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Single Phase Systems 5-11
PROBLEM 5.38 Propylene is hydrogenated in a batch reactor:
C3H 6 (g) + H 2 (g) C3H 8 (g) →
Equimolar amounts of propylene and hydrogen are fed into the reactor at 25°C and a total absolute pressure of 32.0 atm, and some time later the temperature is 235°C. You may assume ideal gas behavior for this problem, although at the high pressures involved this assumption constitutes a crude approximation at best. (a) If the reaction goes to completion at 235°C, what would be the final pressure? (b) If the pressure is 35.1 atm and the temperature is 235°C, what percentage of the propylene fed has reacted? (c) Construct a graph of pressure versus fractional conversion of propylene, assuming T = 235°C. Use a graph to confirm the results in parts (a) and (b). (Note: We'll use E-Z Solve for this part.) Strategy Since we are not told how much of the reaction mixture is charged, we'll choose a basis of 100 mol C3H6, and since the feed is equimolar in propylene and hydrogen there must also be 100 mol H2. We know the extent of reaction but not the pressure in part (a) and vice versa in part (b), so we label the chart as though neither is known. Also, we assume that the reaction volume is the same throughout the reaction. (Put another way, we assume the reactor is a rigid vessel and not an expandable balloon or a cylinder with a movable piston.)
100 mol C3H6 100 mol H2 25°C, 32 atm V (L) n1 (mol C3H6) n2 (mol H2) n3 (mol C3H8) 235°C, Pf (atm) V (L)
(a) If the reaction goes to completion at 235°C, what would be the final pressure? Solution If the reaction is complete, we can easily determine the three unknown molar quantities in the outlet stream labeling. (Hint: Use the expression for n1 to find the extent and then use the extent to find n2 and n3). n1 = 0 mol C3H6, n2 = _____ mol H2, n3 = _____ mo...