PFR

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gfd43tg
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Hello,

In class, my professor said that in a CSTR, the reaction rate is constant throughout a well mixed CSTR. He said in most cases, a PFR will react faster than a CSTR.

I can see how the PFR will have a fast reaction rate at the entrance to the tube, and slowest at the exit. However, what he said that I haven't been able to wrap my head around/convinced of is when he said that the reaction rate at the exit to the tube is equal to the CSTR for the same conditions.

This means that the reaction rate in a PFR is always greater than or equal than the rate in a CSTR. Why is this? Why couldn't the exit have a reaction rate slower than a CSTR?
 
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It was hard to understand due to his accent, but I know for sure there was no assumption of equal exit reaction concentrations. The notion I got was that the lowest possible reaction rate in a PFR is equal to the reaction rate of a CSTR. Maybe it's just better I ask him directly, since now I'm just speculating what he said.