# Question

A liquid mixture contains 600 wt% ethanol (E), 5.0 wt% of a dissolved solute (S), and the balance water. A stream of this mixture is fed to a continuous distillation column operating at steady state. Product streams emerge at the top and bottom of the column. The column design calls for the product streams to have equal mass flow rates and for the top stream to contain 90.0 wt% ethanol and no S.

(a) Assume a basis of calculation, draw and fully label a process flowchart, do the degree-of-freedom analysis, and verify that all unknown stream flows and compositions can be calculated. (Don’t do any calculations yet.)

(b) Calculate (i) the mass fraction of S in the bottom stream and (ii) the fraction of the ethanol in the feed that leaves in the bottom product stream (i.e., kg E in bottom stream/kg E in feed) if the process operates as designed.

(c) An analyzer is available to determine the composition of ethanol—water mixtures. The calibration curve for the analyzer is a straight line on a plot on logarithmic axes of mass fraction of ethanol, x(kg E/kg mixture), versus analyzer reading, R. The line passes through the points (R = 15, x 0.100) and (R = 38, x = 0.400). Derive an expression for x as a function of R(x = ...) based on the calibration, and use it to determine the value of R that should be obtained if the top product stream from the distillation column is analyzed.

(d) Suppose a sample of the top stream is taken and analyzed and the reading obtained is not the one calculated in part (c). Assume that the calculation in part (c) is correct and that the plant operator followed the correct procedure in doing the analysis. Give five significantly different possible causes for the deviation between R measured and R predicted, including several assumptions made when writing the balances of part (c). For each one, suggest something that the operator could do to check whether it is in fact the problem.

(a) Assume a basis of calculation, draw and fully label a process flowchart, do the degree-of-freedom analysis, and verify that all unknown stream flows and compositions can be calculated. (Don’t do any calculations yet.)

(b) Calculate (i) the mass fraction of S in the bottom stream and (ii) the fraction of the ethanol in the feed that leaves in the bottom product stream (i.e., kg E in bottom stream/kg E in feed) if the process operates as designed.

(c) An analyzer is available to determine the composition of ethanol—water mixtures. The calibration curve for the analyzer is a straight line on a plot on logarithmic axes of mass fraction of ethanol, x(kg E/kg mixture), versus analyzer reading, R. The line passes through the points (R = 15, x 0.100) and (R = 38, x = 0.400). Derive an expression for x as a function of R(x = ...) based on the calibration, and use it to determine the value of R that should be obtained if the top product stream from the distillation column is analyzed.

(d) Suppose a sample of the top stream is taken and analyzed and the reading obtained is not the one calculated in part (c). Assume that the calculation in part (c) is correct and that the plant operator followed the correct procedure in doing the analysis. Give five significantly different possible causes for the deviation between R measured and R predicted, including several assumptions made when writing the balances of part (c). For each one, suggest something that the operator could do to check whether it is in fact the problem.

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