A liquid-phase isomerization is carried out in a 1000-gal CSTR that has a single impeller located halfway down the reactor. The liquid enters at the top of the reactor and exits at the bottom. The reaction is second order. Experimental data taken in a batch reactor predicted the CSTR conversion should be 50%. However, the conversion measured in the actual CSTR was 57%.
A) Suggest reasons for the discrepancy and suggest something, e. g., a model, that would give closer agreement between the predicted and measured conversions. Back your suggestions with calculations. P. S. It was raining very hard that day.

The conversion achieved for the first CSTR impeller is 0.382

Discrepancy = 0.188

Explanation:

The impeller divides the CSTR into 2 equal reactors of volume 500gal

Using V = FaoX/ (-ra)

500gal = Fao×Xa/[(KCao^2( 1 -X1)^2]

500gal = CaoVoX1/ KCao^2(1-X1)

500gal= 500gal × X1'/(1 - X1)^2

(1 -X1)^2 = X1

X1^2 - 3X1 + 1 = 0

X1= 0.382

Conversion achieved in the first CSTR is 0.382

Actual measured CSTR = 57% =57/100=0.57

Discrepancy in the conversions= 0.57 -0.383 =0.188

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