8.35. An article in the Journal of Chromatography A

(“Simultaneous Supercritical Fluid Derivatization and Extraction of Formaldehyde by the Hantzsch Reaction,” 2000, Vol. 896, pp. 51–59) describes an experiment where the Hantzsch reaction is used to produce the chemical derivatization of formaldehyde in a supercritical medium. Pressure, temperature, and other parameters such as static and dynamic extraction time must be optimized to increase the yield of this kinetically controlled reaction. A 25!1 fractional factorial design with one center run was used to study the significant parameters affecting the supercritical process in terms of resolution and sensitivity. Ultraviolet–visible spectrophotometry was used as the detection technique. The experimental design and the responses are shown in Table P8.7.

(a) Analyze the data from this experiment and draw conclusions.

(b) Analyze the residuals. Are there any concerns about model adequacy or violations of assumptions?

(c) Does the single center point cause any concerns about curvature or the possible need for second-order terms?

(d) Do you think that running one center point was a good choice in this design?

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P T S d C Experiment (MPa) (C) (min) (min) () Resolution Sensitivity 13 14 15 1234567890 DEAD 13.8 50 55.1 50 13.8 120 55.1 120 2222 13.8 50 15 22222 100 0.00025 0.057 10 0.33333 0.094 10 0.02857 0.017 100 0.20362 1.561 10 0.00027 0.010 55.1 50 15 2 100 0 52632 0.673 13.8 120 15 2 100 0.00026 0.028 55.1 120 15 2 10 0.52632 1.144 13.8 50 2 15 10 0 42568 0.142 55.1 50 2 15 100 0.60150 0.399 11 13.8 120 2 15 100 0.06098 0.767 12 55.1 120 2 15 10 0.74165 1.086 13.8 50 15 15 100 0.08780 0.252 55.1 50 15 15 10 0.40000 0.379 13.8 120 15 15 10 0.00026 0.028 16 55.1 120 15 15 100 0.28091 3.105 Central 34.5 85 8.5 8.5 55 0.75000 1.836