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Suppose A and B are continuously added into a tank, and exit stream consists of A,B,C, and D. I am a little confused on the following point as I follow the example in my textbook.

The reaction is

##A + B → C + D##

It says because (and I quote) ''...Because the system is operated at steady state, if we were to withdraw liquid samples at some location in the tank at various times and analyze them chemically, we would find that the concentrations of the individual species in the different samples were identical. That is, the concentration of the sample taken at 1 P.M. is the same as that of the sample taken at 3 P.M. Because the concentrations are constant and therefore do not change with time,

[itex] \frac {dC_{A}}{dt} = 0 [/itex]

which would lead to

[itex]r_{A} = 0[/itex]

which is incorrect because C and D are being formed from A and B at a finite rate. Consequently, the rate of reaction defined by equation 1-1 cannot apply to a flow system and is incorrect if it is defined in this matter''.

equation 1-1 just equates the change in concentration of a species to the rate of formation/disappearance of a species.

Where I am confused here is exactly what is meant by ##\frac {dC_{A}}{dt}##. It seems to be in the stream where A enters, it is 100% A. When it gets into the tank, it is now mixed with B, so it's concentration is less. So that means ##\frac {dC_{A}}{dt} \ne 0##.

Perhaps the wording is confusing. So it is saying, if I pick an arbitrary location in the tank, the concentration of the chemical species A should be the same at all times. In my head, I am thinking that the ##\frac {dC_{A}}{dt}## is the change in concentration of A as it moves through the CSTR. At ##t = 0##, it enters the reactor as some concentration ##C_{A_{0}}## and leaves the reactor at concentration ##C_{A_{\tau}}##, where ##t = \tau## is the residence time of the CSTR. So in this scenario there is a change in concentration of species A over a finite time, hence that derivative should not be equal to zero. This is clearly not what is meant by that equation, which is somewhat alluding me.

It appears to mean that the change in concentration in a very specific location is not changing with time, hence the derivative is zero. But then that begs the question why are we analyzing it in that way, and not what I mentioned before? What am I missing here?

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# Concentration change in CSTR

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