P4.34 Ethylene glycol (HOCH₂CH₂OH), used as an antifreeze, is produced by reacting ethylene oxide with water. A side reaction produces an undesireable dimer, DEG: The reactor feed is 10 gmol/min ethylene oxide and 30 gmol/min water. If the fractional conversion of ethylene oxide is 0.92 and the selectivity is 0.85, what is the reactor outlet composition and the vield?

2.17.9: Preheater and distillation column. A preheater and distillation column are maintained by engineers Marcella and Julius. A stream of pure acetone (A, C3H6O) and a stream containing acetone, ethanol (E, C2H5OH), and butanol (B, C4H, OH)entering the preheater. One stream exits the preheater containing 144 mol/min butanol, some acetone,and some ethanol; the mole fractions of butanol and ethanol are 0.209 and 0.412, respectively. The stream of pure acetone entering the preheater is 2.42 times larger than the component flow rate of acetone in the other stream entering the preheater. The stream exiting the preheater enters a distillation column, and all of the entering butanol exits in the bottom product stream. The recoveries in the overhead product, which is defined and the ratio of component flow rate exiting to component flow rate entering the distillation column, of acetone and ethanol are 83.1% and 59.2%, respectively. Determine the following three unknowns. Mass fraction of apple in the solid waste =Ex: 0.632 Total flow rate of the concentrate =Ex: 8.82kg/min Flow rate of pure water entering the overall system =Ex: 8.95kg/min

2.17.7: Two distillation columns with three components. A pair of distillation columns are being monitored by Beatrix and Enrico. Benzene (B), toluene (T), and xylene (X) are fed to the first distillation column. The overhead product of the first column contains only benzene and toluene. Toluene is fed to the first column at 1020 mol/hr while 74.4% of the benzene fed to the first column ends up in the overhead product. The stream exiting the bottom of the first column has a flow rate of 1590 mol/hr with 28.5 mol % benzene, 23.8 mol% toluene, and the rest xylene. The bottoms product from the first column is fed to a second distillation column. Pure xylene exits the bottom of the second column while the overhead product contains only benzene and toluene. Determine the following three unknowns. Flow rate of xylene exiting the second column = Ex: 515 mol/hr Mole fraction of toluene exiting the second column = Ex: 0.582 Flow rate of benzene exiting the overhead product of the first column = Ex: 1.50E mol/hr

1. [8 points]. Sketch a graph of the following function. Use the chart provided to keep track of important points and information from the graph. (You may change the scales on the grids if needed). Also label the domain and range of your final graph.

1. [2 points] True or False: The graph of a rational function can have both a Horizontal andOblique asymptote? If false, rewrite to make it a true statement. Determine whether the following functions are One-To-One (answer yes or no).DomainRange One-to-One?----One-to-One?-----One-to-One? s] Use the given figure to find the following: f(5)= g \circ f(5)= 4. [3 points]. Rewrite the following product in simplified form with all real coefficients:(1,−1) (2-3 i)(2+3 i) Find the domain and any holes for the following rational function. R(x)=\frac{(x+3)(x+2)}{x^{2}-4} \text { 6. [3 points]. Given the following function of } y \text { with respect to } x, y=f(x)=x^{3}+3 x^{2}-20 determine whether x=2 is a real zero of the polynomial f(x). Show all work that leads to the final answer.

A saturated liquid feed of 750 kmol/h consists of 20 mol% propane, 35 mol% n-butane and 45 mol% n-hexane. A distillate recovery of 98 mol% n-butane and bottoms recovery of 99 mol% n-hexane is desired. \text { The average relative volatility is } \alpha_{\text {propane-butane }}=2.04 \alpha_{\text {butane-butane }}=1.00 \mathrm{and} \alpha_{\text {hexane-butane }}=0.2 Constant molar overflow (CMO) is valid. Reflux is returned as a saturated liquid. The column has a partial reboiler and a total condenser. Calculate the total vapour flow rate in the enriching section at minimum reflux (Vmin) in kmol/h D = 410.625 kmol/h \phi=0.3197 \text { [Trial and Error] }

1. Draw an open system. Denote the system boundary with dotted lines.

It is desired to separate methanol (CH3OH) from methanol-water mixture in a sieve plate column operating at 2 atm, 83.2 °C (methanol boiling point at 2 atm), and 80% of the flooding velocity. The spacing of the trays is 600 mm and the vapour and liquid flow rates are 650 kmol/hrand 2750 kmol/hr, respectively. Assume ideal gas law, the density of water as 1000 kg/m and that the vapour is entirely methanol and liquid is entirely water. Calculate the liquid-vapour flow factor

]. Prove that the following are inverses of one another: f(x)=2 x-1 \quad f^{-1}(x)=\frac{x+1}{2}

P4.14 Dimethyl carbonate (DMC, C₂H₂O3) can be synthesized by a process called oxidative carbonylation of methanol: A gas containing 80 mol % CH3OH and 20 mol % CO at 2000 gmol/h is mixed with air (79 mol % N₂ and 21 mol % O₂) and then fed to a reactor operating at steady state, where the reaction takes place. The flow rate of the stream leaving the reactor is 2264 gmol/h, and this stream contains no O₂. Draw a flow diagram and write the correct form of the material balance equations for all compounds in this system. Determine the flow rate of air to the reactor, the extent of reaction 4, and the composition (mol %) of the reactor effluent.