Gas streams containing hydrogen and nitrogen in different proportions are produced on request by blending gases from two feed tanks: Tank A (hydrogen mole fraction = x_A) and Tank B (hydrogen mole fraction = x_B). The requests specify the desired hydrogen mole fraction, x_p, and mass flow rate of the product stream, m_p(kg/h).

(a) Suppose the feed tank compositions are x_A = 0.10 mol H2/mol and x_B = 0.50 mol H2/mol, and the desired blend—stream mole fraction and mass flow rate are x_p = 0.20 mol H2/mol and m_p = 100 kg/h. Draw and label a flowchart and calculate the required molar flow rates of the feed mixtures, n_A (k mol/h) and n_B (k mol/h).

(b) Derive a series of formulas for n_A and n_B in terms of x_A, x_B, x_p, and m_p. Test them using the values in part (a).

(c) Write a spreadsheet that has column headings x_A, x_B, x_p, m_p, n_A, and n_B. The spreadsheet should calculate entries in the last two columns corresponding to data in the first four. In the first six data rows of the spreadsheet, do the calculations for XA = 0.10, x = 0.50, and x_p = 0.10, 0.20, 0.30, 0.40, 0.50, and 0.60, all for m_p = 100 kg/h. Then in the next six rows repeat the calculations for the same values of XA, XB, and Xp for mp = 250 kg/h. Explain any of your results that appear strange or impossible.

(d) Enter the formulas of part (b) into an equation-solving program. Run the program to determine A and B for the 12 sets of input variable values given in part (c) and explain any physically impossible results.