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### Topic: Cascade of two CSTRs, Optimal intermediate concentration  (Read 2889 times)

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#### beastenator

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##### Cascade of two CSTRs, Optimal intermediate concentration
« on: August 18, 2012, 08:19:30 AM »
I'm having a hard time figuring the following formula out. How is it applied? What does the |Ca=
Ca* suffix mean?

d(-1/Ra)/ dCa  |Ca=Ca*  = (1/-Ra,f - 1/-Ra* )/ (Ca* - Ca,o)

In the example I have to proof that for a first order reaction Ca*=(Ca,o*Ca,f)1/2

so,
-Ra = k Ca

then I can rearrange d(-1/Ra) and everything containing -1/Ra to one side and everything containing concentrations to the other, but then, how do I integrate, what's with that suffix behind d(Ca)?

#### curious stackhouse

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##### Re: Cascade of two CSTRs, Optimal intermediate concentration
« Reply #1 on: August 18, 2012, 05:34:52 PM »
For d(-1/Ra)/ dCa take the value of Ca to be equal to C*a. That is, the concentration is equal to its concentration when saturated.