Ethyl alcohol can be bacterially oxidized to acetic acid in the following two-step fermentation sequence:

2 C2H5OH + O2 → 2 CH3CHO + 2 H2O

2 CH3CHO + O2 → 2 CH3COOH

If the alcohol-containing feedstock is wine, cider, or a malt solution, the resulting solution is vinegar. An aqueous solution containing ethyl alcohol in water is fermented to produce dilute acetic acid. The feed mixture (the ethanol solution and the bacteria that make the fermentation occur) and air are fed at a temperature T0. The product solution contains ethanol, acetaldehyde (CH3CHO), acetic acid, and water. All liquid and gaseous effluents are at temperature T. The variables involved in the process are nf (mol feed solution), xef (mol ethanol/mol feed solution), nair (mol air fed). PXS (percent excess air), ne, nah, naa, nw, (gram-moles of ethanol, acetaldehyde. acetic acid, and water, respectively, in the product mixture), n0x, nn (gram-moles of oxygen and nitrogen, respectively, emerging from the reactor), T0, T, and Q (kJ heat transferred).

(a) Calculate the number of degrees of freedom of the process. How would the answer differ if the reactor were adiabatic?

(b) Outline the solution procedure to determine all unknown variables from given values of nf, xef, Pxs, ne, nah, T0, and T.

(c) Specify a set of design variables that would require an iterative solution for the remaining state variables.

(d) Specify an infeasible set of design variables.